Page 233 - Physical chemistry understanding our chemical world

200 PHASE EQUILIBRIA

The normal boiling point of water
Applied pressure p p Solid Liquid Pressure p O 2
O

p
T
100 °C
Gas Temperature 2
100 °C
Temperature T
Figure 5.12 Phase diagram to show how a pressure cooker works. Inset: applying a high pressure
◦
from p O to p 2 causes the boiling temperature of the water to increase from temperature 100 C
to T 2

shows why the water inside the pressure cooker boils at a higher temperature as a
consequence of the pan’s large internal pressure.
Having qualitatively discussed the way a pressure cooker facil-
The Clausius–Clapey- itates rapid cooking, we now turn to a quantitative discussion.
ron equation quantifies The Clapeyron equation, Equation (5.1), would lead us to suppose
the way a boiling tem- that dp ∝ dT , but the liquid–gas phase boundary in Figure 5.12
perature changes as a is clearly curved, implying deviations from the equation. There-
function of the applied fore, we require a new version of the Clapeyron equation, adapted
pressure. At the boil- to cope with the large volume change of a gas. To this end, we
ing points of T 1 and introduce the Clausius–Clapeyron equation:
T 2 , the external pres-
sures p 1 and p 2 are the
O
same as the respective p 2 at T 2 H (boil) 1 1
ln =− − (5.5)
vapour pressures.
p 1 at T 1 R T 2 T 1
where R is the familiar gas constant, and H O is the enthalpy
(boil)
O
of vaporization. H (boil) is always positive because energy must be
It does not matter put in to a liquid if it is to boil. T 2 here is the boiling temperature
which of the values we
choose as ‘1’ and when the applied pressure is p 2 , whereas changing the pressure to
p 1 will cause the liquid to boil at a different temperature, T 1 .
‘2’ provided that T 1
We need to understand that the Clausius–Clapeyron equation is
relates to p 1 and T 2
relates to p 2 .It isper- really just a special case of the Clapeyron equation, and relates to
phase changes in which one of the phases is a gas.
missible to swap T 1
for T 2 and p 1 for p 2
simultaneously, which
Worked Example 5.2 What is the boiling temperature of pure water
amounts to multiply- inside a pressure cooker? Let T 1 be the normal boiling temperature
ing both sides of the ◦
O
T (boil) of water (i.e. 100 C, 373 K, at p )and let p 2 of 6 × p be the
O
equation by ‘−1’. −1
pressure inside the pan. The enthalpy of boiling water is 50.0kJ mol .