IntroductionIntroduction to Chemistry and Agricultural Chemistry

Science and chemistry, Pure chemistry and analytical chemistry:

Science: Science is the systematic knowledge of material universe.

Chemistry: Chemistry is the science of properties of matter and changes in materials.

Pure chemistry: Pure chemistry deals with the basic principles of chemistry. It includes-

a) Inorganic chemistry- deals with the compounds formed mainly by electrovalent bond.

b) Organic chemistry- deals with the compounds formed mainly by covalent bond.

c) Biochemistry- deals with the compounds of biological organisms.

d) Physical chemistry- deals with the physical properties of matter related to the chemical changes.

Analytical chemistry: Analytical chemistry deals with the chemical characterization, identification and estimation of matter.

Applied Chemistry: Applied chemistry deals with the application of basic principles of chemistry to produce useful commodities (goods).

Branches of applied chemistry:

a) Industrial chemistry- deals with the production of industrial goods by applying basic principles of chemistry.

b) Agricultural chemistry- deals with the production of agricultural commodities by applying the basic principles of chemistry.

Analysis and Chemical Analysis: Analysis is a non technical term but chemical analysis is the technical term to describe the method of determining the

properties of matter and changes in materials. Analysis means discussion, observation, experimentation, investigation and determination where as

chemical analysis means characterization, identification and estimation of a matter.

Needs of chemical analysis

a) To identify the samples and its constituents of a matter.

b) To determine the amounts of constituents of a matter.

c) To establish the suitability and potentiality of a matter.1

d) To diagnose the condition of the matter investigated.

Types of chemical analysis

a. Qualitative analysis - To determine the presence of a constituent.

b. Quantitative analysis - To determine the amount of constituen

Classification of qualitative analysis

The analytical method to find out the presence of an element or compound is called qualitative analysis. The element or compound present in a sample is

identified by qualitative method of analysis. The substance like acids, bases, salts, element and radical (group) are identified by qualitative analysis.

There are two methods which are generally used for the identification of these radicals. They are -

i) Dry test: Identification of dry salt by the action of heat and chemical.

ii) Wet test: Identification of a clear solution by the action of various chemicals.

Classification of quantitative analysis

a. Gravimetric method of analysis: Estimation by precipitation, separation and Weighing.

b. Volumetric method of analysis: Estimation by volume measurement.

c. Instrumental method of analysis: Estimation by measuring physical properties.

d. Electrical method of analysis: Estimation by measurement of electrical quantity.

Gravimetric method of analysis

Gravimetric method of analysis is the measure of the amount of a substance present in a sample from the weight of the precipitate obtained. In gravimetric

analysis a sample is brought into solution and the element or compound to be determined is precipitated as an insoluble stable compound then the

precipitate filtered, washed, dried, ignited and weighed accurately. With the weight of precipitate, the amount of the element or substance is determined by

its formula and atomic weight of its constituents.

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Volumetric method of analysis

Volumetric analysis is the measure of volume of a solution to determine the amount of solid in a unknown solution. In volumetric analysis it is necessary to

determine the equivalence point with sufficient accuracy.

Based on the nature of reactions, volumetric analysis can be subdivided into the following methods:

a) Acid-base titration method

b) Oxidation-reduction titration method

c) Precipitation titration method

d) Complexometric titration method

Instrumental method of analysis: The method of determining the amount of solid in a solution by measuring any physical properties with the help of an

instrument.

Electrical analysis: Amount determination by measuring electrical properties.

Atomic Structure

Old and modern concept of Atom

Atom: Atom is the smallest possible particle of matter. Atom means ‘not to cut’. In other words atom means "incapable of being divided". Atoms are the

basic building blocks of all matter.

In ancient time it was believed that "matter is continuous". Up to John Dalton (1803) the concept of atom was-

-Atoms are smallest possible particle

-Atoms are indivisible

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-Atoms of different materials were different (unlike)

-Atoms of same matter are alike

After the discovery of proton and electron, neutron and isotopes, concepts of Dalton changed and proposed that-

1) Atoms can be divided into smaller particles like proton, electron, neutron, pion, meson; α, β, etc. can be obtained from an atom.

2) Atoms of the same element not alike (unlike)

The concept of isotopes ('iso' means same and 'topus' means place) proved that atoms of the same element are exist as differently in their mass. This is

called isotopes of the same element.

Isotopes and radio isotopes:

The atoms of same the element having the same atomic number but different atomic masses and occupy the same place in the periodic table are called

isotopes. The isotopes which emit α, β and γ radiation from nucleus are called radioisotopes. A neutron in the nucleus sometimes is transformed into an

electron and proton. The transformed electrons escape(emitted) from the nucleus. This type of emitted electron is called β rays. (i.e. n p + e), when two

protons and two neutrons escape from the uncles is called α rays. The atomic number is the number of protons in nucleus and the atomic mass is the total of

protons and neutrons. After the discovery of isotope, it is established that the atomic weight (mass) of an element is an average of the weights of the

isotopes of that elements occur in nature.

For example, chlorine, with an atomic weight of 35.46 is composed of two kinds of chlorine atoms containing masses 35 and 37. But both types of the

atoms have the atomic number 17. This means that both have 17 protons in the nucleus and the serial number of chlorine is 17 and also placed in the 17 th

place of the periodic table. The difference in atomic mass (weight) is due to the number of neutrons in the nuclei of the different isotopic atoms. Chlorine-

35 has 18 neutrons and chlorine-37 has 20 neutrons. It may also note that chlorine-35.46 indicates that the atoms of isotopic weight or mass number 35 are

more abundant than the isotope of chlorine having mass number 37.

Isotopes of an element are generally written by the following symbols 17Cl37 and 17Cl35. The subscripts stand for the atomic number of the elements and

superscripts denotes the mass number.

Atomic Model

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J. J. Thomson (1898) at first proposed that atoms are uniform spheres of positively charged matter in which electrons are embedded; much like a fruit cake

is situated with nuts.

Fig. 2.1. Thomson model

Rutherford’s atomic model: Rutherford in 1911 assumed that –

a) Positive charge is concentrated in a very small region at the centre called nucleus.

b) Electron is situated outside the nucleus in some sorts of configuration.

c) Electron revolving around the nucleus as the planets revolves around sun in solar system.

Fig. 2.2. Rutherford atom model

Limitation of Rutherford's atomic model: According to Rutherford's atomic model, an atom has a nucleus and the negative electrons which are

revolving round the nucleus in the same way as the planets revolve round the sun in the solar system. This model could not say anything as to how and

where these electrons were arranged. This model could also not explain how the spectral lines are produced by the atom when an electron jumps

from one orbit to another.

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In order to explain a) why an electron revolving round the nucleus, does not lose energy and consequently does not fall into the nucleus, b) how the spectral

lines of the emission from atom are produced when an electron jumps from one energy level to the other; Niels Bohr, a Danish Physicist, in 1913, put

forward a new atomic model which is based on Planck's quantum theory of radiation.

Quantum Theory of Emission of Radiation (Quantum concepts of radiation):

When energy is applied on an atom then the electron jumped from lower energy level to a higher energy level by absorbing energy. This process is called

excitation. The electron at lower energy level is called ground state electron and the jumped electron at higher energy level is called excited electron. After

certain period the excited electron come back from higher energy level to lower energy level. Excited atom emits radiation of definite wave. This type of

discontinuous radiation from electronic structure is called quantum (plural is quanta) or photon.

In short, energy emitted from an excited atom is called quantum. The term quanta comes from the concepts “the energy of electron in an energy level is

definite (specified) or quantized and all the electrons are arranged in four energy levels. But at present it is proved that electrons are arranged in more than

four energy levels. So the term quantum may be discarded.

Planck’s quantum theory explain how the emission of radiation takes place from electronic structure of an atom and calculate the energy of an electron at

an energy level.

According to Planck’s quantum theory the amount of energy absorbed or emitted by the electron is coming from energy level-1 to energy level -2 is equal

to E2-E1=hυ where h is Planck’s constant and υ is the frequency of the radiation.

Excited state electron Energy emitted (=E2-E1=hυ)

Ground state electron

Lower energy level Heat/electric energy absorbed (E2-E1=hυ) Higher energy level

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Fig. 2.3. Showing excitation and emission of radiation from electronic structure of an atom

Explanation of Planck's Quantum Theory

In 1900 Max Planck studied the spectral lines obtained from thermal radiations emitted by a hot (black) body at different temperatures and put forward a

theory which, after his name, is known as Planck's quantum theory of radiation ('quantum' is a Latin word which means 'how much'). Various postulates of

this theory are:

1. When heat or energy supply to a matter, then it emits radiant energy not continuously but discontinuously as small packets or bundles or discrete

(separate) units of the waves. Each of these units is called a quantum (plural is quanta) which can exist independently. The emission of radiant energy in

continuous waves and in discontinuous waves as individual quantum from a heated iron ball is shown bellow:

Iron ball

(a) (b)

In case of light which is also a form of radiation, light energy is emitted or absorbed in the form of packets or bundles each of which is called Photon

(instead of quantum). Photon is not a material body. It is considered to be a mass- less bundle of energy.

Thus according to this theory, light is composed of mass- less particles which are called photons. The presence of photons in light can not be detected

readily under normal conditions, since even light of low intensity consists of billions of photons. It was in 1905, when Einstein, while explain the

photoelectric effect, could prove the existence of photons.

2. The energy associated with each quantum or photon of a given radiation or light is proportional to the frequency (v/nu) of the emitted radiation or light,

i.e.,

E ∞ v,

or, E = hv.

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Fig. 2.4. Emission of radiant energy from a heated iron ball in (a) continuous waves (Maxwell's theory-old theory) and (b) discontinuous waves (Max Planck's quantum theory- Modern theory)

Where, h = a constant known as Planck's constant whose numerical value is 6.624 10-27 erg. s (in C. G. S. units) or 6.624 10-34 j-s (in S. I. units).

E = energy associated with each quantum or photon of a given radiation. E is in ergs or in KJ.

v = frequency of the emitted radiation or light.

This equation is applicable to all types of radiation and is called Planck's equation. This equation shows that the energy associated with a quantum or a

photon, E is equal to hv.

Now since, ; [Here, c = velocity and = wave length of radiation]

As E = hv. So, we can write, E = h. ; This equation shows that smaller the wavelength (or higher the frequency) of radiation, larger the energy associated

with a quantum or a photon. For example a photon transmitted by violet light, which has higher frequency, has more energy than that of transmitted by red

light which has lower frequency.

In 1905 Einstein said that the energy in a photon (E) is associated with mass m and velocity c is also given by: E = mc2. This equation is called Einstein's

equation or Einstein mass-energy relationship.

3. The energy emitted or absorbed by a body can be either equal to one quantum of energy (= hv) or any whole number, say, n multiple of this unit, i. e.,

Energy emitted or absorbed = n hv.

Thus the energy emitted or absorbed by a body can be equal to 1 hv, 2 hv, 3 hv etc. but never equal to any fractional value of hv like 1.5 hv, 2.4 hv, 4.9 hv

etc. Thus we find that the energy emitted or absorbed by a body is quantized and this is called the concept of quantization of energy.

It is clear from the study of quantum theory of radiation as given above that the atoms would transfer energy in photon units. The absorption of a photon by

an atom increases its energy by a definite quantity which is equal to hv. An atom which has absorbed energy in this way is said to be an excited atom or in

the excited state. When an excited atom radiates energy, energy is given out in photon units.

The description given above makes it evident that this theory is also known as photon theory, since according to this theory, light radiations are supposed to

be composed of photons each of which is associated with energy equal to hv.

Bohr's atomic model: Bohr’s atomic model retains the two essential features of Rutherford’s atomic model which are:

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i) The atom has a very small positively charged nucleus at its center. All the protons and neutrons are contained in the nucleus. Thus most of the mass of

atom is concentrated in the nucleus.

ii) Negatively charged electrons are revolving round the nucleus in the same way as planets are revolving round the sun.

However he applied Plank’s quantum theory to the revolving electrons and thus explained a) why the electrons are revolving round the nucleus b) Why

not the electrons lose energy and consequently do not fall into the nucleus.

Bohr made the following postulates.

1. Fixed circular orbits: Bohr assumed that an electron is a material particle which is revolving round the nucleus in concentric circular orbits situated at

definite (i.e., fixed) distance from the nucleus and with a definite velocity.

2. Stationary energy levels: As long as an electron remains in a particular orbit, it neither emits (i.e., radiates or loses) nor absorbs (i.e., gains) energy.

Thus in a particular orbit the energy of a revolving electron remains constant or stationary. Hence each of the fixed orbits is associated with a definite

amount of energy, i.e., with a definite whole number of quanta of energy. The orbits are, therefore also called stationary energy levels or simply energy

levels or energy shells. This concept of stationary energy levels explains the stability of the atom, since an electron cannot lose energy gradually and so

does not fall into the nucleus.

Different energy levels have been represented by n which can have integer (whole number) values like 1, 2, 3,……….∞, starting from the nucleus, n has

been called Principal quantum number by Bohr. Different values of n are also represented by capital letters K, L, M, N, etc. Thus:

Principal quantum number (n) 1 2 3

Letter designation of energy level K (1st shell) L (2nd shell) M (3rd shell)

Thus for K shell (1st shell) n =1, for L shell (2nd shell) n = 2 and so on. K, L, M, N……shells are also called n =1 shell, n =2 shell, n =3 shell, n =4 shell etc.

respectively. Representation of various orbits is depicted in Fig. 2.5. The energy associated with a certain energy level increases with the increase of its

distance from the nucleus. Thus, if E1, E2, E3 ….etc. are the energies associated with the energy levels numbered as 1 (K-shell), 2 (L-shell), 3 (M-shell)

…….etc. the order of the energies is as:

E1 < E2 < E3 <..............etc.

n= 5

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n = 4

n = 3 Energy n = 2

increasing n = 1

E5 E4 E3 E2 E1 Circular orbits (energy levels)

K L M N O

Nucleus

Fig. 2.5. Representation of various orbits (energy levels) round the nucleus. E1, E2, E3 .......etc. are the energies associated with orbits having n = 1 (K-shell), 2 (L-

shell)......etc. Energies of different orbits are in the order: E1 < E2 < E3 < E4 < E5 <......

3. Jumping of an electron from one energy level to the other- Ground state and excited state of an electron: As long as an electron remains in a

particular orbit, it neither emits (i.e. radiates or loses) nor absorbs (i.e. gains) energy. But when the electron is excited from a lower energy level to a

higher energy level, it absorbs energy. On the other hand when it comes back from a higher energy level to a lower energy level, it emits energy. According

to Planck's quantum theory of radiation, the absorption or emission of energy takes place not continuously but discontinuously (discretely), i.e. the

absorption or emission of energy takes place not as continuous waves but as small packets or bundles or discrete (separate) units of the waves, each of

which is called a quantum (plural is quanta) or photon. In short we say that the absorption or emission of energy takes place in the form of quanta or

photons. When an electron is present in energy level-1(which is the lowest energy level), the electron is said to be in the ground state. Thus energy level-1

is called the ground state of the electron or atom. Since energy level-1 (i.e. ground state) has the minimum energy, ground state is the most stable state of

the atom. Now if energy is supplied to the electron residing in energy level-1, it will absorb the supplied energy in the form of quanta or photons (Planck's

quantum theory) and hence will move to one of the higher energy level-2, 3 ...... etc., depending on the amount of the energy absorbed by the electron. The

electron present in these energy levels is said to be in the excited state.

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Suppose an electron moves from energy level-1 to energy level-2. Let the energies associated with the electron present in these levels be E 1 and E2

respectively. Then the amount of energy absorbed by the electron in coming form the energy level-1 to energy level-2 is equal to E2 - E1, i.e.,

Energy absorbed by the electron = E2 - E1.

Now if ν is the frequency of the radiation absorbed by the electron, then, according to Planck's quantum theory of radiation, energy absorbed by the

electron will be equal to hν (h= Planck's constant). Thus:

Energy absorbed by the electron = E2 - E1 = hν

Now the electron has reached in the energy level-2 which is the excited state of the electron. The electron in the excited state is unstable and hence has a

tendency to come back to the ground state (i.e. energy level-1). Thus the electron comes back from energy level-2 to energy level-1. In doing so, the

electron emits the same amount of energy as it had absorbed earlier in going form energy level-1 to energy level-2. Thus the quantity of energy emitted by

the electron in the excited state is equal to E2 - E1 = hν, i.e.

Energy emitted by the electron in the excited state = E2 - E1 = hν

Whatever has been said above is shown pictorially in Fig. 2.6. Electron Electron Energy emitted

Energy absorbed = E2 - E1 = hν = E2 - E1 = hν

(a) (b)

Fig. 2.6. (a) When an electron in energy level-1 (ground state) moves to energy level-2 (excited state), it absorbs energy equal to E 2 - E1 = hν. (b) When the electron in energy level-2

comes back to energy level-1, it emits the same amount of energy as it had absorbed earlier in going from energy level-1 to energy level-2, i.e., it emits energy equal to E2 - E1 = hν.

Origin of spectral lines: The electron in an atom (suppose hydrogen) exists normally in the ground state or lowest energy level when n or n=1 i.e., nearest

to the nucleus. If the atom is excited by heat or electric energy, the electron will move to higher energy level; from this it will tend to drop back to the

lowest energy level (in the stable position, if not ionized). When the electron is returning from a higher energy level to a lower one, excess energy will be

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liberated as radiation of some definite frequencies. This is the spectral lines. It is the emission spectral line and the absorption of definite spectral line may

also be occurs in the reverse way.

Add fig 1-11 from Haider book 29 page....

4. Principle of quantization of angular momentum of the moving electron: Bohr postulated that an electron cannot move in all the orbitals. It can move

only in that orbit in which the angular momentum of the electron (= mvr) moving round the nucleus is integral whole number multiple of h/2π such as

1h/2π, 2h/2π, 3h/2π,..............nh/2π. Thus according to this postulate the angular momentum of a moving electron is given by:

mvr = nh/2π............................................. (1)

Thus according to the postulates represented by equation (1), angular momentum of the moving electron is quantized. In equation (1), m = mass of the

electron; v = velocity of the electron; h = Planck's constant = 6.624 X 10-27 erg s-1; r = radius of the orbit in which the electron is moving; and n = an

integral which has been called principal quantum number by Bohr. n gives the number of the orbit in which the electron is moving. It can have the values 1,

2, 3,...... for the orbit numbered as 1 (K orbit), 2 (L orbit), 3 (M orbit) from the nucleus. This for K, L, M,.......orbits n = 1, 2, 3,......respectively as shown

below-

Orbit K L M N .................

Principal quantum number 1 2 3 4 ...................

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Fig. 2.4. Bohr atomic model

Schrödinger and other modern scientists conclude that the energy levels of electrons in atoms are not planet like orbit such as those postulated by the Bohr

and Rutherford theories of atom; they are instead volume of space around the nucleus where an electron will found. These regions of space are called

orbital. The electron is traveling at a high speed. It would look not a small particle moving in a path but rather like a cloud. As like as the propeller of a

plane.

Fig. 2.5. a) Bohr atom b) Modern atom

Energy Level, Sub-shell, Orbit, Orbitals

Energy level

The term energy level is used to referred the energy of electron and it distance from the nucleus. The energy level represented by 'n' is called the principal

quantum number. Greatest number of electrons (is possible in any one level) is 2n2. Energy level may also be referred to as shell. The word shell is used for

orbit of Bohr atom. Shell is represented by K, L, M...............corresponds to 1, 2, 3.....................quantum number. n = 1, 2, 3...................... Shell = K, L,

M..................

Sub Shell

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Energy level is made up of some sub level spectrum studies have shown that it is not true that electrons in one shell have the same energy. Energy level is

actually made up of many energy levels closely grouped together, these are called sub shell. n th energy levels have n sub shell. Sub shell can be divided into

one or more orbital.

Orbital

The term orbital refers to the description of the volume or three dimensional region, around the nucleus in which an electron is found. Each orbital has a

cloud of characteristics shape. Energy levels of electron are not planet like orbit but a volume of space around a nucleus. These regions of space are called

orbital. There are four different kind of orbital designated as s, p, d, f. Each possesses a characteristics geometric shape. s orbital contain one pair of

electrons. p orbital contain three pair of electrons. d orbital contain five pair of electrons. f orbital contain seven pair of electrons.

Shape of orbital

y

z

x

x

z

y y z

An s orbital (Spherical shaped) px py pz

p

orbital (Dumb-bell shaped)

Energy level Sublevel Total no. of orbital Designation

First (n = 1) S 1(s) 1s

Second (n = 2) s, p 4 (s, p, pp) 2s, 2p

Third (n = 3) s, p, d 9 (s, ppp, ddddd) 3s, 3p, 3d

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Fourth (n = 4) s, p, d, f 16 (s, ppp, ddddd, fffffff) 4s, 4p, 4d, 4f

Electron configuration: H- 1s1, He- 1s2, Na- Electron no. 11-1s2 2s2 2p6 3s1

Modern atom

1. Path of electron can be represented by a cloud.

2. Electron present in a volume of space called orbital.

3. Electron present in any where of the orbital.

4. Orbital has a definite shape.

5. Idea of orbit is replaced by orbital.

6. Each orbital has a cloud of characteristics shape.

7. The sum of the clouds is the cloud of the sub shell.

Classification of nuclides

a) Isotopes: Greek, isos = same; topos = place. Nuclides that have the same atomic number but different mass numbers are called isotopes.

For example, 20Ca 40, 20Ca42, 20Ca43 and 20Ca45 are isotopic atoms.

Isotopes may be- 1. Naturally occurring.

2. Artificially prepared.

3. Stable or unstable.

4. Radioactive or non-radioactive.

b) Isobars: Greek, isos = same; barys = heavy. Nuclides that have the same mass number but different atomic numbers are called isobars.

For example, 18Ar40, 19K40 and 20Ca40 are isobaric atoms.

c) Isotones: Nuclides that have the same neutron number but different proton number are called isotones. e.g., 6C14, 7N15 and 8O16 are isotones.

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d) Isomers: Nuclides that have the same mass number and same atomic number but different in structural arrangement are called isomers.

Nucleus: The nuclear particles (neutrons and protons) are often referred to as nucleus.

Constituents of nucleus: Nucleon - nuclear particle.

a) Proton, b) Neutron, c) Meson.

Meson: The particle having both positive, negative and neutral charges and mass intermediate between those of electron and proton are called meson. The

attractive force between two nucleons resulting from meson.

There are two types of meson:

a) π-meson (Pi on) and

b) μ-meson (mu on)

a) π-meson: 1. Sub atomic particle

2. Positive, negative or no charge

3. Mass 276 times of an electron.

b) μ-meson: 1. Sub atomic particle

2. Positive or negative charge

3. Mass 207 times heavier than an electron.

Nuclear force: The forces that hold the nucleus together are called nuclear forces. The attractive force between two nucleuses.

Nuclear stability: A nucleus is stable when it has the lowest possible energy. Stability of nucleus depends on- 1. Binding energy

2. Neutron-proton ratio

3. An even number of proton and neutron.

Nuclear radiation: Spontaneous emission of radiation from unstable atomic nucleus is called nuclear radiation. 16

04. Electronic Configuration and Periodicity of Elements

Electronic configuration

4.1. Definition of electronic configuration

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The arrangement of electrons among the various atomic orbitals of specific sub-shell of different energy level, in order to understand electronic behavior

of an atom is called electronic configuration.

4.2. Quantum number

Quantum numbers describe the energy of an electron in an orbit, its orientation in space and its possible interaction with other electrons. There are four

quantum numbers:

a) Principal quantum number (n)

b) Azimuthal / angular quantum number (l)

c) Magnetic quantum number (m)

d) Spin quantum number (s)

a) Principal quantum number (n)

Principal quantum number (n) relates to the average distances of the electron from the nucleus in a particular orbital. The larger the n is, the greater the

average distances of an electron in the orbital from the nucleus and therefore the larger the orbital. n represent the number of shell (orbit) or main energy

level in which the electron revolves around the nucleus. n = 1, 2, 3, 4 ….etc. represents the 1 st (K), 2nd (L), 3rd (M), 4th (N) ….etc. shell respectively.

Maximum number of electron in nth shell = 2n2. Thus 1st (n = 1), 2nd (n = 2), 3rd (n = 3), 4th (n = 4) shell contains 2, 8, 18, 32 electrons respectively.

b) Azimuthal / angular quantum number (l)

The azimuthal / angular quantum number (l) tells us the ‘shape’ of the orbital. Different values of l (0, 1, 2, 3……) represent different sub-shells (of which

the shells are composed) which are designated by small letters s, p, d, f,……derived from the words sharp, principal, diffuse and fundamental respectively,

which have been used to identify the spectral lines in the atomic spectral of different atoms. However after the letter f, the orbital designations follow

alphabetical order. The value of l depends on the value of the principal quantum number, n. For a given value of n, l has possible integral values from 0 to

(n-1). Total number of l values gives us the total number of sub-shells within a given main shell. If n = 2, there are two values of l, given by 0 and 1. Two

values of l imply that there are two sub-shell namely 2s and 2p in 2nd shell (L). i.e., 1st (n = 1), 2nd (n = 2), 3rd (n = 3) and 4th (n = 4) shell have one (1s), two

(2s, 2p), three (3s, 3p, 3d) and four sub-shell (4s, 4p, 4d, 4f) respectively. Maximum number of electron that may be accommodating in a given sub-shell is

equal to 2(2l + 1). Thus s, p, d, f can have 2, 6, 10 and 14 electrons respectively.

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c) Magnetic quantum number (m)

Magnetic quantum number (m) describes the orientation of the orbital in space of which a given sub-shell is composed. m can have integral values ranging

form –l through 0 to +l. i.e. m = 0, ±1, ±2, ±3...±l.

Thus for a given value of l, total number of m values is equal to (2l + 1). e. g.,

i) If l = 0 (s sub-shell), m = 0 (only one value) → s

ii) If l = 1 (p sub-shell), m = 0, ±1 (three values) → px, py, pz

iii) If l = 2 (d sub-shell), m = 0, ±1, ±2 (five values) → dxy, dyz, dzx, dx2-y

2, dz2.

iv) If l = 3 (f sub-shell), m = 0, ±1, ±2, ±3 (seven values) → Complicated shape.

Total number of orbitals in a main shell is equal to the total number of m values for a given value of l. in terms of n; number of orbitals in the n th shell is

equal to n2. Thus,

i) In 1st shell (n = 1), the number of orbitals = n2 = 12 = 1 (1s orbital)

ii) In 2nd shell (n = 2), the number of orbitals = n2 = 22 = 4 (2s; 2px, 2py, 2pz orbital).

iii) In 3rd shell (n = 3), the number of orbitals = n2 = 32 = 9 (3s; 3px, 3py, 3pz; 3dxy, 3 dyz, 3dzx,

3dx2-y

2, 3dz2 orbital)

iv) In 4th shell (n = 4), the number of orbitals = n2 = 42 = 16 (one 4s, three 4p, five 4d and seven 4f orbitals).

d) Spin quantum number (s)

Spin quantum number (s) indicates the spin of electron about their own axis. Maximum capacity of each orbital to contain electrons is two. Here both the

electrons present in an orbital have opposite spin i.e. for one electron the value of spin quantum is + ½, showing the clock wise direction of the spinning of

the electron, while for the other electron, s = - ½, showing the anti-clock wise direction of the spinning of the electron. It also indicates as [↑↓].

4.3. Rules for writing electronic configuration of different elements

1. Maximum number of electrons in a shell: According to Bohr-Bury scheme, the maximum number of electron in a shell is equal to 2n2, where n is the

number of shell (i.e. principal quantum number). Thus 1st (n = 1), 2nd (n = 2), 3rd (n = 3), 4th (n = 4) shell contains maximum 2, 8, 18, 32 electrons

respectively.

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2. Maximum number of electrons in a sub-shell: According to azimuthal quantum number, maximum number of electrons in a sub-shell is equal to

2(2l+1), where l = 0, 1, 2, 3 for s, p, d, f respectively. Thus s, p, d, f can have maximum 2, 6, 10 and 14 electrons respectively.

3. Aufbau principle: German word ‘Aufbau’ mean ‘build up’ or ‘construction’. According to this principle the orbitals are filled up with electrons in the

increasing order of their energy. The relative order of energy of different orbitals can be determined with the help of (n + l) value for a given orbital (n =

principal and l = azimuthal quantum number). The orbital having the lowest value of (n + l) has the lowest energy and hence is filled up first with

electrons. When two or more orbitals have the same value of (n + l), the orbital with lower value of n is lower the energy and hence is filled up first with

electrons. The relative order of energy of various orbitals if an atom is as:

1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<5f<6d<7p<8s……showing that the various orbitals are filled with electrons in the same

order. The sequence given above can be represented in Fig. 3.1.

n = 7 7s

n = 6 6s 6p 6d

n = 5 5s 5p 5d 5f

n = 4 4s 4p 4d 4f

20

n = 3 3s 3p 3d

n = 2 2s 2p

n = 1 1s Start from here

Fig. 3.1. The sequence in which various orbitals are filled up with electrons

4. Pauli’s exclusion principle: This principle states that the values of all the four quantum numbers for the two electrons residing the same orbital like s,

px, py, pz, dxy, dyz, dzx etc. cannot be same. This principle deals with the manner in which two electrons should be placed in an orbital. According to this

principle, if two electrons are to be placed in an orbital, they should be placed in such a way that they should have opposite spins [ ↑↓] so that the value of

at least one quantum number of each of the two electrons may be different. Thus an electrons in an orbital should be placed as [ ↑↓] and not as [↑↑] or

[↓↓]. Pauli’s exclusion principle can also be stated as that if two electrons have the same spin, they should not occupy the same orbital; rather they should

occupy the different orbitals. On the other hand, if two electrons have opposite spins, they should occupy the same orbital.

5. Hund’s rule: According to this rule, the electron in degenerate orbitals (e.g, set of 3 degenerate p orbitals viz., px, py and pz) should first be placed

singly and then, if the number of electrons exceeded the number of the degenerate orbitals, pairing of electrons in the same orbital should be allowed. Thus

according to this rule, the arrangement of three electrons in three degenerate orbitals viz., px, py and pz should be shown as [↑] [↑] [↑] and not as [↑↓] [↑]

or as [↓] [↑] [↓] .

e.g., O (8) =

1s2 2s2 2px2 2py

1 2pz1

21

↑↓ ↑↓ ↑↓ ↑ ↑

Electronic configuration and reactivity of element: From the electronic configuration, it is clear that the inert gases have the configuration of s2p6 (except

He, s2) which is a stable configuration. The electrons which have no these configurations want to gain the same. And for this reason atoms gain, lose or

share electrons to form a bond. When atoms do this function, they need energy. There are two kinds of energy need to form a bond. They are as – 1)

Ionization potential and 2) Electron affinity.

1. Ionization potential: It may be defined as the energy needed to remove a single electron from an atom of the element in the gaseous state, e.g., M (g) + 1

E1 = M+(g) + e-. It is expressed in election volts (ev) per atom or KJm-1. (1 ev atom-1 = 96.48 KJm-1)

2. Electron affinity: It is the amount of energy released when an electron is added to a gaseous atom to form an anion, e.g., Cl (g) + e- = Cl-(g) + E1. It is also

expressed in KJm-1.

Periodicity of elements

4.4. Periodic law

Mendeleef's periodic law

"If the elements are arranged in the increasing order of their atomic weights, the properties of the similar elements are repeated after definite regular

intervals or periods".

Mendeleef's periodic table

Working on this law, Mendeleef arranged the elements in the increasing order of their atomic weights in the form of a table which is known as Mendeleef'

periodic table after his name. In this table the elements are arranged in groups (or column) and periods (or row).

Mosley's modern periodic law

"The properties of elements are a periodic function of their atomic numbers, i. e. if the elements are arranged in the increasing order of their atomic

numbers; the properties of the elements (i. e. similar elements) are repeated after definite regular intervals or periods".

Extended or long form of periodic table or Modern periodic table

22

This is the most simple and widely accepted periodic table out of various periodic tables. It is also called Bohr's periodic table, since it is based on the

Bohr's scheme of the classification of the elements into four types depending on the number of incomplete shells of electrons in the atom. This table was

proposed by Rang (1893), and then modified by Werner (1905) and extended by Bury (1921).

4.5. Groups

The vertical columns present in the periodic tables are called groups or families or simply columns. There are 18 vertical columns in the long form of the

periodic table. A group consists of elements whose atoms have the same outermost electronic configuration. There are two system of numbering the

groups. According to IUPAC (International Union of Pure and Applied Chemistry) system, the groups are numbered as 1, 2, 3, 4, ...........,17, 18 while

according to another system, the groups are numbered as IA (for 1), IIA (2), IIIB (3), IVB (4), VB (5), VIB (6), VIIB (7), VIIIB (8, 9, 10), IB (11), IIB

(12), IIIA (13), IVA (14), VA (15), VIA (16), VIIA (17) and VIIIA or Zero (18).

**The elements of group IA (1) and IIA (2) are called "s-block elements" because of their valance shell electronic configuration varies from ns1 to ns2 and

those of groups IIIA (13), IVA (14), VA (15), VIA (16), VIIA (17) and VIIIA or Zero (18) are called "p-block elements" due to their valance shell electronic

configuration varies from ns2p1 to ns2p6. s- and p-block elements are taken together are called "main group elements". The elements of group IA (1), IIA

(2), IIIA (13), IVA (14), VA (15), VIA (16) and VIIA (17) have their outermost shell incomplete while each of their inner shell is complete and these are

called normal or representative elements and those of group VIIIA (18) or group zero have all their shells are completely filled and these are called "noble

gases".

**The elements belonging to group IIIB (3), IVB (4), VB (5), VIB (6), VIIB (7), VIIIB (8, 9 and 10), IB (11) and IIB (12) have their two outermost shells

incomplete and these are called "d-block". Their valance shell electronic configuration varies from (n-1) d1. ns2 to (n-1) d10. ns2. They are also called

'transition elements' due to their properties are intermediate between s- and p-block elements.

**Two rows of 14 elements lying in group IIIB (3) [Cerium (Ce58) to Lutetium (Lu71) and Thorium (Th90) to Lawrencium (Lw103)] have their three outermost

shells incomplete. These are called lanthanides or 4f-block elements and actinides or 5f-block elements respectively.4f- and 5f-block elements are

collectively called f-block elements or inner-transition elements or rare-earth metals. The valance shell electronic configuration of these elements is

represented as (n-2) f1.....7, 9.....14. (n-1) d0,1. ns2.

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4.6. Periods

The horizontal rows present in the periodic table are called periods or simply rows. There are seven periods in the table. In each period, the elements have

been placed in the increasing order of their atomic number.

**1st, 2nd and 3rd periods which contain 2, 8 and 8 elements respectively are called "short periods" while 4th, 5th and 6th periods which contain 18, 18

and 32 elements respectively are called "long periods". The elements of 3rd period namely Na, Mg, Al, Si, P, S and Cl are called typical elements because-

i) They show their group characteristics as valancy, chemical behavior etc.

ii) They form a connecting link between the first member of their respective groups and with the elements of B-subgroups. Here, these elements serve as a

bridge between the two sub-groups. However they show very little resemblance with elements of B-subgroups. e. g. Na and Cl which are the typical

elements of IA and VIIA groups respectively, resemble more closely with the elements of their own sub-groups and show a very little resemblance with the

elements of B-subgroups.

**7th period is an incomplete period and at present it consists of 22 elements which are Francium (Fr87) to Meitnerium (Mt109). All the elements of these

periods are radioactive. The elements after Uranium (U92) are called 'transuranic' elements. These elements are the result of atomic research and hence

are synthetic elements.

4.7. General properties of groups and periodsGeneral properties of groups

1. The number of valancy electrons remains unchanged of all the elements in the same group.

2. There is a regular gradation in physical and chemical properties of elements in a same group from top to bottom. e. g.

* The alkali metals (group IA) resemble each other and their base-forming tendency increases from Lithium (Li) to Cesium (Cs).

* The reactivity of halogens (group VIIA) decreases as we pass from Fluorine (F) to Iodine (I).

3. Atomic size increases on descending a group. e. g. in group IA, atomic size increases from Li to cesium. Thus, Li < Na < K < Rb < Cs.

4. Metallic characters of the elements increases in moving from top to bottom in a group. This is particularly apparent in groups IVA, VA and VIA, which

is begin with non-metals (C, N and O respectively) and end with metals [Lead (Pb), Bismuth (Bi) and polonium (Po) respectively]. e. g.

24

Elements of group VA: N, P, As, Sb, Bi.

Non-metal Metalloids MetalsMetallic characters: Metallic character increasing

The reason behind gradual increase of metallic character of the elements from top to bottom is that the oxides of the elements become more and more

basic in the same direction. e. g.

Oxides of the elements of group VA: N2O3, P2O5, As2O3, Sb2O3, Bi2O3

Acidic Amphoteric Basic Basic characters: Basic character increasing

5. The number of electron shells increases by one at each step of the elements belongs to the same group and ultimately becomes equal to the number of

period. e. g. Elements of group IA:

Elements Electronic configuration No. of shells

Li 2, 1 2

Na 2, 8, 1 3

K 2, 8, 8, 1 4

Rb 2, 8, 18, 8, 1 5

Cs 2, 8, 18, 18, 8, 1 6

Fr 2, 8, 18, 32, 18, 8, 1 7

General characteristic of periods

1. Number of valancy electrons increases from 1 to 8 when we proceed from left to right in a period.

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2. The valancy of the elements with respect to hydrogen in each short period increases from 1 to 4 and then falls to one while the same with respect to

oxygen increases from 1 to 7 as shown below for the elements of 2nd and 3rd period:

Elements of 2nd period: Li Be B C N O F

Hydrides of the elements: LiH BeH2 BH3 CH4 NH3 H2O HF

Valancy of elements with

respect to hydrogen: 1 2 3 4 3 2 1

Elements of 3rd period: Na Mg Al Si P S Cl

Oxides of the elements: Na2O MgO Al2O3 SiO2 P2O5 SO3 Cl2O7

Valancy of elements with

respect to hydrogen: 1 2 3 4 5 6 7

3. Atomic size decreases from left to right in a period. Thus alkali metals have the largest size while the halogens have the smallest size.

4. The properties of the elements of a given periods differ considerably but the elements in the two adjacent periods show marked similarity between

them. e. g. In 2nd and 3rd period Na resembles Li, Mg resembles Be, Si resemble C etc.

5. Metallic character of the elements decreases from left to right in a period. e. g. in 3rd period, Na, Mg and Al are metals while Si, P, S and Cl are non-

metals.

6. Number of electron shells remains the same from left to right in a period and number of period corresponds to the number of the shells found in the

elements of that period. e. g. all the elements of 2nd period have the electrons only in first two shells as shown below:

Element of 2nd period: Li Be B C N O F Ne

Atomic number : 3 4 5 6 7 8 9 10

Electronic configuration: 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 2, 7 2, 8

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Number of shells : 2 2 2 2 2 2 2 2

7. The elements of the 2nd period have resemblance of the properties with their diagonally opposite members lying in 3rd period than with other members

of their own sub-groups. Thus, Li resembles more in its properties with Mg. Similarly Beryllium (Be) shows similarities with Al and B resemble with Si.

4.8. Characteristics of s, p, d and f block elements

Characteristics of s-block elements

1. Atomic size and volume: Atomic size of s-block elements decreases on moving horizontally from group IA to group IIA while the same increases on

moving down the group. Since atomic radius decreases horizontally from group IA to IIA so, atomic volume also decreases in the same direction and

increases on moving vertically the groups.

2. Binding energy: Binding energies of s-block elements are low since there are one (for IA group) or two (for IIA group) s-electron per atom available for

bond formation in the crystal lattice of the metal. Binding energies decreases with the increase of the atomic radius. Thus binding energy on going down a

group whiles the same increases on moving horizontally from group IA to IIA.

3. Melting and boiling points: Since the binding energies of s-block elements decrease on going down a group whiles the same increases on moving

horizontally from group IA to IIA, the melting and boiling points of these elements invariably show the same trend.

4. Ionization energy: Ionization energy increases on moving horizontally from group IA to IIA and decreases on moving down a group. The values of first

ionization energies of s-block elements are comparatively lower than those of p-block elements.

5. Electropositive or metallic characters: Electropositive or metallic characters of an element is defined as its tendency to lose one or more electrons to

form cations. The greater is the tendency to lose the electron by an element, greater its metallic or electropositive characters. It depends on ionization

energy. With the decrease of ionization energy, the metallic character of the element increase. Since all the s-block elements have low values of ionization

27

energy, these elements have strongly electropositive characters, i. e. all elements belongs to s-block are metals. In other word, these elements have a grate

tendency to lose one or two s-electrons to form M+ (group IA) or M2+ (group IIA) cations.

M - e- M+ (Group IA)

M - 2e- M2+ (Group IIA)

6. Electronegativity: The relative tendency (or ability or power) of a bonded atom (covalent bond) in a molecule to attract the shared electron pair

towards itself is termed as its electronegativity. s-block elements have low values of electronegativity due to their higher electropositivity.

7. Electron affinity: Electron affinity of alkali metals are decreasing when we move from Li to Rubidium (Rb) but the electron affinity values of the

elements of group IIA are practically zero. This is because of the ns orbitals of the valance shell of these elements are completely-filled and hence the

addition of an extra electron from outside to these atoms is not possible.

8. Flame coloration: When s-block elements or their salts are heated in a Bunsen flame, they give characteristics color in the flame because the electrons

of the elements get energy and are excited to higher energy levels. When these electrons come back to the original (ground) energy level, the energy

absorbed by them during excitation (excited energy) is given out in the form of light which appears in the visible region of the spectrum. Thus the following

characteristic colors are given.

Elements Characteristic color Elements Characteristic color

Lithium (Li) Crimson Barium (Ba) Apple green

Sodium (Na) Yellow Beryllium (Be) -

Potassium (K) Violet Magnesium (Mg) -

Calcium (Ca) Brick red

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Since Be and Mg are smaller atoms, the electrons in these atoms ate more strongly bound to the nucleus and hence are not excited by the energy of flame

to higher energy levels. Thus these elements do not give any color in Bunsen flame.

9. Action of air-formation of oxides: These elements have a strong affinity for oxygen and tarnish quickly in air because they form a film of their oxides on

their surface. The reactivity of alkaline earth metals (group IIA) towards oxygen is less than that of alkali metals (group IA).

10. Action of water-formation of hydroxides: These elements vigorously decompose water with the formation of metallic hydroxides and liberation of

hydrogen. The reaction with water increases on moving the group and decreases as we move from group IA to group IIA.

Characteristics of p-block elements

1. Atomic size

Size of an atom of p-block elements decreases on moving from left to right in a period and the same increases on descending a group.

2. Ionization energy

First ionization energy value of p-block elements are generally increase on moving from left to right in a period and decrease on descending the group but

there are some exceptional.

3. Electropositive or metallic characters

With the increase of ionization energy, the metallic character of the elements decreases. So electropositive characters of p-block elements decreases on

moving in a period and increases down the group.

4. Electronegativity

As it is opposite to the electropositive characters, so the electronegativity of p-block elements decreases down the group and increases in a periods.

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5. Oxidation states and inert electron pair effects

The lighter element of p-block like those of 2nd and 3rd periods shows both positive and negative oxidation states. The heavier elements of p-block like

those of groups IIIA [Gallium (Ga), Indium (In), Thallium (Tl)], IVA [Germanium (Ge), Tin (Sn) and Lead (Pb)], VA [Arsenic (As), Antimony (Sb),

Bismuth (Bi)] and VIA [Tellurium (Te), Polonium (Po)] shows two oxidation states. The higher oxidation state for most of the elements is equal to their

group number, G while the lower one is equal to (G - 2) as shown below:

IIIA

(ns2p1)

G = 3

IVA

ns2p2)

G = 4

VA

(ns2p3)

G = 5

VIA

(ns2p4)

G = 6- - - -

- - - -

Ga (+1, +3) Ge (+2, +4) As (+3, +5) -

In (+1, +3) Sn (+2, +4) Sb (+3, +5) Te (+4, +6)

Tl (+1, +3) Pb (+2, +4) Bi (+3, +5) Po (+4, +6)

Group number oxidation states, G (i. e. higher oxidation states) is obtained when all the ns and np-electrons from ns2px configuration of p-block elements

(x = 1, 2, 3 and 4 for the elements of group IIIA, IVA, VA and VIA respectively) are lost, while the lower oxidation state equal to (G - 2) is obtained when

only np-electrons are lost and the ns-electrons pair, due to its extra stability, remains inert, i. e. it is not lost. Such a pair of ns-electrons is called inert

electron pair and the effect caused by it is known as inert pair effect.

e. g. Electrovalence's of Sn = +2 and +4. These are explained as follows:

5p2 electron lost 5s2 electron lostSn0 (- 2e-) Sn2+ (- 2e-) Sn4+

(2, 8, 18, 18, 5s2, 5p2) (2, 8, 18, 18, 5s2) (2, 8, 18, 18) (Oxidation state = 0) (Oxidation state = +2) (Oxidation state = +4)

Electrovalence's of As = +3 and +5. These are explained as follows:

30

4p3 electron lost 4s2 electron lostAs0 (- 3e-) As3+ (- 2e-) As5+

(2, 8, 18, 4s2, 4p3) (2, 8, 18, 4s2) (2, 8, 18) (Oxidation state = 0) (Oxidation state = +3) (Oxidation state = +5)

The inert electron pair effect increases as we move down a group. For example, in group IVA the order of this effect is Ge < Sn < Pb, indicating that this

effect is not much marked in Ge compounds. In order to show how this effect changes the properties of the elements we can consider the elements of group

IVA. In this group, the first two elements namely C and Si uniformly show +4 oxidation states while the remaining three elements viz. Ge, Sn and Pb show

both +2 and +4 oxidation states.

6. Oxidation and reducing property

An element with higher value of electron affinity can easily accept electron (s) and hence can act as a good oxidizing agent. Now electron affinity

decreases on descending a group and increases along the period, the oxidizing property of p-block elements decrease on descending the group and

increases from left to right across the period. Thus the halogens which lie at the extreme right pf the periodic table and have high value of electron affinity

are strong oxidizing agents.

7. Flame coloration

p-block elements or their salt does not gives characteristics color in bunsen flame, when it is heated on it. Because the excitation energy given out by the

electrons does not appear in the visible region of the spectrum.

Characteristics of d-block elements

1. Metallic characters

All the transitional elements are metals, since the number of electrons in the outermost shell is small, being equal to 2. They are hard, malleable and

ductile and possess high tensile strength.

2. Melting and boiling points31

These are very heavy metals and have high melting and boiling points. The last members of each series i. e. Zn, Cd and Hg have comparatively lower

values. these is because these metals have completely filled d-orbitals with no unpaired electrons (n) as is evident from their valance-shell electronic

configurations given below:

Zn 3d104s2 with n = 0

Cd 4d104s2 with n = 0

and Hg 5d106s2 with n = 0

3. Ionization potentials

The d-block elements are less electropositive than the s-block elements and more so than p-block elements. Consequently, these elements do not form ionic

compounds so readily as s-block elements. In general, compounds with metals in lower valancy state are ionic and others are covalent.

4. Low reactivity

These elements have low reactivity and this tendency is most pronounced in Au and Pt. Their low reactivity is due to the high values of their melting and

boiling points, heats of sublimation and ionization potential.

5. Color

The transition metals usually form colored compounds. The color is due to the promotion of unpaired d-electrons from one energy level to the other in d

level. In general the atoms, ions or molecules which have unpaired electrons in d-orbitals (i. e. partially filled d-orbitals) are colored because it is only in

case of such orbitals that the promotion of unpaired d-electrons to higher energy level within the same sub-shell is possible. On the other hand, atoms, ions

or molecules having completely filled d-orbital or vacant d-orbital are colorless.

For example,

Ion Configuration No. of unpaired electron (s) Color

Cu+ 3d10 0 Colorless

Zn2+ 3d10 0 Colorless

32

Ti3+ 3d1 1 Purple

V3+ 3d2 2 Green

Cr3+ 3d3 3 Green

Fe2+ 3d6 4 Pale green

Fe3+ 3d5 5 Yellow

6. Catalytic properties

Most of the transitional metals, their alloys and compounds are used as catalysts e. g. Pt, Ni, Fe, Cr, V 2O5 etc. Catalytic power of these metals is due to

either the use of their d-orbitals or due to the formation of interstitial compounds which absorb and activate the reacting substances.

7. Magnetic properties

Most of the transition metals are paramagnetic i. e. they tend to set themselves with their lengths parallel to the field, when they are placed between the

magnetic poles. Thus these are attracted into magnetic field. This property is due to the presence of unpaired electrons in d-orbitals. Thus the transitional

elements having all the electrons paired are diamagnetic. Fe and Co are ferromagnetic and can be magnetized.

8. Tendency to form complexes

The cations of transitional elements have a great tendency to form complexes with several ligands. This tendency is due to the following reasons:

a) The cations are relatively very small in size and hence have high positive density which makes it easy for the cations to accept the lone pairs from the

ligand.

b) The cations have vacant (n-1)d orbitals which are of appropriate energy to accept lone pair of electrons from the ligand for bonding with them.

Characteristics of f-block elements

General Characteristics of Actinides Elements

1. Occurrences

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Actinium (Ac89), Thorium (Th90), Protactinium (Pa91) and Uranium (U92) are found in nature in uranium minerals. The remaining actinides are unstable

and made artificially by nuclear transmutations and these elements are called trans-uranium or transuranic elements. All the actinides are radioactive.

2. Electronic configuration

The atoms of actinides have a total of seven shells in their electronic configuration. Out of these seven shells, first four shells namely 1st, 2nd, 3rd and 4th

are completely filled while the remaining three shells namely 5th, 6th and 7th shells are partially filled. The valance-shell configuration of these elements

can be represented as-

5f 0, 1......7, 9.......14, 6d 0, 1, 2, 7s2

3. Oxidation state

Generally +3 oxidation states is shown by all the actinides and this states becomes more and more stable as the atomic number increases. +4 oxidation

states is shown by Thorium (Th), Protactinium (Pa), Uranium (U), Neptunium (Np), Plutonium (Pu), Americium (Am) and Curium (Cm) while +5

oxidation state is shown by Th, Pu, U, Np and Am. +6 oxidation state is exhibited by U, Np, Pu and Am while +7 oxidation state is shown by Np and Pu.

4. Radii of tripositive and tetraposititive cations: Actinide contraction -

The values of the radii of tripositive and tetrapositive actinide cations (M3+ and M4+ cations) reveals that these values for both the cations decreases as we

move from Ac to Cm. This steady decrease in the size of M3+ and M4+ cations in the actinide series is called actinide contraction.

Radii of M3+ and M4+ cations-Ac > Th > Pa > u > Np > Pu > Am > Cm

Decreasing5. Colors of M3+ and M4+ cations

Most of the tripositive and tetrapositive actinides cations are colored. M3+ and M4+ cations having 5f 0, 5f 1 and 5f 7 configuration are colourless while those

containing 5f 2, 5f 3, 5f 4, 5f 5 and 5f 6

configuration are colored. These colors are produced when an electron jumps from one energy level to other with in 5f

orbital.

e .g. Ac3+ (5f 0, 6d 0, 7s 0, ) Colourless

U3+ (5f 3, 6d 0, 7s 0,) Red

Th4+ (5f 0, 6d 0, 7s 0,) Colourless

34

U4+ (5f 2, 6d 0, 7s 0,) Green

6. Formation of complexes

Most of the actinide halides form complex compounds with alkali metal halides. Actinides also form chelates with organic compounds like EDTA and

Oxine. The degree of complex formation for the ions M4+, MO22+, M3+ and MO2+decreases in the following order-

M4+> MO22+ >

4.9. Periodicity in the main group elements

Periodicity of properties and magic number

The term 'periodicity of properties' indicates that the elements with similar properties reappear at certain regular intervals of atomic number in the

periodic table. The repetition of the elements with similar properties in the order of increasing atomic number as in the periodic table is called periodicity

of properties and the numbers 2, 8, 18 and 32 are called magic numbers.

Causes of periodicity of properties

An examination of the valance shell electronic configurations of the elements of group IA, zero and VIIA given below shows that the elements showing

periodicity of properties i. e. the elements belonging to the same group have the same valance shell electronic configuration.

Group IA Group zero Group VIIA

H (1) - 1s1 He (2) - 1s2

Li (3) - 2s1 Ne (10) - 2s2p6 F (9) - 2s2p5

Na (11) – 3s1 Ar (18) - 3s2 p6 Cl (17) - 3s2p5

K (19) – 4s1 Kr (36) - 4s2 p6 Br (35) - 4s2p5

Rb (37) – 5s1 Xe (54) - 5s2 p6 I (53) - 5s2p5

Cs (55) – 6s1 Rn (86) - 6s2 p6 Astatine-At (85) - 6s2p5

Fr (87) – 7s1

35

Thus we see that in any group similar valance shell electronic configurations of the elements reoccur after certain regular intervals of atomic number and

it is this reoccurrence of similar valance shell electronic configurations of the elements at certain regular intervals of atomic number which becomes the

cause of periodicity of properties.

05. Chemical Bonding

5.1. Chemical bond

At present there are two concepts of chemical bond formation- a) classical concept and b) electrical concept. According to classical concept, a chemical

bond is defined as the attractive force that holds various constituent particles (atoms, ions or molecules) in different chemical species or the combining

36

capacity (valancy) of different elements with atom of hydrogen. On the other hand, electronic concept of chemical bond is forming between atoms by

losing, gaining, sharing of electrons or lone pair of electrons.

5.2. Types of chemical bond

Based on the electronic concept and classical concept, chemical bonds are of following types:

a) Ionic or electrovalent bond: Bonding by transfer of electrons.

b) Covalent bond: Bonding by mutual sharing of electrons.

c) Co-ordinate bond or dative bond: Bonding by lone pair of electron donation.

d) Metallic bond: A variable number of electrons are shared simultaneously by a variable number of atoms of the metal.

e) Hybrid bond

f) Sigma bond (σ) and pi (π) bond

g) Hydrogen bond: This bond involves the bonding of a hydrogen atom with two strongly electronegative atoms (e.g., N, O and F) simultaneously.

h) van der Walls Interaction: This bond involves the interaction between atoms or molecules having inert gas configuration.

5.3. Formation and properties of electrovalent, covalent and co-ordinate bond

A. Ionic or electrovalent bond

The chemical bond formed between two atoms by the transfer of one or more electrons from one atom to other is called ionic bond. This bond is also called

electrovalent or polar bond. This type of bond is commonly found in inorganic compounds. The atom that loses electrons becomes positively charged

(cations) while the atom that accepts electrons becomes negatively charged (anions). The cations and anions are then attracted towards each other by the

electrostatic force of attraction and are thus linked together by an ionic bond. Thus ionic bond can also be defined as the electrostatic force of attraction

existing between the cations and anions which are produced by the transfer of electron in an ionic compound. e. g. NaCl, MgO, CaF2, Al2O3 etc.

Formation of ionic bond in CaF2

Electronic configuration of Ca (20) = 1s22s22p63s23p64s2

37

Electronic configuration of F (9) = 1s22s22p5

In the formation of CaF2 molecule, each Ca atom loses two electrons and is converted into Ca2+ ion. Each F atom accepts one electron and is converted into

F- ion. One Ca2+ ion attacks two F- ions and forms CaF2 molecule.

2e-

Ca [ Ca ] 2+ + 2e-

(2, 8, 8, 2) (2, 8, 8)

2 :F: + 2e- 2 [:F:]- or, 2F-

Ca2+ + 2F- F- Ca2+ F- or, Ca2+ 2F- or, CaF2

Properties of ionic compounds:

1. Physical state: Ionic compounds are crystalline solids at room temperature.

2. Electrical conductivity: Ionic compounds do not conduct electricity when they are in the solid state because the anions and cations are fixed rigidly in

their position. But their aqueous solutions conduct a current when placed in an electrolytic cell.

3. High melting and boiling point: In ionic compound, the cations and anions are held together very tightly in their allotted position by very strong

electrostatic forces of attraction. So very high amount of energy is required to separate these ions from one another to make them free to move, as in liquid

or gas. Consequently, the ionic solids are quite hard and have high melting and boiling point.

4. Solubility in polar and non-polar solvents: Ionic compounds are freely soluble in polar solvents like water, liquid ammonia etc. because the

electrostatic force of attraction holding the cations and anions together in the ionic solids is reduced by the high value of dielectric constant of the polar

solvent and makes the ions moves freely and interact with solvent molecules to form the solvated ions. On the other hand, ionic solids are not insoluble or

slightly soluble in non-polar solvents like C6H6, CCl4 etc. due to their low value of dielectric constant.

5. Stability: Ionic crystals are very stable compounds sue to the oppositely charged ions are close to one another and the similarly charged ions are as away

from one another as possible.

6. High density: The electrostatic force of attraction existing between the cations and anions in an ionic crystal bring these ions very close to one another.

This decreases the volume of crystal and consequently the ionic crystals have high density.

38

7. Rapid ionic reactions: Ionic compounds give reactions between ions and formation of new ionic compounds and these are very fast.

e. g. NaCl Na+ + Cl-

AgNO3 Ag+ + NO3-

Cl- + Ag+ AgCl

8. Ionic compounds show isomorphism: Ionic solids made up of ions with identical electronic configurations show an identity or similar in crystalline

form which is called isomorphism. Two such pair of isomorphism compounds is:

a) Sodium fluoride and Magnesium oxide

Na+ F- Mg2+ O2-

(2, 8) (2, 8) (2, 8) (2, 8)

b) Calcium chloride and Potassium sulphide

Cl- Ca2+ Cl- K+ S2- K+

(2, 8, 8) (2, 8, 8) (2, 8, 8) (2, 8, 8) (2, 8, 8) (2, 8, 8)

9. Not exhibit isomerism: Ionic bond involving electrostatic lines of force between opposite ions is non-rigid and non-directional, so they are incapable of

exhibiting stereoisomerisms.

B. Covalent bond

The chemical bond formed between atoms by mutual sharing of electrons from both the participating atoms is called covalent bond. This type of bond is

commonly found in organic compounds. Let, an atom 'A' has one valance electron and another atom 'B' has seven valance electrons. As these atoms come

nearer to each other, each atom contributes one electron and the resulting electron pair fills the outer shell of both the atoms. Thus atom 'A' acquires two

electrons and 'B' acquires eight electrons in their respective outer shells and the shared electron pair constitutes a covalent bond between 'A' and 'B'.

A :B: or, A B

39A

Covalent bond

Formation of covalent bond in methane (CH4)

Carbon atom (2, 4) has four electrons in the valance shell. It can achieve the stable octet by sharing these electrons with H atoms, one with each H atom.

These can be written as follows:

H H

C + 4 H H C H H C H or, CH4

H H

Properties of covalent compounds:

1. Physical state: Covalent compounds are gases, liquids or relatively soft solids under normal temperature and pressure due to the weak intermolecular

forces between the molecules.

2. Melting and boiling points: Covalent compounds have generally low melting points or boiling points because of the attractive forces between covalent

molecules are weak van der Walls forces.

3. Electrical conductivity: Since there are no cations or anions in covalent molecules, the covalent compounds are incapable of conducting electricity.

4. Solubility in polar and non-polar solvents: Covalent compounds soluble in non-polar solvents but insoluble in polar solvents are due to the similarity

in covalent nature of the molecules of the solute and solvent i. e., their solubility is based on the principle-"Like dissolves like". Some of the covalent

compounds like alcohols; amines etc. are soluble in water due to hydrogen bond.

5. Molecular reactions: Covalent compounds give molecular reactions in solution.

6. Isomerism: Since covalent bonds are rigid and directional, they can give rise to different arrangements of atoms in space i. e., exhibit stereoisomerisms.

7. Covalent compounds are neither hard nor brittle.

C. Co-ordinate Bond

40

A chemical bond formed by giving the lone pair of electrons (which are provided entirely) by one of the bonding atoms or ions is called a co-ordinate

bond. It is also sometimes referred to as co-ordinate covalent bond or dative bond. The atom which furnishes the lone pair of electrons is called donor or

ligand while the other atom which accepts the electron pair is called acceptor. A co-ordinate bond is represented by an arrow ( ) which points away

from the donor to the acceptor.

For example, when ammonia combines with boron trifluoride, the lone pair electron of the nitrogen atom is involved in the formation of the new bond. In

boron trifluoride, the boron has only six electrons in its valancy shell; hence it can accommodate two more electrons to complete its octet. Thus, if the

nitrogen atom uses its lone pair, the combination of ammonia with boron trifluoride may be shown as (I) or (II).

F H F H F H

F B + N H F B N H or, F B N H

F H F H F H

(I) Co-ordinate bond (II)Formation of co-ordinate covalent bond in Disodium-calcium ethylene diamine tetra-acetate (Na2-Ca-EDTA)

A Na2-EDTA (Disodium salt of ethylene diamine tetra acetic acid) molecule contains two nitrogen atoms and each of nitrogen contains lone pair of

electrons. When Ca++ react with Na2-EDTA molecules than these lone pair of electrons given to the Ca++ and formed co-ordinate Na2-Ca-EDTA

compounds.

HOOC - H2C CH2 - COOH

N - CH2 - CH2 - N + Ca++

NaOOC - H2C CH2 - COONa

Na2-EDTA

O = C - O O - C = O

Ca

41

H2C CH2

N N

NaOOC - H2C H2C ― CH2 CH2 - COONa

Na2-Ca-EDTA

Formation of co-ordinate bond: The formation of co-ordinate bond between two atoms viz. A and B, may be regarded to occur in the following two

steps:

1st Step: In this step, the donor atom A transfers one electron of its lone pair to the acceptor atom B. This results in that atom A develops unit positive

charge (+) and atom B develops a unit negative charge (-). This charge is known as formal charge. This step is similar to the formation of an ionic bond. A:

+ B → A.+ + .B-

2nd Step: In this step the two electrons; one each with A+ and B- are shared by both the ions. This step is similar to the formation of a covalent bond.

A.+ + .B- → A:B or, A→B

Thus we see that, a co-ordinate bond is equivalent to a combination of an electrovalent bond (polar) and a covalent bond (non-polar). It is for this reason

that a co-ordinate bond is also sometimes called semi-polar bond.

Properties of co-ordinate compounds

1. Physical state: These compounds are gases, liquids or solids.

2. Melting and boiling points, and viscosity: Co-ordinate compounds is a combination of an ionic and covalent bond and for this reason they have

melting and boiling points, and viscosities which are higher than those of purely covalent compounds but lower than those of purely ionic compounds.

3. Semi-polar character: These compounds are semi-polar in character (A+ - B-), i. e. they are more polar than covalent compounds and less polar than the

ionic compounds.

4. Solubility: These are usually insoluble in polar solvents like water but are soluble in non-polar solvents.

5. Conductivity: They do not conduct electric current through their aqueous solutions.

6. Molecular reactions: Co-ordinate compounds are molecular and hence undergo molecular reactions which are slow.

42

7. Isomerism: They show isomerism because of this bond is rigid and directional.

8. Stability: They are stable but when they are made up of two different stable molecules, they are not very stable.

06. Chemical Reactions Kinetics and Equilibria6.1. Introduction

In analytical chemistry, for quantitative determination of reactants and products two important considerations of chemical reactions are the reaction

kinetics and the equilibrium condition of the reactants and products. The reaction kinetics (speed of reaction) indicates whether the rate of reaction is very

fast or very slow. On the other hand chemical equilibrium indicates the concentration (activity) of the reactants and products at a particular state of

reaction. There are two significant reasons why rapid chemical reactions are highly desirable for separation and measurement in analytical chemistry.

Slow reaction may seriously affect the accuracy and precision of a given determinations. Rapid reactions lead to attainment of a state of chemical

equilibrium by which we can calculate the concentration (activity) of reactants and products. The law of conservation of mass, stoichiometry and

thermodynamic is the basis of chemical equilibria.

6.2. Stoichiometry

Stoichiometry deals with the relationship of the reactants and products in chemical reactions based on the fundamentals laws of conservation of mass. That

is mass can be neither created nor destroyed in a chemical reaction. From this law it can be concluded that the total mass of the products formed must be

equal to the total mass of the reactants. Thus stoichiometry represents the balanced condition of the total mass, energy (heat, light or electricity) and

gaseous reactants and products of a chemical reaction. It is described by a short hand notation called balanced chemical equation. To make a

stoichiometric relation one should know the formula, molecular weights, percent composition, mole and molecular formula, equations, ionic equations,

molarity, normality of solution and gases, universal gas laws, energy in chemical reaction and its changes due to temperature and pressure that is

thermodynamics.

6.3. Universal gas law: The universal gas law or ideal gas law may be stated as: the volume of a given amount of a gas is directly proportional to the

number of moles of gas and temperature, and also inversely proportional to the pressure i. e.

6.5. Derivation of the ideal gas equation: Universal gas law derived from the following three laws. 43

Boyle's Law (T, n constant)

Charles' Law (n, P constant)

Avogadro's Law (P, T constant)

These three laws can be combined into a single more general gas law:

......................................................(1)

Introducing the proportionality constant R in the expression (1) we can write-

or, ................ (2)

Where, n is the number of moles of a gas and R is a constant which is characteristics of all gases. The numerical value of R depends on the units chosen to

express Pressure (P), Volume (V) and Temperature (T).

The equation (2) is called the Ideal Gas Equation or simply the general Gas equation. The constant R is called the Gas constant. The ideal gas equation

holds fairly and accurately for all gases at low pressure. For one mole (n = 1) of a gas, the ideal-gas equation is reduced to-

....................................................... (3)

The ideal gas equation is called an Equation of state for a gas because it contains all the variables (T, P, V and n) which describe completely the condition

or state of any gas sample. If we know the three of these variables, it is enough to specify the system completely because the fourth variable can be

calculated from the ideal-gas equation.

6.4. Molar volume

One mole of any gas at a given temperature (T) and pressure (P) has the same fixed volume. It is called the molar gas volume or molar volume. In order to

compare the molar volume of gases, chemists use a fixed reference temperature and pressure. This is called standard temperature and pressure

(abbreviated, STP). The standard temperature used is 273 K (0ºC) and the standard pressure is 1 atm. (760 mm Hg). At STP we find experimentally that

one mole of any gas occupies a volume of 22.4 liters. To put it in the form of an equation, we have-

1 Mole of a gas at STP = 22.4 Liters

44

6.6. Numerical value of 'R'

From the ideal-gas equation, we can write- R = ......................................................... (4)

We know that one mole of any gas at STP occupies a volume of 22.4 liters. Substituting the values in the equation (4), we have-

1 atm. X 22.4 Liters

R = 1 mole X 273 K

(At STP T= 273K and P= 1 atm. V= 22.4L)

(1 atm.) (22.4 Litres)R =

(1 Mole) (273 K.)

R

or R = 0.0821 atm. liter mol-1 K.-1

= 0.0821 atm. liter mol-1 K-1

It may be noted that the unit for R is complex; it is a composite of all the units used in calculating the constant. If the pressure is written as force per unit

area and volume as area x length, form (4) we get,

(Force/area) x (area x length) force x length WorkR = = =

n x T n x T n THence R can be expressed in units of work or energy per degree per mole. The actual value of R depends on the units of P and V used in calculating it. The

more important values of R are listed in the following Table-

Value of R in different units

0.0821 liter-atm K-1 mol-1 8.314 X 107 erg K-1 mol-1

82.1 ml-atom K-1 mol-1 8.314 Joule K-1 mol-1

62.3 liter-mm Hg K-1 mol-1 1.987 Cal K-1 mol-1

45

6.7. Dalton's law of partial pressure: John Dalton visualized that in a mixture of gases, each component gas exerted a pressure as if it were alone in

the container. The individual pressure of each gas in the mixture is defined as its Partial Pressure. Based on experimental evidence, in 1807, Dalton,

enunciated what is commonly known as the Dalton's Law of Partial Pressures. It states that-"the total pressure of a mixture of gases is equal to the sum of

the partial pressures of all the gases present". Mathematically the law can be expressed as Ptotal = P1 + P2 + P3........ (V and T are constant) where P1, P2

and P3 are partial pressure of the three gases 1, 2 and 3; and so on.

Dalton's Law of Partial Pressures follows by application of the ideal-gas equation separately to each gas of the mixture. Thus we can write the

partial pressures P1, P2 and P3 of the three gases as-

P1 = n1 P2 = n2 P3 = n3

Where n1, n2 and n3 are moles of gases 1, 2 and 3. The total pressure, Pt of the mixture is-

Pt = (n1+ n2 + n3) or, Pt = nt

In the words, the total pressure of the mixture is determined by the total number of moles present whether of just one gas or a mixture of gases.

6.8. Energy relation in chemical reaction: Many chemical reactions are carried out for producing energy and some reactions can take place only if

sufficient energy is provided. There are important relationships between energy and chemical change. The law of conservation of energy shows that energy

can be neither created nor destroyed. The different form of energy, such as heat, light, mechanical energy, electrical energy and chemical energy can be

converted into one another, but in every case the total quantity of energy is unchanged. Among the forms of energy, heat is unique, any other form of

energy can be completely transformed into heat energy, but at a constant temperature heat can not be completely transformed into any other form of

energy. The quantity of heat within an object at a given temperature is directly proportional to its mass. The common unit of heat is calories or in electrical

measurement joules (1 calorie = 4.184 joules). The quantity of heat is required to raise the 1ºC temperature of 1 mole of a substance is called heat 46

capacity. The symbol Cp denotes the heat capacity of a gas at constant pressure and the symbol Cv denotes the heat capacity at constant volume. Reactions

which occur with the evolution of energy are said to be exothermic; reactions in which energy is absorbed are endothermic. For example, the process

represented by the following equation is an endothermic reaction.

2 HgO (s) + 43.4 K.cal 2 Hg (l) + O2 (g), ∆= + 43.4 K.Cal25ºC

The following are the examples of an exothermic reaction:

C (s) + O2 (g) CO2 (g) + 94.05 K.cal,∆= -94.05 K.Cal

47

6.9. Terminology used in thermodynamics

Thermodynamics: The energy relations in chemical reaction can be explained by thermodynamics. Thermos means heat (energy) and dynamics means

works. The science of heat and work is called thermodynamics. In a chemical process either heat is absorbed or evolved. So a chemical changes may be

described in term of thermodynamics. Thermodynamics deals with the initial and final state of a system. In a chemical reaction, A + B

C + D, thermodynamics does not deal with the reactants and products but it deals with the energy needed in the process. For better understanding of

thermodynamics the following terminology need to discuss-

System: In thermodynamics the portion of reactants or products (matter) being investigated is referred to as a system.

Surroundings: All other objects in the universe which may interact with the system are called the surroundings.

State of the system: A complete description of the system including all interacting objects, energy, temperature, pressure etc. are called state of the system.

Initial state: State of the system before it undergoes a change.

Final state: The state of the system after the change has occurred.

Standard state: Standard state (not to be confused with STP) of each element and each compound is defined as its most stable physical form at 1 atm.

pressure and at a specified temperature usually at 298 K or at 25oC.OR State of the system at 1 atm. and 250C.

State variable: The measurable and changeable properties of thermodynamics variable like temperature, pressure, volume, number of molecules, enthalpy,

entropy and Gibbs free energy is called state variable.

Equation of state: The equation representing the relation among the state variables is called equation of state. The equation is known as

equation of state.

State function: When the value of any state variable depends on the other state variables then the dependent variable is called the state function of the

other variables. E = E (T, V) or,

E = f (T, V). It means that E is the state function of the state variable T and V.

The followings are the state function in thermodynamic study:

i) E = Internal energy

ii) H = Enthalpy

48

iii) S = Entropy

iv) A = Helmholtz free energy function or work function

v) G = Gibbs free energy

Internal Energy (E): A matter has within itself a definite quantity of energy (heat , electric and atomic energy). The total of all the possible kinds of

energy, is called its internal energy . Internal energy is represented by 'E'. Internal energy of a system is a function of temperature i. e. E = E (T, V),

where E = all types of energy. The exact value of internal energy cannot be determined but the change in internal energy (∆E) can be accurately measured

experimentally. That is, ∆E = E product - E reactant OR,, ∆E = E2 – E1

Enthalpy (H): When the energy of a system is expressed in terms of heat content, it is called enthalpy. Enthalpy is represented by 'H'. Enthalpy includes

the all other form of energy (E) as well as pressure x volume (PV) type work. i. e. H = E + PV. The change in enthalpy (∆H) at constant pressure is the

difference between the sums of the enthalpies of the products and the sum of the reactants.

Products - Reactants OR H2 – H1

When, ∆H = (-) it is exothermic reaction (Heat evolved)

When, ∆H = (+) it is endothermic reaction (Heat absorbed)

Examples,

2 HgO (s) 2 Hg (l) + O2 (g), ∆H298 = 43.4 K. cal (endothermic)25ºC

C (s) + O2 (g) CO2 (g), ∆H298 = -94.05 K. cal (exothermic)

Entropy(S): In real reactions some energy is always lost and never recovered or never be utilized and some of the energy can be used. The energy which is

lost forever is termed as entropy, represented by the letter 'S'. Products - Reactants OR S2 – S1

Helmholtz free energy : The useful energy which is free to be converted to other forms of energy or the useful energy which is used as pressure x volume

type of work is called Helmholtz free energy, represented by A, or

Gibbs free energy (G): The available energy which can be used as pressure x volume type work and also as additional some other type of work is called

Gibbs free energy, represented by 'G'. or, , T is the absolute temperature.

When, ∆G = (-) or less than zero, the process can occur spontaneously (a change which requires no energy from the surroundings).49

∆G = zero (0), the system is at equilibrium.

∆G = (+) or greater than zero, the process is not spontaneous i. e. the process will not occurs naturally.

Thus thermodynamics properties or state functions are useful in predicting whether a given process is spontaneous or not.

Absolute Zero Temperature: Volume of all gases increases or decreases with temperature. If temperature is very low then at first the gases liquefies by

decreasing volume and ultimately the volume become zero. The temperature at which the volume of gases becomes zero is called absolute zero temperature

and this volume is called absolute zero volume. At -273.16ºC (0 Kelvin), the volume of all gases is zero.

6.10. Laws of thermodynamics

First law of thermodynamics may be defined as 'energy of the universe is constant'. The law of conservation of energy is also known as the first law of

thermodynamics. In other word, "total energy of an isolated system remains constant though it may change from one form to another". The first law

describes the change in internal energy (E) and enthalpy (H). When a system is changed from state A to state B, it undergoes a change in the internal

energy from EA to EB. Thus we can write-

∆E = EB - EA

These energy changes are brought about by the evolution or absorption of heat and/or by work being done by the system. Because the total energy of the

system must remain constant, we can write the mathematical statement of the First law as:

∆E = q - w ......................................................... (1)

Where, q = the amount of heat supplied to the system

w = work done by the system

Thus First law may also be stated as "the net energy change of a closed system is equal to the heat transferred to the system minus the work done by the

system".

To illustrate the mathematical statement of the First law, let us consider the system 'expanding hot gas' (see following fig.)

W out

Final Position

50

∆V Original Position

∆E = q - w

Heat q inFig. Illustration of First law; Heat add to internal energy, while work subtracts

The gas expands against an applied constant pressure by volume ∆V. The total mechanical work done is given by the relation (work done by the system

then w is –ve)

X ∆V ............................................ (2)

From (1) and (2), we can restate-

∆E = q - P X ∆V

Conclusion from first law of thermodynamics

1. Whenever energy of a particular type disappears equivalent amount of another type must be produced.

2. Total energy of a system and surroundings remains constant (or conserved)

3. It is impossible to construct a perpetual motion machine that can produce work without spending energy on it.

Some special case or state of First law of Thermodynamics

The First law of Thermodynamics, ∆E = q - w, may be expressed in different form at different condition.

Case I: For a cyclic process involving isothermal (at a constant temperature) expansion of an ideal gas ∆E = 0, Therefore, q =w

Case II: For an isochoric process (no change in volume) there is no work of expansion

i. e., w = 0, Hence, ∆E = q v

Case III: For an adiabatic process (no heat flow) there is no change in heat gained or lost

i. e., q = 0. Hence, ∆E = - w

In other words, the decrease in internal energy is exactly equal to the work done on the system by surroundings.

Case IV: For an isobaric process there is no change in pressure, i. e. P remains constant. Hence, ∆E = q - w or, ∆E = q - P ∆V

51

Enthalpy of a system: In a process carried at constant volume (say in a sealed tube), the heat content of a system is the same as internal energy (E), as

no PV work is done. But in a constant-pressure process, the system (a gas) also expends energy in doing PV work. Therefore, the total heat content of a

system at constant pressure is equivalent to the internal energy E plus the PV energy. This is called the Enthalpy (Greek, en = in; thalpos = heat) of the

system and is represented by the symbol H. Thus enthalpy is defined by the equation

H = E + PV.................................................. (1)

In the equation (1) above, E, P, V is all state functions. Thus H, the value of which depends on the values of E, P, V must also be a function of state. Hence

its value is independent of the path by which the state of the system is changed.

Change in enthalpy: If ∆H be the difference of enthalpy of a system in the final state (H2) and that in the initial state (H1), that is, H2 -

H1............................................... (2)

Substituting the values of H2 and H1, as from (1) and (2), we have-

(E2 + P2V2) - (E1 + P1V1) = (E2 - E1) + (P2V2 - P1V1) = ∆E + ∆(PV)= ∆E +P∆V+V∆P

=∆E + w+ V∆P [No other work is performed except expansion work. Then, P∆V=w]

=q – w + w + V∆P [According to first law, ∆E= q – w, (Where, q = heat transferred)]

=q+ V∆P

=q [At constant pressure ∆P=0 ]

So, ∆H = q, When change in state occurs at constant pressure.

The relationship is usually written as, ∆H = qp, Where subscript 'p' means constant pressure.

Thus ∆H can be measured by measuring the heat of a process occurring at constant pressure.

Relation between ∆H and ∆E

Calorific values of many gaseous fuels are determined in constant volume calorimeters. These values are, therefore, are given by the expression

qv = ∆E

When any fuel is burnt in the open atmosphere, additional energy of expansion, positive or negative, against the atmosphere is also involved. The value of

q thus actually realized, i. e., qp = ∆H, may be different from the equation52

............................................. (1)

If gases are involved in a reaction, they account for most of the volume change as the volumes of solids and liquids are negligibly small in comparison.

Suppose we have n1 mole of gases before reaction, and n2 mole of gases after it. Assuming ideal gas behavior, we have

= n2 RT

1 = n1 RT

(V2 - V1) = (n2 - n1) RT

or, P∆V = n RT

Substituting equation (1), we have, ∆H = ∆E + ∆n RT

Molar heat capacity

By heat capacity of a system we mean the capacity to absorb heart and store energy. As the system absorbed heat, it goes into the kinetic motion of the

atoms and molecules contained in the system. This increased kinetic energy raises the temperature of the system.

If q calories is the heat absorbed by mass m and the temperature rises from T1 to T2, the heat capacity (c) is given by the expression

........................................ (1)

Thus heat capacity of a system is the heat absorbed by unit mass in raising the temperature by one degree (K or ºC) at a specified temperature.

When mass considered is 1 mole, the expression (1) can be written as

............................................ (2)

Where" C" is denoted as Molar heat capacity.

The molar heat capacity of a system is defined as the amount of heat required to raise the temperature of one mole of the substance (system) by 1 K.

Since the heat capacity (C) varies with temperature; its true value will be given as

53

Where dq is a small quantity of heat absorbed by the system, producing a small temperature rise dT. Thus the molar heat capacity may be defined as the

ratio of the amount of heat absorbed to the rise in temperature.

Units of Heat Capacity

The usual units of the molar heat capacity are calories per degree per mole (cal K-1mol-1), or joules per degree per mole (J K-1 mole-1), the latter being the

SI unit.

Heat is not a state function, neither is heat capacity. It is, therefore, necessary to specify the process by which the temperature is raised by one degree. The

two important types of molar heat capacities are those: (1) at constant volume; and (2) at constant pressure.

Molar heat capacity at constant volume

According to the first law of thermodynamics-

........................................... (i)

Dividing both sides by dT, we have-

...................................... (ii)

At constant volume dV = 0, the equation reduces to –

Thus the heat capacity at constant volume is defined ads the rate of change of internal energy with temperature at constant volume.

Molar heat capacity at constant pressure

Equation (ii) above may be written as, ............................................... (iii)

We know,

Differentiating this equation w. r. t. T at constant pressure, we get-

........................... (iv)

Comparing it with equation (iii) we have,

54

Thus heat capacity at constant pressure is defined as the rate of change of enthalpy with temperature at constant pressure.

Relation between Cp and C v

From the definitions, it is clear that two heat capacities are not equal and Cp is greater than Cv by a factor which is related to the work done. At a constant

pressure part of heat absorbed by the system is used up in increasing the internal energy of the system and the other for doing work by the system. While at

constant volume the whole of heat absorbed is utilized in increasing the temperature of the system as there is no work done by the system. Thus increase in

temperature of the system would be lesser at constant pressure than at constant volume. Thus Cp is greater than C v.

We know, ................................. (i)

and ................................. (ii)

By definition for 1 mole of an ideal gas.

or,

Differentiating w. r. t. temperature, T, we get –

Or, [By using equations (i) and (ii)]

Or,

Thus Cp is greater than Cv by a gas constant whose value is 1.987 cal K-1 mol-1 or 8.314 J K-1mol-1 in S. I. units.

Calculation of ΔE and ΔH

(A) ΔE: For one mole of an ideal gas, we have -

or,

For a finite change, we have-

55

And for n moles of an ideal gas we get-

(B) ΔH: We know,

And for n moles of an ideal gas we get-

Second law of thermodynamics

The entropy of the universe either increases or unchanged for any process. i. e., ΔS ≥ 0.

According to the first law of thermodynamics "energy of the universe is constant", i. e., energy can neither be created nor destroyed. It can only be

transformed from one form to another. But during transformation some energy is always lost and never recovered. This type of energy is called

unavailable energy and is termed as entropy. Entropy increases with temperature. First law says loss and gain is equal but second law point out that some

energy is always lost and never recovered. This type of energy loss is increases with temperature. So, the contradiction arises between 1st and 2nd law were

minimized by 3rd law, as stating that at absolute zero temperature the entropy also zero.

Thus entropy may be defined as a thermodynamic state quantity that is a measure of the randomness or disorder of the molecules of the system. The change

in entropy ΔS, for any process is given by the equation-

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When S final > S initial than ΔS is positive. That is a change in a system which is accompanied by an increase in entropy, tends to be spontaneous. For a

reversible change taking place at a fixed temperature (T), the change in entropy (ΔS) is equal to heat energy (q) absorbed or evolved divided by the

temperature (T).

That is or, or, (in differential language)

If heat is absorbed, than ΔS is positive and there will be increase in entropy. If heat is evolved, ΔS are negative and there is a decrease in entropy.

Entropy is equal to heat energy divided by absolute temperature, therefore, it is measure in entropy unit ('eu') which are calories per degree per mole i. e.

Cal mole-1K-1 or J mol-1K-1, represented by 'Eu'. From the idea if entropy the second law of thermodynamics may stated as "the entropy of a system

increases in any spontaneous process and attains a maximum for a reversible process". Thus second law explains the direction of reactions, what type of

reaction will occur and what reaction will not occurs.

If dS internal = 0, the process is reversible.

If dS internal > 0, the process is irreversible.

If dS internal < 0, the process will not occur.

For any process, dS ≥ 0 and dS system ≥ .

Because, dS system = dS internal + dS surroundings.

At equilibrium dS internal = 0

So, dS system = 0 + dS surroundings, since dS surroundings =

So, dS system =

So, dS system ≥

Third law of thermodynamics

At the absolute zero of temperature perfect crystal of all compounds possess zero entropy.

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i. e. S = 0 when T = 0.

Statement of the third law

The entropy of a substance varies directly with temperature. The lower the temperature it will lower the entropy. For example, water above 100ºC at one

atmosphere exists as a gas and has higher entropy (higher disorder). The water molecules are free to roam about in the entire container. When the system

is cooled, the water vapor condenses to form a liquid. Now the water molecules are confined below the liquid level but still can move about somewhat

freely. Thus the entropy of the system has decreased. On further cooling, water molecules join together to form ice crystal. The water molecules in the

crystal are highly ordered and entropy of the system is very low.

If we cool the solid crystal still further, the vibration of molecules held in the crystal lattice gets slower and they have little freedom of movement (very

little disorder) and hence very small entropy. Finally, at absolute zero all molecular vibration ceases and water molecules are in perfect order. Now the

entropy of the system will be zero.

Fundamental equation of state

Show that the fundamental equation of state, ..

From the definition of internal energy (E) and 1st law of thermodynamics we have ‘the energy of the universe is constant’ or ‘total energy of a system is

remain constant’ though it may change from one form to another. These changes are brought about by evolution or absorption of heat and work done by

the system. Therefore,

Heat absorbed = increase in internal energy + work done by the system

or , increase in internal energy = Heat absorbed – work done

or, where, EB = State B, EA = State A

q = Heat absorbed or evolved, w = Work done

or,

in differential notation, Since, Work = Pressure x Change in volume

or,

or,

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................................................ (1)

From 2nd law we have, Entropy (S) = Total energy absorbed divided by temperature

or, or, or, ................................................... (2)

Putting the value of dq of equation (1),

So the fundamental equation of state, (Showed).

Relation between Gibb's free energy and useful work

Show that "Gibbs free energy is either less than useful work or equal to useful work".

When only pressure volume work is considered than dE = dq – dw = TdS – PdV.

If an additional work is done, then,

or,

From the definition of Gibbs free energy –

We have, [Since H=E+PV]

or,

or,

Putting the value of dE for additional work-

dG = TdS – PdV + + PdV + VdP – TdS - SdT

or, dG = VdP – SdT + ,

If dP = 0, dT = 0, Then, dG = [ i. e. at constant temperature and pressure dG = ]

Since, dG = VdP – SdT + ,

So, dG <

So, dG ≤

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Therefore, we can conclude that Gibbs free energy is either less than useful work or equal to useful work. Or, ≥ dG

When work is performed in the system then the (+) sign is used but when work is performed on the surroundings then (-) sign is used.

When, ΔG < 0, or ΔG = (-), then the process can occur spontaneously.

When, ΔG = 0, then the system is at equilibrium.

When, ΔG > 0, or ΔG = (+), then the process will not occur naturally.

6.11. Chemical potential

Show that .

Chemical Potential (µ) Chemical potential is the ability to perform chemical work. It is a function of Gibbs free energy and mole fractions. µ = µ (G, n). It

is related with Gibbs free energy. Chemical potential is equal to Gibbs free energy divided by number of moles. i. e., , Where, n is number of mole, G

is Gibbs free energy and µ is chemical potential. From the laws of thermodynamics and equation of state we have, dE = dq – dw = TdS – PdV

and from the definition of Gibb’s free energy we have, G = H – TS

Or, G = E + PV – TS (since, H = E + PV)

Or, dG = dE + PdV + VdP – TdS – SdT

Or, dG = TdS - PdV + PdV + VdP – TdS – SdT

Or, dG = VdP - SdT

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At constant temperature, dT = 0 ............................................ (ii)

From combined Boyles and Charles law, we have, PV = nRT.......................... (iii)

Or, V = ................................................. (iv)

From equation (ii), we have,

[P0 = 1 atm. i. e., lnP0 = ln1 = 0]

This is the chemical potential of an ideal gas. Where µ = chemical potential, chemical potential at standard state, R = universal gas constant, T =

absolute temperature and P = pressure.

The value of µ (chemical potential) at different conditionFor ideal gas:

For ideal solution: , where xi is the mole fraction of ith components.

For real solution: , where , γ is the activity coefficient and xi is the mole fraction of ith components.

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6.12. Activity

Activity (a)

Activity is the effective concentration or idealized concentration. It is one kind of collegative properties (the properties which depends on number of

particles in the solution). In other words activity is the corrected concentration. Activity may be expressed as a = γM, where, a is the activity, γ is the

activity coefficient and M is the molarity. An ideal solute has an activity coefficient of unity. Deviation of the activity co-efficient from unity expresses the

degree of deviation from ideal behavior.

Activity co-efficient (γ): The ratio of the activity to the actual concentration is known as activity co-efficient. i. e., . The molar concentration is

expressed with square brackets [M], whereas the activity expressed with parentheses (a).

Chemical equilibrium

6.13. Definition of chemical equilibrium

The state of a reaction which can go in the forward and backward direction simultaneously at the same rate and the concentration of the reactants and

products do not change with time is called chemical equilibrium. Let us consider the reaction,

A + B C + D

If we start with A and B in a closed vessel, the forward reaction proceeds to form C and D. The concentration of A and B decrease and those of C and D

increase continuously. As a result the rate of forward reactions also decreases and the rate of reverse reaction increases. Eventually the rate of the two

opposing reactions equals and the system attains a state of equilibrium.

Law of mass action or equilibrium constant expression: The general definition of the equilibrium constant may be stated as "the product of molecular

concentrations of the resultants (reaction product) divided by the product of the molecular concentrations of the reactants, each concentration being raised

to a power equal to the number of molecules of that substance taking part in the reaction, is constant. That is, the equilibrium constant expression is -

[C]c [D]d

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Kc = [A]a [B]b

For a generalized reaction -

a A + b B c C + d D

Where a, b, c and d are numerical quotients of the substance A, B, C and D respectively

This equation is known as the equilibrium constant expression or equilibrium law or law of mass action.

6.14. Show that,

We know, the velocity or rate of a chemical reaction is proportional to the product of the concentrations of the reacting specie, each concentration raised

to a power equal to the number of molecules, atoms or ions of each reactant. Let us consider a general reaction-

1A + 1B 1C + 1D

Mathematically, it is expressed that-

Rate of forward reaction, Vf ∞ [A]1[B]1 or, Vf = Kf [A]1[B]1

And rate of backward reaction (also expressed as reverse reaction), Vb ∞ [C]1[D]1

or, Vb = Kb [C]1[D]1

At equilibrium, the rate of forward reactions = rate of backward or reverse reaction

Therefore, Vf = Vb

or, Kf [A]1[B]1 = Kb [C]1[D]1

or, ............................................................. (1)

At any specific temperature Kf / Kb is constant. Since both Kf and Kb are constant, the ratio Kf/Kb is called equilibrium constant and is represented by the

symbol 'Kc' or simply 'K'. The subscript 'c' indicates that the value is in term of molar concentration (mole/L) of the reactants and products. Now the above

equation (1) may be written as -

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or,

or, Kc =

This equation is known as the equilibrium constant expression or equilibrium law or law of mass action. For a generalized reaction it may be written as -

a A + b B c C + d D

Where a, b, c and d are numerical quotients of the substance A, B, C and D respectively. Then the equilibrium constant expression is -

[C]c [D]d

Kc = [A]a [B]b

How to write the Equilibrium constant expression?

1. Write the balanced chemical equation for the equilibrium reaction. By convention, the substances on the left of the equation are called the reactants

and those on the right, the products.

2. Write the product of concentrations of the 'products' and raise the concentrations of each substance to the power of its numerical quotient in the

balanced equation.

3. Write the product of concentrations of 'reactants' and the concentration of each substance to the power of its numerical quotient in the balanced

equation.

4. Write the equilibrium expression by placing the product concentrations in the numerator and reactant concentrations in the denominator. That is,

Product of concentrations of 'products' from step-2 Kc =

Product of concentrations of 'reactants' from step-3

6.15. Equilibrium constant expression in terms of partial pressures

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When all the reactants and products are gases, we can also formulate the equilibrium constant expression in terms of partial pressures. The relationship

between the partial pressure (P) of any one gas in the equilibrium mixture and the molar concentration follows from the general ideal gas equation-

or

The quantity is the number of moles of the gas per unit volume and is simply the molar concentration. Thus,

P = (Molar concentration) X RT

i. e., the partial pressure of a gas in the equilibrium mixture is directly proportional to its molar concentration at a given temperature. Therefore, we can

write the equilibrium constant expression in terms of partial pressures instead of molar concentrations. For a general reaction-

lL(g) + mM(g) yY(g) + zZ(g)

The equilibrium law or the equilibrium constant may be written as-

(PY)y (PZ)z

Kp = (PL)l (PM)m

Here, Kp is the equilibrium constant, expressed in term of partial pressure; the subscript 'p' referring to partial pressure. Partial pressures are expressed in

atmospheres

6.16. Relationship between Kp and Kc

Let us consider a general reaction, jA + kB lC + mD

Where all reactants and products are gases. We can write the equilibrium constant expression in terms of partial pressures as (PC)l (PD)m

Kp = ........................................ (1)(PA)j (PB)k

Assuming that all these gases constituting the equilibrium mixture obey the ideal gas equation, the partial pressure (P) of a gas is -

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Where, is the molar concentration. Thus the partial pressures of individual gases, A, B, C and D are;

PA = [A] RT; PB = [B] RT; PC = [C] RT; PD = [D] RT

Substituting these values in equation (1), we have-

[C]l (RT)l [D]m (RT)m

Kp = [A]j (RT)j [B]k (RT)k [C]l [D]m (RT) l+ m

or, Kp = X [A]j [B]k (RT) k+ j

or, Kp = Kc X (RT)(l + m) - (j + k)

Kp = Kc X (RT) ∆n......................................... (2)

Where ∆n = (l + m) - (j + k), the difference in the sums of the coefficients for the gaseous products and reactants. From the expression (2) it is clear that

when ∆n = 0 then Kp = Kc.

6.17. Factors influencing chemical equilibrium

The change in concentration (C) pressure (P) or temperature (T) greatly influences the rate of chemical reactions and thus equilibrium. The principles of

Le Chatelier's explain how the chemical equilibrium affected by the change of concentration, pressure and temperature of the reactants and products. Le

Chatelier's principle may be stated in general form, "when a stress is applied to a system at equilibrium, tends to shift in such a direction as to diminish or

relieve that stress."

Let us consider a general reaction

A + B C

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When a reactant, say, A is added at equilibrium, its concentration is increased. The forward reaction alone occurs momentarily. According to Le

Chatelier's principles, a new equilibrium will be established so as to reduce the concentration of A. Thus the addition of A causes the equilibrium to shift to

right. This increase the concentration (yield) of the product C.

A +B C A +B C

Here A addition and equilibrium shift to right; Here A removal and equilibrium shift to left.

Following the same line of argument, a decrease in the concentration of A by its removal from the equilibrium mixture, will be undone by shift of the

equilibrium position to the left. This reduces the concentration (yield) of the product C.

Conclusion:

The thermodynamics properties or state function is useful in predicting whether a given reaction process is at equilibrium, spontaneous or not.

When ΔG = 0, the process is at equilibrium

ΔG > 0, i.e. negative, the process will occurs spontaneously

ΔG < 0, i.e. positive, the process will not occur.

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