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THERMODYNAMICS AND THE EXTENT OF REACTION 163

+
+ H 3 O . This reaction has an equilibrium constant K of about 2 ×
10 −5 at room temperature (298 K) when formulated in the usual units The correct use of the
−3 van’t Hoff isotherm
of concentration (mol dm ). What is the associated change in Gibbs
function of this reaction? necessitates using the
thermodynamic tem-
perature (expressed
in kelvin).
Inserting values into the van’t Hoff isotherm (Equation (4.55)):
−5
O
G =−8.314 J K −1 mol −1 × 298 K × ln(2 × 10 )
O
G =−2478 J mol −1 ×−10.8 A process occurring
with a negative value
−1
O
G =+26 811 J mol
of G is said to be
exogenic. A process
so
occurring with a posi-
O
G =+26.8 kJ mol −1 tive value of G is said
to be endogenic.
O
Note how G is positive here. We say it is endogenic.
Justification Box 4.6

We start with Equation (4.49):

O
G = G + RT ln Q
At equilibrium, the value of G is zero. Also, the value of Q is called K:

O
0 = G + RT ln K (4.56)
Subtracting the ‘−RT ln K’ term from both sides yields the van’t Hoff isotherm
(Equation (4.55)):
O
G =−RT ln K
O
This derivation proves that equilibrium constants do exist. The value of G depends
on T , so the value of K should be independent of the total pressure.

O
We sometimes want to know the value of K from a value of G , in which case
we employ a rearranged form of the isotherm:

− G O
K = exp (4.57)
RT
so a small change in the Gibbs function means a small value of K. Therefore, a weak
acid is weak simply because G is small.
O