Page 173 - Physical chemistry understanding our chemical world

140 REACTION SPONTANEITY AND THE DIRECTION OF THERMODYNAMIC CHANGE

Sections 3.1 and 3.2 describe heat capacity and explain how it
The heat capacity
C p(ice) = 39 J K −1 mol −1 may be determined at constant pressure C p or at constant volume
tells us that adding 39 J C V . Most chemists need to make calculations with C p , which repre-
of energy increases the sents the amount of energy (in the form of heat) that can be stored
temperature of 1 mol within a substance – the measurement having been performed at
of water by 1 K. constant pressure p. For example, the heat capacity of solid water
−1
(ice) is 39 J K −1 mol . The value of C p for liquid water is higher,
−1
at 75 J K −1 mol , so we store more energy in liquid water than when it is solid;
stated another way, we need to add more energy to H 2 O (l) if its temperature is to
−1
increase. C p for steam (H 2 O (g) ) is 34 J K −1 mol . C p for solid sucrose (II) – a major
−1
component of any jam – is significantly higher at 425 J K −1 mol .

OH
H
H
OH O
OH H
H OH

CH 2 OH O

H OH
H CH 2 OH

OH H
(II)

The heat capacity of a liquid is always greater than the heat capacity of the respec-
tive solid because the liquid, having a greater amount of energetic disorder, has a
greater entropy according to

T 2

C p
S = S 2 − S 1 = dT (4.9)
T
T 1
More energy is ‘stored’ within a liquid than in its respective solid, as gauged by
the relative values of C p implied by the connection between the heat capacity and
entropy S (of a pure material). This is to be expected from everyday experience:
to continue with our simplistic example, when a freshly baked jam tart is removed
from the oven, the jam burns the mouth and not the pastry, because the (liquid)
jam holds much more energy, i.e. has a higher C p than does the solid pastry, even
though the two are at the same temperature. The jam, in cooling to the same tem-
perature as the tongue, gives out more energy. The tongue cannot absorb all of this
energy; the energy that is not absorbed causes other processes in the mouth, and hence
the burn.