Lecture 4 Physical Equilibria
Text Chapter 8
Vapor Pressure is the partial pressure of the vapor when it is in dynamic
equilibrium with the liquid.
X(l)
X(g)
²H vap Molar enthalpy of
vaporization
X(g)
X(l)
–²H vap
X(l)
X(g)
When allowed to come to Equilibrium
X(g)
Equilibrium when:
rate of vaporization
equals
rate of condensation
X(l)
ΔG = 0 at equilibrium
ΔGo “standard state” ≡ 1atm (vapors), 1M (solutions), any one temperature
boiling point  T where Pvap = Pexternal
melting point  T where Pvap(sol) = Pvap(liq)
normal boiling point  T where Pvap = 1 atm
normal m.p.  melting point at 1 atm.
For vaporization at any one temperature: ΔG = 0 = ΔGo + RT∙lnP
ΔGo = -RT∙lnP
lnP = -ΔGo / RT = -[ΔHo – TΔSo]/RT
To find vapor pressure at different temperatures:
ln(P2/P1) = -[ΔHo/R]∙[1/T2 – 1/T1]
ln(P2/P1) = [ΔHo/R]∙[1/T1 – 1/T2]
Self-tests 8.1,2
Phase Diagrams
Temperature (oC)
Typical substance
Water
Critical Temperature – the highest temperature at which a substance can exist as a
liquid.
Triple point - temperature and pressure where solid, liquid, and gas are in
equilibrium.
The Solution Process
Solute - solvent
Understood in terms of balance between forces of attraction
Solute…Solute + Solvent…Solvent <=> Solute…Solvent ΔH, ΔS
Heats of Solution
exothermic
ex. NaOH
endothermic
ex. NH4NO3 KCl
energy of solvation interactions vs. lattice energy (forces holding solid together)
separated separated
solvent + solute
particles
particles
separated separated
solvent + solute
particles
particles
² H2
² H2
separated
Solvent + solute
particles
separated
Solvent + solute
particles
² H3
² H1
² H1
Solvent + solute
Net
Exothermic
Process
² H3
Solution
² Hsoln
Solution
Net
Endothermic
Process
² Hsoln
Solvent + solute
 Processes in which the energy content of the system decreases tend to occur
spontaneously.
 Processes in which the disorder of the system increases tend to occur
spontaneously.
 Formation of solutions is favored by the increase in disorder that accompanies
mixing.
Solubility
saturation - solution in equilibrium with undissolved solid.
NaCl (s) in equilibrium with Na+(aq) and Cl-(aq)
dissolve
Solute + Solvent
Solution
crystallize
1) Liquids in liquids
The stronger the attractions between solute and solvent molecules, the greater the
solubility.
miscible vs. immiscible
miscible
polar-polar (water-ethanol)
nonpolar-nonpolar
immiscible polar-nonpolar (water-oil)
2) Solids in liquids
yes:
in water - salts, sugar
in benzene - (nonpolar) naphthalene
no:
naphthalene will not dissolve in water
sugar will not dissolve in benzene
Substances with similar intermolecular attractive forces tend to be soluble in one
another; "like dissolves like"
3) Gases in liquids
a) Pressure Effects
Henry's Law, the solubility of the gas increases in direct proportion to its partial
pressure above the solution.
Cg  kPg
Cg is solubility of gas
k is Henry’s law constant
Pg is partial pressure of gas
b) Temperature Effects
Most solid and liquid substances are more soluble in water at higher temperatures.
The solubility of gases in water decreases with increasing temperature.
(Thermal pollution of lakes and streams.)
Solution Composition
mole fraction, moles of species A divided by the total number moles
nA
nA  n B  nC ...
XA  nA ntot 
molarity moles of A per liter of solution
MA  n A V
molality, m, of species B equals the number of moles of B divided by the mass of
solvent, A, (kilograms of solvent)
mB 
nB
wA (kg)
weight percentage of species B,
wB w 100%
Colligative Properties (dependent on the number of solute particles, not the
identity)
Raoult's law
The vapor pressure of a solvent is proportional to its mole fraction in a solution.
PA  X A PA
solvent, A
Po ≡ vapor pressure of pure solvent
“involatile solute” in a solvent, solid solutes, have a vapor pressure that is
negligible.
This will not hold for liquid or gas solutes.
Self-tests 8.11
Boiling-Point Elevation
Tbp  Kbp msolute
Freezing Point Depression
T f  K fpmsolute
Ion Pairing (imperfect dissociation of ions in solution)
van't Hoff factor, i, (number of ions in salt)
dilution
charge on ions
Using change in bp or fp to find molar mass
•
Divide the change in temperature by the freezing point depression constant
or boiling point elevation constant. This should give the molality.
Tbp
Kbp
T fp
 msolute
K fp
 msolute
Use mass of solvent to determine the number of moles of solute
Divide mass of solute by moles of solute to find molar mass
Self-tests 8.12,13,14
Osmotic Pressure
There is a natural tendency for the solvent to pass from the pure solvent chamber
through the membrane into the solution chamber.
The excess pressure that must be applied to the solution to produce equilibrium is
known as osmotic pressure, .
n 
V 
  MRT   RT
-osmotic pressure
M - molar concentration of solute
R - gas constant (0.082057 L amt/mol K)
T - temperature in Kelvins
Using osmotic pressure
Divide osmotic pressure by RT to find concentration

 CB
RT
Self-tests 8.15
Using vapor pressure
Divide lowered pressure by pressure of pure solvent to determine mole fraction of
solvent, XA. Find mole fraction of solute by 1-XA=XB.
Colloids
Particles that are large on the molecular scales but are still small enough to remain
suspended indefinitely in a solvent system.
 scatter light
 high molecular weight
 high surface area