1. Peter Atkins • Julio de Paula Atkins’ Physical Chemistry
Eighth Edition
Chapter 4 – Lecture 2
Physical Transformations
of Pure Substances
Copyright © 2006 by Peter Atkins and Julio de Paula

2. The effect of applied pressure on vapor pressure
Pressure applied to condensed phase squeezes molecules out of the liquid
Papplied ∝ Pvapor

3. Fig 4.11
Two methods of
applying pressure
to a condensed phase

4. The effect of applied pressure on vapor pressure
Pressure applied to condensed phase squeezes molecules out of the liquid
Assumptions:
Pressurizing gas does not change properties of the liquid
Gas solvation does not occur
Papplied ∝ Pvapor
where P* = vapor pressure of liquid at 1 atm
ΔP = applied pressure

5. Water is subjected to an applied pressure of 10 bar.
At 25 °C, density = g/cm3, ∴ Vm = 18.1 cm3 mol-1.
Since VmΔP/RT << 1,
Or an increase of 0.73 %

6. Fig 4.12 P vs T plot for a system of two phases
When pressure is applied to
a system in a two-phase
equilibrium, the equilibrium is
disturbed
System can regain equilibrium
by changing temperature
i.e.,
Clapeyron eqn

7. Location of Phase Boundaries
For two phases α and β in equilibrium:
μα(P,T) = μβ(P,T)
Phase boundaries most simply discussed
in terms of their slopes, dP/dT
The solid-liquid boundary:
which approximates to:

8. Fig 4.13 Typical solid-liquid phase boundary
(P2, T) ●
●(P1,T)

9. Location of Phase Boundaries
The liquid-vapor boundary
with PV = RT becomes
and finally:
Clausius-Clapeyron eqn

10. Fig 4.14 Typical liquid-vapor phase boundary
(T, P2) ●
(T1, P) ●
●(T2, P)
●(T, P1)

11. Clausius-Clapeyron Equation
Molar heat of vaporization (DHvap) ≡ the energy required to vaporize 1.00 mole of a liquid
ln P = −
DHvap RT
+ C
Clausius-Clapeyron Equation
P = (equilibrium) vapor pressure
T = temperature (K)
R = gas constant (8.314 J/K•mol)
m = −DHvap/R
ln P
1/T

12. Clausius-Clapeyron Equation
ln P1 = −
DHvap
RT1
+ C
ln P2 = −
DHvap
RT2
+ C
m = −DHvap/R
ln P
1/T

13. Fig 4.15 Typical triple point
ΔHsub > ΔHvap