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THE EFFECT OF TEMPERATURE ON THERMODYNAMIC VARIABLES 171

SAQ 4.11 Water and carbon do not react at room temperature. Above
what temperature is it feasible to prepare synthesis gas (a mixture of CO
and H 2 )? The reaction is

C (s) + 2H 2 O (g) −−−→ CO (g) + H 2(g) (4.75)
O
Take H = 132 kJ mol −1 and S = 134 J K −1 mol −1 .
O

Justification Box 4.9

We start with Equation (4.21):

O
G = 0 = H − T S
When just ‘poised’, the value of G is equal to zero. Accordingly, 0 = H = T S.
O
Rearranging slightly, we obtain

H = T S (4.76)

which, after dividing both sides by ‘ S’, yields Equation (4.74).

Why does recrystallization work?

The effect of temperature on K: the van’t Hoff isochore

To purify a freshly prepared sample, the preparative chemist will crystallize then
recrystallize the compound until convinced it is pure. To recrystallize, we first dissolve
the compound in hot solvent. The solubility s of the compound depends on the
temperature T . The value of s is high at high temperature, but it decreases at lower
temperatures until the solubility limit is first reached and then surpassed, and solute
precipitates from solution (hopefully) to yield crystals.
The solubility s relates to a special equilibrium constant we call
We say the value of
the ‘solubility product’ K s , defined by
[solute] (s) = 1because
its activity is unity; see
K s = [solute] (solution) (4.77)
Section 7.3.
The [solute] term may, in fact, comprise several component parts
if the solute is ionic, or precipitation involves agglomeration. This
The word ‘isochore’
equilibrium constant is not written as a fraction because the ‘effec- implies constant pres-
tive concentration’ of the undissolved solute [solute] (s) can be taken sure, since iso is Greek
to be unity. for ‘same’ and the root
Like all equilibrium constants, the magnitude of the equilibrium chore means pressure.
constant K s depends quite strongly on temperature, according to