i. demethe liquid phase1 9a. the liquid phase liquids and solids (condensed phases) are formed by...

I. Deme The liquid phase 1

9A. The Liquid Phase

Liquids and solids (condensed phases) are formed by many atoms, ions, or molecules held closely together.

In liquids the particles (atoms, ions, or molecules) can move freely but remain adjacent to the other particles.

In solids not only are the particles adjacent, but the motion of the particles is limited.

In gases the particles move freely and independently; that is, without attaching to other particles.


Comparison of the phases


The atoms, ions, or molecules are held together by intermolecular forces. All these forces are based on the attraction of a positive charge to a negative charge. The magnitude of the lattice energy (U) is expressed by Coulomb's law

U = k (Q1Q2 / d) [J] Q is the charge of ions,

d is the distance between the nuclei, k is a proportionality constant.

9.1. Intermolecular forces


The strongest intermolecular force is ion-ion attraction. This is the intermolecular force in ionic compounds (salts). The force is stronger for ions with higher charges (greater Q) or with smaller distances (d) between ions. d depends on the size of the ions and the arrangement of ions, known as the lattice structure. Substances with ionic forces of attraction exist in the solid state at room temperature.


Polar molecules have partial charges and are held to each other by dipole-dipole forces. Because these are only partial charges, unlike the full charges of ions, these forces are much weaker. Thus substances with dipole-dipole forces of attraction tend to be gases (occasionally liquids) at room temperature.


When ionic compounds are mixed with polar compounds, they may dissolve. The many small dipoles of the solvent may be more attractive than the other ions of the salt, creating ion-dipole forces.

Dissolution will only occur if the ion-ion attraction is sufficiently weak and the ion-dipole forces are sufficiently strong. Because there is both a full and a partial charge in ion-dipole forces, these forces are stronger than dipole-dipole forces, but not as strong as ion-ion forces.

Another special case of dipole-dipole forces is hydrogen bonding. Hydrogen bonds occur between molecules that have a hydrogen covalently bonded with an oxygen, nitrogen, or fluorine atom. O, N, and F are the most electronegative atoms, which therefore attract most of the electrons of the covalent bond. When the other end of that covalent bond is a hydrogen, the electronegative atom is pulling all electrons associated with H away from it and H acts almost as a positive charge. This high charge makes hydrogen bonds a very strong type of dipole-dipole force. Substances which hydrogen bond are typically liquids at room temperature.


Nonpolar molecules are attracted to each other by temporary dipoles, which are called London or dispersion forces. Deforming the electron clouds surrounding the molecules creates temporary dipoles. With more electrons the electron cloud is more easily and more greatly deformed; thus the dipoles are larger and the attraction greater. Molecules with easily deformed electron clouds are called polarizable.Molecules with London forces are normally gases at room temperature.

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9.2. Solubility and miscibility

Forces of attraction determine the solubility of substances. The forces between the solute and solvent must be stronger than the solute-solute and the solvent-solvent interactions for a substance to be soluble. Polar substances dissolve in polar solvents and nonpolar substances dissolve in nonpolar solvents. In the case of ionic compounds, the solute-solvent forces can overcome the ion-ion forces since there are usually many more solvent molecules than solute molecules (the weaker ion-dipole forces can sometimes overcome the ion-ion forces). When water is the solvent, six waters typically surround each ion (sphere of hydration). When two liquids dissolve in each other in all proportions, they are called miscible.


Forces of attraction can be overcome by increasing temperature and thus the kinetic energy (movement) of the particles. When the temperature is sufficient to overcome some of the attraction, solids will melt. That temperature is called the melting point. (= freezing point)The stronger the force of attraction, the higher the melting point.

Kinetic energy allows particles on the surface of a liquid to escape the attractive forces and become a vapor. When the number of particles escaping the liquid and the number of particles being captured by the liquid are the same, the system is in equilibrium. The pressure of the gaseous particles in such a system is called the vapor pressure.The vapor pressure depends on the attractive forces and temperature. Substances with stronger attractive forces have lower vapor pressures. An increase in temperature increases the vapor pressure. When the vapor pressure reaches the atmospheric pressure, any molecule can escape the liquid and the liquid boils. This temperature is called the boiling point.

9.3. Vapor pressure, freezing and boiling

Vapor pressure of solutions: is always smaller than that of the pure solvent.

Raoult’s law:

For ideal solutions of substances of negligible vapor pressure


9.4. Colligative properties: Solution properties that are affected by the amount (number of moles) of solute and not the identity of the solute.

Osmotic pressure


Boiling point elevation

Freezing point depression

T b= Kb m

T b= i Kb m

T f = Kf m

T f = i Kf m

For non-ionizing solutes (like alcohols, sugars, etc)

For ionizing solutes (salts):

m : molality (mol solute per kg solvent)i : van’t Hoff factor (mol ions from 1 mole solute)Kb: ebullioscopic constant, characteristic of the solvent

For non-ionizing solutes (like alcohols, sugars, etc)

For ionizing solutes (salts):

m : molality (mol solute per kg solvent)i : van’t Hoff factor (mol ions from 1 mole solute)Kb: cryoscopic constant, characteristic of the solvent

Add saltAdd saltAdd salt

Add saltAdd salt


The van’t Hoff factor:

Because ions often associate with each other in solution, forming ion pairs, the true van't Hoff factor is often less than its theoretical value. True van't Hoff factors can be calculated from any of the colligative properties, by adding the van't Hoff factor i to the equation. (e.g., T = iKm). If the van't Hoff factor is used in the equation, the concentration refers to the moles of overall solute rather than to moles of particles.

ps = ps* xs = ps* (1-x)

x = n / (n+ns) n / ns = (mM(msMs)

Where s subscript denotes solvent no subscript denotes solute * superscript denotes pure solventm: massn: mol numberM: molar mass

ps, Tb and Tf are related to the molecular mass of the dissolved material

1+/2-

Tf Tb

p

solid

solvent

solution

9.5. Surface phenomena:

Surface tension

The steel needle is floating on the surface of water

= F / 4 R [N/m] or [J/m2]

Surface tension:

Temperature dependence of surface tension -the Eötvös rule:

Vm2/3 = k (Tcr – 6 – T)

when T = Tcr - 6 , = 0

Vm : molar volumeVm

2/3 : molar surface Vm

2/3: energy of molar surfacek [J K-1 mol 2/3]Tcr . Critical temperature

k=2.0-2.2 x10-7 for several liquids

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Surface tension is the resistance of a liquid to increase its surface area. It is higher with stronger attractive forces and weaker at higher temperatures.The attraction of the substance to the wall of a container is called the adhesive force, and the attraction of the substance to itself is called the cohesive force. When the adhesive forces are stronger than the cohesive forces, the substance creeps up the sides of the container, forming a curved surface called a meniscus. In capillaries, there is sufficient wall that the substance actually climbs the walls of the capillary until gravity overcomes the adhesive forces. The rising of a liquid up a capillary tube is called capillary action.

.

Meniscus risen to height h isin equilibrium with the originalliquid if its vapor pressure (ph) is:

ph = p0 exp [ gh Vm / RT] == p0 exp [ LVcosVm/ r RT]

From the force equilibrium for perfectly wetting liquid: 2r LV = r2gh h = 2LV g r

Vm: molar volume of the liquid : density of liquidr : radius of meniscus curvature • radius of capillary for convex menisci• -1 times radius of capillary for concave menisciLV : surface (interfacial) tension of liquid : contact angle of the liquid wit the capillary wall

h > 0 h < 0

h

r : radius of capillary

Extra vapor pressure above curved surfaces relative to flat ones:capillary pressure = p = 2cos/r , where 1/r is the curvature


Wetting

Solid

Vapor

SVSL

LV

Young’s equation: SV = SL + LV (cos ) where is the contact angle

S = SV - SL - LV Spreading coefficient:

Condition of complete wetting: S >=

Adhesion:

When surfaces of condensed phases (SV, SL)get into contact the energy of the new surface (SL)is always lower than the sum of those of thedisappearing surfaces.The energy liberated:

Wa = - SV - LV + SL <= 0 [J m-2]

Immersion wetting:

When a powder is mixed with a wetting (<90o)liquid the heat of wetting (Qw) is lower than Wa as the voids (LV surfaces) for the solid needs to be created:

Qw = Wa + LV = - SV + SL

SV

LV SL


Adsorption Concentration of some species in the interfacial layer changesrelative to the bulk phase

Gibbs equation: = - (c / RT) d/ dc

surface excess concentration of a species in the surface layer relative to the same surface are chosen in the bulk liquid [mol/m2]

c : volume concentration of the species in questiond/ dc: rate of change of surface tension with concentration of the dissolved material

Those materials accumulate in the liquid/vapor interface that decrease surface tension of the liquid (positive adsorption, ie.d/ dc < 0). These are called surface (capillary) active.The ones that increase surface tension suffer negative adsorption (surface concentration is smaller than at the same area taken at the bulk liquid).

Surfactants are themost important capillary active substances

c

solvent

Capillary active

Capillary inactive


9.6. Viscosity: The resistence of materials to flow (transport of momentum)Newton’s law: = dV/dH = d(D/H) / dt

: shear stress = F/A [Pa]dV/dH : shear rate = d(D/H) / dt = velocity gradient [s-1]viscosity = constant [Pa.s]D/H : shear (deformation)

Non-newtonian fluids: is not constant constant and/or there is a yield stress (y

a. power law (pseudoplastic) = m (dV/dH)n (n<=1)b. plastic (Bingham) = y + (dV/dH)c. combined (shear thinning) = y + m’ (dV/dH)n (n<=1)d. dilatant – shear thickening

Thixotropy: time dependent viscosity at constant shear rate

t

Temperature dependence

Liquids = A exp [B/T] number and size of voids increase with T

Gases: = C T1/2 number of collisions increases with T

Shear rate

Shear stress

Yield stress

newtonian

a

bcd

i. demethe liquid phase1 9a. the liquid phase liquids and solids (condensed phases) are formed by...

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