Third Year Chemistry
•2nd semester: Physical (2007-2008)
•May exams
•Physical: 4 lecturers 8 topics
•Dónal Leech: one topic
•Thermodynamics
•Mixtures and phase diagrams
1
Phase Equilibria
Phase transitions
Changes in phase without a change in chemical composition
Gibbs Energy is at the centre of the discussion of transitions
Molar Gibbs energy
Gm = G/n
Depends on the phase of the substance
A substance has a spontaneous tendency to change into a phase
with the lowest molar Gibbs energy
2
Variation of G with pressure




We can derive (see
derivation 5.1 in textbook)
that DGm = VmDp
Therefore DGm>0 when
Dp>0
Can usually ignore
pressure dependence of G
for condensed states
Can derive that, for a gas:
DGm = RT ln(pf/pi)
3
To be presented in Lecture
4
Variation of G with temperature
DGm = -SmDT
Can help us to understand why transitions occur
The transition temperature is the temperature when the
molar Gibbs energy of the two phases are equal.
The two phases are in EQUILIBIRIUM at this temperature
5
Phase diagrams


6
Map showing conditions
of T and p at which
various phases are
thermodynamically
stable
At any point on the
phase boundaries, the
phases are in dynamic
equilibrium
Location of phase boundaries

Clapeyron equation (see derivation 5.4)
D trsH
Dp 
DT
TD trsV

Clausius-Clapeyron equation
(derivation 5.5)
D ln p  
D vap H
RT
2
DT
D vap H  1 1 
    constant
ln p2  ln p1 
R  T2 T1 
7
Constant is
DvapS/R
Derivations
dGm = Vmdp – SmdT
dGm(1) = dGm(2)
Vm(1)dp – Sm(1)dT = Vm(2)dp – Sm(2)dT
{Vm(2) – Vm(1)}dp = {Sm(2) – Sm(1)}dT
DtrsV dp = DtrsS dT
T DtrsV dp = DtrsH dT
dp/dT = DtrsH/(T DtrsV)
8
Derivations: liquid-vapour transitions
l
9
To be presented in lecture
Characteristic points
When vapour pressure is equal to external pressure bubbles
form: boiling point
Normal bp: 1 atm, Standard bp: 1 bar
 When a liquid is heated in a closed vessel the liquid density
eventually becomes equal to the vapour density: a
supercritical fluid is formed.

10
Using the C-C equation
The vapour pressure of mercury is 160 mPa at 20°C.
What is its vapour pressure at 50°C given that its
enthalpy of vapourisation is 59.3 kJ/mol?
 The vapour pressure of pyridine is 50.0 kPa at 365.7 K
and the normal boiling point is 388.4 K. What is the
enthalpy of vapourisation of pyridine?
 Estimate the normal and standard boiling point of
benzene given that its vapour pressure is 20.0kPa at
35°C and 50.0kPa at 58.8°C.
Remember:
 BP: temperature at which the vapour pressure of the
liquid is equal to the prevailing atmospheric pressure.
 At 1atm pressure: Normal Boiling Point (100°C for water)
 At 1bar pressure: Standard Boiling Point (99.6°C for
water; 1bar=0.987atm, 1atm = 1.01325bar)

11
Phase Rule


Can more than 3 phases co-exist (for a
single substance)?
Gibbs energies are equal:
Gm(1)=Gm (2) Gm(2)=Gm(3) Gm(3)=Gm(4)
All a function of p and T. Need to solve 3
equations for 2 unknowns: impossible!
Phase rule
F = C-P+2
12
CO2
Dry ice fog-special effects
Supercritical fluids
Caffeine extraction from coffee beans
Dry-cleaning
Polymerisations
Chromatography
13
Water
Ice I structure
 Solid-liquid boundary
slopes to the left with
increasing pressure
volume decreases when
ice melts, liquid is denser
that solid at 273 K
14
Introduction to mixtures


Homogeneous mixtures of a
solvent (major component) and
solute (minor component).
Introduce partial molar property:
contribution that a substance makes
to overall property.
V = nAVA + nBVB
Note: can be negative, if adding solute to solvent results in
decrease in total volume (eg MgSO4 in water)
15
The chemical potential, m

We can extend the concept of partial molar
properties to state functions, such as Gibbs
energy, G.
G = nAGA + nBGB

This is so important that it is given a special
name and symbol, the chemical potential, m.
G = nAmA + nBmB
16
The chemical potential of perfect
gases in a mixture
Recall that
Gm(pf) = Gm(pi) + RT ln (pf/pi)
At standard pressure
Gm(p) = Gm° + RT ln (p/p°)
Therefore, for a mixture of gases
mJ = mJ° + RT ln (pJ/p°)
More simply (at p° = 1 bar)
System is at equilibrium when m
for each substance has the same value
mJ = mJ° + RT ln pJ
in every phase
17
Spontaneous mixing
to be presented in lecture
18
Gas mixtures
Perfect gases mix spontaneously in all proportions
Compare
DGmix = nRT {xAln xA+ xB ln xB}
DG = DH – TDS
Therefore
DH = 0
DSmix = − nR {xAln xA+ xB ln xB}
19
Ideal Liquid Solutions
Raoult’s Law
pJ = xJpJ*
Due to effect of solute on
entropy of solution
20
Real Solutions
21
Chemical potential of a solvent

At equilibrium mA(g) = mA(l)
mA(l)= mA°(g) + RT ln pA
mA(l)= mA°(g) + RT ln xApA*
mA(l)= mA°(g) + RT ln pA* + RT ln
xA
└────────────────┘
mA*

mA(l)= mA*+ RT ln xA
22
Is solution formation
spontaneous?
G = nAmA + nBmB
Can show that
DGmix = nRT {xAln xA+ xB ln xB}
and
DH = 0
DSmix = −nR {xAln xA+ xB ln xB}
23
Ideal-dilute solutions


Raoult’s law generally describes well solvent vapour pressure
when solution is dilute, but not the solute vapour pressure
Experimentally found (by Henry) that vp of solute is
proportional to its mole fraction, but proportionality constant is
not the vp of pure solute.
Henry’s Law
pB = xBKB
24
Gas solubility
Henry’s law constants for gases dissolved in water at 25°C
KH/(kPa m mol )
3
Ammonia, NH3
5.69
Carbon dioxide, CO2
2.937
Helium, He
282.7
Hydrogen, H2
121.2
Methane, CH4
67.4
Nitrogen, N2
Oxygen, O2
1
155
74.68
Concentration of 4 mg/L of oxygen is required to support
aquatic life, what partial pressure of oxygen can achieve this?
25
Application-diving
Gas narcosis caused by nitrogen in normal air dissolving into nervous tissue
during dives of more than 120 feet [35 m]
Pain due to expanding or contracting trapped gases, potentially leading to
Barotrauma. Can occur either during ascent or descent, but are potentially
most severe when gases are expanding.
Decompression sickness due to evolution of inert gas bubbles.
Table 1
Increasing severity of nitrogen narcosis symptoms with depth in feet and pressures in
atmospheres.
26
Depth
P Total
P N2
Symptoms
100
4.0
3.0
Reasoning measurably slowed.
150
5.5
4.3
Joviality; reflexes slowed; idea fixation.
200
7.1
5.5
Euphoria; impaired concentration;
drowsiness.
250
8.3
6.4
Mental confusion; inaccurate
observations.
300
10.
7.9
Stupefaction; loss of perceptual faculties.
Real Solutions-Activities
mJ = mJ° + RT ln aJ
Substance
Standard state
Activity, a
Solid
Pure solid, 1 bar
1
Liquid
Pure liquid, 1 bar
1
Gas
Pure gas, 1 bar
p/po
Solute
Molar concentration of
1 mol dm
3
[J]/co
po  1 bar ( 105 Pa), co  1 mol dm3.
* Activities are for perfect gases and ideal-dilute solutions; all activities are dimensionless.
27
Colligative properties
Properties of solutions that are a result of changes in the
disorder of the solvent, and rely only on the number of
solute particles present
Lowering of vp of pure liquid is
one colligative property
Freezing point depression
Boiling point elevation
Osmotic pressure
28
Colligative properties



Chemical potential of a solution (but
not vapour or solid) decreases by a
factor (RTlnxA) in the presence of
solute
Molecular interpretation is based on
an enhanced molecular randomness
of the solution
Get empirical relationship for FP and
BP (related to enthalpies of transition)
DT f  K f m
DTb  K b m
29
Cryoscopic and ebullioscopic constants
Solvent
1
Kb/(K kg mol )
1
Acetic acid
3.90
3.07
Benzene
5.12
2.53
Camphor
40
Carbon disulfide
3.8
2.37
Naphthalene
6.94
5.8
Phenol
7.27
3.04
Tetrachloromethane
Water
30
Kf/(K kg mol )
30
1.86
4.95
0.51
Osmotic pressure
Van’t Hoff equation
  MRT
31
Phase diagrams of mixtures
We will focus on twocomponent systems
(F = 4 ─ P), at constant
pressure of 1 atm
(F’ = 3 ─ P), depicted
as temperaturecomposition diagrams.
32
Fractional Distillation-volatile liquids
Important in oil refining
33
Exceptions-azeotropes
Azeotrope: boiling without changing
High-boiling
and
Low-boiling
Favourable interactions between
components reduce vp of mixture
Trichloromethane/propanone
HCl/water (max at 80% water, 108.6°C)
34
Unfavourable interactions between
components increase vp of mixture
Ethanol/water (min at 4% water, 78°C)
Liquid-Liquid (partially miscible)



Hexane/nitrobenzene as example
Relative abundances in 2 phases
given by Lever Rule
n’l’ = n’’l’’
Upper critical Temperature is limit
at which phase separation occurs.
In thermodynamic terms the Gibbs
energy of mixing becomes negative
above this temperature
35
Other examples
Water/triethylamine
Weak complex at low temperature
disrupted at higher T.
36
Nicotine/water
Weak complex at low temperature
disrupted at higher T. Thermal motion
homogenizes mixture again at higher T.
Liquid-solid phase diagrams
37