Page 203 - Physical chemistry understanding our chemical world

170 REACTION SPONTANEITY AND THE DIRECTION OF THERMODYNAMIC CHANGE

so
G 1
G 2 /T 2 T 2
= H (4.72)
T T
G 1 /T 1 T 1
So, for a single chemical:

G 2 G 1 1 1
− = H − (4.73)
T 2 T 1 T 2 T 1
And, for a chemical reaction we have Equation (4.62):

G 2 G 1 1 1
− = H −
T 2 T 1 T 2 T 1
We call this final equation the Gibbs–Helmholtz equation.

At what temperature will the egg start to denature?

Reactions ‘poised’ at the critical temperature

If G goes from positive to negative as the temperature alters,
O
Care: the nomenclature then clearly the value of G will transiently be zero at one unique
O
T (critical) is employed temperature. At this ‘point of reaction spontaneity’, the value of
in many other areas O
of physical chemistry G = 0. We often call this the ‘critical temperature’ T (critical) .
(e.g. see pp. 50 and The value of T (critical) , i.e. the temperature when the reaction first
189). becomes thermodynamically feasible, can be determined approxi-
mately from
H
The reaction is ‘poised’ T (critical) = S (4.74)
at the critical tempera-
ture with G = 0.
Worked Example 4.13 At what temperature is the denaturation of
egg albumen ‘poised’?

We will employ the thermodynamic data from Worked Example 4.12. Inserting
values into Equation (4.74):

This method yields only H 35 000 J mol −1
◦
an approximate value T (critical) = = −1 −1 = 356 K or 83 C
of T (critical) because S S 98.3J K mol
and H are themselves
functions of tempera- We deduce that an egg will start denaturing above about T =
◦
ture. 83 C, confirming what every cook knows, that an egg cooks in
boiling water but not in water that is merely ‘hot’.