Physical Chemistry

Sixth Form Practicals - 2016

Porter Laboratory

INTRODUCTION

Physical chemistry is a quantitative science. Skill in practical work is as important as a

knowledge of theory. Many important discoveries have resulted from observations of small

inconsistencies in repeated measurements or minor discrepancies between theory and

experiment. Well known examples are the discovery of the noble gases from the precise

measurement of relative molar masses; the development of the idea of electron and nuclear

spin from observations on the fine splitting of spectral lines; the discovery radioactivity from

the fogging of photographic plates left in the proximity of uranium salts. These developments

would not have taken place without the acute observation of the researchers and an

appreciation of the reliability and significance of their measurements.

The main objective of physical chemistry laboratory work is to provide training and practice

in the collection and critical evaluation of experimental data and in the preparation of reports.

The emphasis in the practical work is in making measurements and assessing the errors in

the measurements and final results. There is also the opportunity to use a computer for

tabulating data, calculating results and plotting graphs.

Two programs are available:

Microsoft Excel – most students will have used this package previously.

OriginPro - A graph drawing package with spreadsheet facilities. It will plot straight line

graphs and calculate the gradient and intercept with error limits. Very easy to use!

Each student will be able to perform two experiments.

1. The Ionisation Energy of the Hydrogen Atom

2. Kinetics of a first order reaction (hydrolysis of t-butyl chloride) by measurements of

conductivity.

EXPERIMENT 1

The Ionisation Energy of the Hydrogen Atom

The OBJECTIVES of this experiment are:

1. To measure the wavelengths of the first three lines of the Balmer series in the emission

spectrum of the H atom using a spectrometer.

2. To calculate the Rydberg constant and the ionisation energy of the H atom.

BACKGROUND

Spectra refer to patterns of emission and absorption of light from atoms. The observation of

spectra was a important step in the development of atomic theory and led to the Bohr model

of atoms. In this model, electrons orbiting the nucleus can exist only in discrete orbits and at

specific energies.

Absorption spectrum - Shows atoms changing states on absorption of electromagnectic

radiation. Atomic states are defined by the arrangement of electrons in atomic orbitals. An

electron in one orbital i.e. the ground state, may be excited to a more energetic orbital by

absorbing one photon of energy. Absorption spectra can be used to identify elements present

in liquids and gases.

Emission spectrum - a molecule undergoes a transition from higher energy level to a lower

energy level, usually the ground state. It gives out energy of a particular wavelength showing

the discrete lines of an emission spectrum. The spectra can be used to determine the

composition of a material, i.e. composition of stars.

Frequency, wavelength, wavenumber and energy

Em

issi

on

Ab

sorp

tion

E1

E2

En

erg

y

Em

issi

on

Ab

sorp

tion

E1

E2

En

erg

y

Electromagnetic radiation is characterised by its frequency and its wavelength . These are

related to the speed of propagation c by the equation c = . The energy possessed by one

quantum of radiation (a photon) of frequency is given by the Planck equation = h,

where h is Planck’s constant and has the value 6.62607 10-34 J s.

The frequency of a photon is expressed in the SI unit reciprocal seconds (s1). The energy of

one mole of photons is given by E = NAh, where NA is the Avogadro’s constant and has the

value 6.02214 1023 mol1. This equation yields energy in J mol1.

Spectroscopists usually characterise radiation by its wavenumber, 1/ . In SI units the

wavenumber would be m1 but invariably the unit used is cm1 (1 cm1 = 100 m1).

Hydrogen Spectrum

This figure illustrates the energy levels of the hydrogen atom and the possible transitions

occurring in the emission spectrum. To the far left is the Paschen series which was

discovered by Friedrich Paschen in 1908 and is in the Infra-red region of the electromagnetic

spectrum.

The middle series was discovered by Theodore Lyman in 1906 and is in the far Ultraviolet

region. On the right is the Balmer series and the part of most interest for this experiment.

In 1885, the Swiss Physicist Johann Balmer, observed the emission spectrum of hydrogen in

the visible region of the electromagnetic spectrum. He deduced that the frequency of each

line was given by a formula. This formula related the energy levels that the electron in

question left, (n2) and decayed to, (n1). and included a constant. The formula was later refined

by Johannes Ryberg, for whom the constant was named.

2 21 2

1 1 1

HRn n

(1)

RH is the Rydberg constant for the H atom, is wavenumber and n1 and n2 are positive

integers (n1 < n2)

In this experiment, the different energy levels accessible to the electron in a hydrogen atom

are examined using a spectrometer. The wavelengths of the emission lines from a hydrogen

discharge lamp will be measured. From these, the values of the electronic energy levels can

be calculated, and by extrapolation, the ionisation energy of the hydrogen atom can be

determined. Modern spectrometers are made up of a fibre optic cable into a box with the

output to a computer.

Experimental

The spectroscopic method involved in this experiment involves exciting electrons within the

hydrogen atoms by means of an electrical discharge. Electrons are promoted to excited

states and then emit a photon as they fall back to lower states. When large numbers of atoms

undergo such transitions, the emission is of sufficient intensity for spectral lines to be

observed by eye. The discharge method is not very discriminating and so a large number of

different excited states are produced in the gas which gives rise to several series of lines.

The wavelengths of the spectral lines are measured using a spectrometer.

Calibration of the spectrometer

The first stage in a spectroscopic investigation typically involves an accurate calibration of

the spectrophotometer. Commercial instruments have a wavelength scale marked on

them, but it may not be sufficiently accurate for our purpose.

The calibration is obtained by comparing the measured wavelength of a set of emission

lines for which the wavelength is already precisely known, see table on results page.

The calibration for each instrument has previously been carried and you will be provided

with a value, , which describes the extent to which the spectrometer is inaccurate. This

has been calculated as the average of the difference between the observed wavelength

and true wavelength ( ( ) ( )true obs ) of lines in the Cadmium and Krypton sprecta.

To learn how to use the spectrometer and to check the calibration, measure the red line at

643.8 nm from the cadmium lamp - See instructions.

Remember that each spectrometer will have a different value of .

You will need to use the value of for your spectrometer to correct the readings that

you take in the experiment.

Emission lines from the H atom (Balmer series)

Set up the hydrogen discharge tube with its capillary section horizontal and just in front of

the spectrometer slit, see picture below. Switch it on. Set the wavelength drum to 650 nm

and adjust the vertical position of the spectrometer until brightest image is obtained.

The first and second Balmer lines are red and green; they are easily seen. The violet third

line is fainter and will be found at about 430 nm. Open the slit slightly if you have difficulty

in seeing the third line. Your eyes may need to be dark adapted for a few minutes. Take

two or three independent readings of the lines. You will not be able to see the fourth line,

which is at 410.2 nm.

Turn the hydrogen lamp off when finished.

Results - Write your results on the results page in this script.

Use your correction value to obtain the true wavelengths from your measured values

and then convert these to the corresponding wavenumbers.

Remember that wavelegth is in nanometers and wavenumber is in cm-1

/ / -1cm 1 1 nm = 1 10-9 m

Identify the transitions. In each case, we know that the lower energy level has a principal

quantum number n1 = 2. The lines must therefore correspond to transitions from higher

levels, with n2 = 3, 4 etc. Look back at the diagram of the hydrogen spectrum.

To help with the assignment, consider the following questions:

which transition in the Balmer series has the lowest energy change?

which of the observed lines corresponds to the lowest energy?

In this way, assign the principal quantum number n2 of the excited state to each of the

observed lines and enter the value of 1/ 22n in the final column in each case.

Plot a graph of against 1/ 22n using the computer and obtain the gradient and intercept

Gradient = ±

Intercept = ±

Equation 1 can be written in a straight line form;

2 2 2 21 2 1 2

1 1 1 1 1multiplying out gives

y = c m x

H H HR R R

n n n n

from the gradient: RH = ± cm-1

from the intercept: RH = ± cm-1

Mean value: RH = ± cm-1

Compare your result with the literature value: RH = 1.09677 105 cm-1

The Ionisation energy for a hydrogen atom is the energy required to remove the electron from

the ground state where n1 = 1 to the state corresponding to complete removal of the electron,

i.e. n =

Using your value of RH estimate the ionisation energy for the hydrogen atom from the

equation E = RH c h N A

where c = Speed of light = 2.998 108 m s-1

h = Planck’s constant = 6.62607 10-34 J s

NA = Avogadro’s constant = 6.02214 1023 mol1

Ionisation energy of the H atom = ± kJ mol1

Compare your result with the literature value: E = 1312 kJ mol-1

RESULTS SHEET

CALIBRATION

The true wavelengths for the calibration lines are given in the table:

Cadmium /nm Krypton /nm

red 643.8 yellow 587.0

green 508.6 green 557.0

blue 480.0

blue 467.8

violet 441.5

Average correction factor: = nm

HYDROGEN ATOM (Balmer series)

Colour (observed) /nm Mean (observed) /nm

RED

GREEN/BLUE

VIOLET

(true) /nm / -1cm n21

2

2n

RED

GREEN/BLUE

VIOLET

VIOLET 410.2

EXPERIMENT 2

Kinetics Of Hydrolysis Of Halogenoalkanes

The OBJECTIVES of this experiment are:

1. To follow the rate of hydrolysis of t-butyl chloride (2-chloro-2-methylpropane) using

conductivity measurements.

2. To determine the value of the rate constant for this reaction.

3. To determine the activation energy EA for this reaction.

BACKGROUND

Determination of the rates of reactions provides vital clues as to how a process is taking place

on molecular scale i.e. the reaction mechanism.

A classic illustration of how kinetics can provide evidence for a reaction

mechanism is given by the work of Sir Christopher Ingold, a Professor of

Organic Chemistry at Leeds between 1924 –1930. He suggested that

there were two possible mechanisms of nucleophilic substitution.

So, for example, primary haloalkanes react directly with the nucleophile

Y¯ (an SN2 process):

CH3CH2CH2X + Y¯ CH3CH2CH2Y + X¯

whereas tertiary haloalkanes form water-stabilised carbocations in a rate-determining step (an

SN1 process):

(CH3)3CX (CH3)3C+ + X¯

(CH3)3C+ + Y¯ (CH3)3CY

Hence the rate of an SN1 reaction is independent of the nucleophile concentration.

slow

In this experiment, you will follow the rate of hydrolysis of tertiary butyl chloride (t-BuCl) to give

an alcohol and hydrochloric acid:

3 2 3 33 3CH CCl 2H O CH COH H O Cl

As water plays the role of both nucleophile and solvent in this reaction, it is not possible to

distinguish between an SN1 and SN2 mechanism from changes in the nucleophile concentration.

However other evidence suggests that the reaction proceeds via two processes:

slow3 33 3

CH CCl CH C Cl (2)

fast3 2 3 33 3

CH C 2H O CH COH H O (3)

The reaction rate equation can be written as;

[ BuCl][ BuCl]

d tk t

dt

(4)

Integration of equation (4) to obtain the concentration [t-BuCl]t at any time t in terms of the initial

concentration [t-BuCl]0 and the rate coefficient k gives;

ln[t-BuCl]t = ln[t-BuCl]0 − kt (5)

The reaction will be monitored by measuring the change in conductivity G (in S m-1), which

is proportional to the concentration of the ions H+ and Cl−, as the hydrolysis proceeds. The

concentration of t-BuCl in time is given by:

BuCl tt G G (5)

where G∞ is the final conductivity. Thus a graph of1

ln

tG G

S mversus time will give a straight

line if the reaction is first order and the gradient will be -k.

The units of conductivity are included to make the log dimensionless.

Experimental

The reaction is carried out in a jacketed reaction vessel. The temperature is maintained by

water pumped through the jacket from a thermostatted water bath. The conductivity cell is a

pair of platinum black electrodes with electrical connections and an integrated thermometer.

Instructions for the use of the conductivity meters and computer data acquisition units are

provided with the apparatus.

Each pair of students will follow the variation of conductivity with time at two different

temperatures (20C or 30C and 35C or 40C): The rate constant values from the other

temperatures can be obtained from another group of students.

RunNumber

TargetTemperature/°C

Time of Run / mins Frequency of readings / s

1 20 20 20

2 30 10 10

3 35 5 1

4 40 5 1

If t-BuCl is added to water at room temperature, the reaction is too rapid to be followed by the

techniques available to us in this experiment. The reaction rate can be reduced by diluting the

water with a suitable organic solvent, 80/20 (v/v) water/acetone mixture is used in this

experiment.

Procedure

Read the additional instructions with each set of apparatus before starting the run.

Each run can be performed in any order.

Measure 100 cm3 of the 80/20 water / acetone reaction solvent and pour this into the reaction

vessel. Make sure the magnetic stirrer bar is rotating.

Note the temperature of the mixture. You should not begin your run until you are satisfied

that the temperature of the solvent has settled to a constant value.

Record the actual temperature to 0.1°C of your solvent at least 3 times during the run.

For runs 1 and 2, you will be using the data logger within the conductivity meter to record the

results.

For runs 3 and 4, a network connection will allow you to save all your work in a directory

(Z:) which will be accessible on any networked PC. Get the computer ready.

The reaction is started by introducing 1 cm3 of t-BuCl solution via the metered pipette into the

water/acetone solvent. Immediately start the data logger or acquisition unit.

The conductivity of the reaction mixture will increase with time.

For run 1, readings of conductivity will be logged every 20 s.

For run 2, readings of conductivity will be logged every 10 s.

For runs 3 and 4, the conductivity will be recorded at 1 second intervals and displayed via the

computer data acquisition unit.

When you have finished each run, raise the cell out of the vessel by pressing the clamp and

lifting. Wash the cell with deionised water. Carefully remove the reaction vessel from the

clamp and empty the waste into a plastic bowl. Rinse the vessel and stirrer bar with water,

clamp the reaction vessel in place so that it is clean and ready for the next user.

Dispose of the solvent into the waste solvent container under the fume cupboard.

RESULTS

Run __1__ Target temperature = 20°C Actual temperature /°C =

Time/ s

Conductivity/ S m-1

Time/ s

Conductivity/ S m-1

Time/ s

Conductivity/ S m-1

Time/ s

Conductivity/ S m-1

0 240 480 720

20 260 500 740

40 280 520 760

60 300 540 780

80 320 560 800

100 340 580 820

120 360 600 840

140 380 620 860

160 400 640 880

180 420 660 900

200 440 680

220 460 700 G

Run __2__ Target temperature = 30°C Actual temperature /°C =

Time/ s

Conductivity/ S m-1

Time/ s

Conductivity/ S m-1

Time/ s

Conductivity/ S m-1

Time/ s

Conductivity/ S m-1

0 130 260 390

10 140 270 400

20 150 280 410

30 160 290 420

40 170 300 430

50 180 310 440

60 190 320 450

70 200 330 460

80 210 340 470

90 220 350 480

100 230 360 490

110 240 370 500

120 250 380 G

Run __3__ Target temperature = 35°C Actual temperature /°C =

Filename _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Run __4__ Target temperature = 40°C Actual temperature /°C =

Filename _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

If you plot the raw data, i.e. conductivity against time, you should get graph 1.

Unfortunatly this does not give the rate of reaction so we need to do a little bit of maths on

the data. Conductivity values at time t = Gt. Conductance at the end of the run = G.

Take the Gt values away from the G value and then take the natural logarithm of these

values. This gives ln(G- Gt) for all the values of time. Only process the results where the

conductance is changing significantly, i.e. before it starts to level off. In graph 1 this is

~150 seconds.

For each of your runs, plot a graph of ln(G - Gt) versus time, see graph 2. This should give

a straight line if the reaction is first order and for which the gradient will be – k.

Graph 1 Graph 2

If your plots show any scatter at long times, see graph 2, replot your data using only the points

showing a linear relationship. This may give a slightly different result for the gradient and,

hence, the rate constant in each case.

Run Actual Temperature/C T/K k/s-1

1 or 2

3 or 4

You should get to this point.

We can now show by looking at the values of k for the whole group that as the temperature

increases, the rate of reaction also increases.

The results can then be used in the next part to determine the activation energy of the reaction.

Your School can do this bit with you at a later date.

0 100 200 300 400 500 600 700 800 900 10000.0

0.1

0.2

0.3

0.4

0.5

0.6

Co

nd

uct

an

ce/

-1

Time / seconds

Gt values

G value

Co

ndu

ctiv

ity

/m

Sm

-1

Time / s0 50 100 150 200 250

-5

-4

-3

-2

-1

0

ln(G

-

Gt)

Time / seconds

Do not includethese points whencalculating gradient

Plot of ln(G

- Gt) against Time/s

for run 2 at 30.1°C

Gradient = rate constant = -k / s-1

Activation Energy

The final part of the experiment involves determining the activation energy from the rate

constants. The activation energy, Ea - is the minimum kinetic energy required for a collision to

result in reaction.

The Arrhenius equation expresses how rates of chemical reaction vary with temperature.

k = A exp (-Ea/RT) where Ea is the activation energy, A is the pre-exponential factor

R is the gas constant, T is temperature.

Transformation of the Arrhenius equation into a form that can be used to obtain Ea and A from

the gradient and intercept of a straight-line plot gives;

aa

E 1ln k = ln A - E / RT which is the same as ln k = ln A -

R T

y = c m x

You have obtained values of the rate constant at two temperatures and should obtain values

at the other temperatures from another group of students.

A graph of ln k versus 1/T (where T is in Kelvin) should be a straight line with

gradient = -Ea/R and intercept= ln A.

Complete the following table:

Run T / K k / s-1 T-1/K-1 ln(k / s-1)

From the plot, calculate the activation energy Ea.

where R = Gas Constant = 8.314 J K-1 mol-1

Ea / kJ mol-1

Compare your result with the literature value: Ea = ≈ 80 kJ mol-1