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Section 11.9
T S°
Gibbs Energy Change for a Reaction
de

H°
Figure 11.7
de
Typical temperature dependences
of thermodynamic quantities for
protein denaturation in water.

G°
de
0
0 50 t/°C 100

The breaking of hydrogen bonds during denaturation requires energy and pro-
duces a more disordered protein structure, and therefore makes positive contributions
to H° and S° (where de stands for denaturation). In addition, the interactions
de
de
between the two forms of the protein and the solvent water lead to negative contribu-
tions to H° and S°, which rapidly become less important as T increases.
de
de
Therefore, H° and S° increase rapidly with increasing T (Fig. 11.7). The net
de
de
result is the G°-versus-T curve in Fig. 11.7, which shows that denaturation occurs
de
when T is raised. In the temperature range in which denaturation occurs, H° is large
de
(typically 200 to 600 kJ/mol), so denaturation occurs over a small range of T. For ex-
ample, the digestive enzyme chymotrypsin in aqueous solution at pH 2 is 97% in its
native (globular) form at 37°C and is 96% denatured at 50°C. Note from Fig. 11.7 that
H° and S° can each be positive or negative, depending on T. The parabolic
de
de
shape of the G° curve indicates that G° becomes negative at some temperature
de
de
below 0°C; in fact, denaturation of proteins in supercooled water has been observed
(P. G. Debenedetti, Metastable Liquids, Princeton, 1996, sec. 1.2.2).
11.8 SUMMARY OF STANDARD STATES
n
The equilibrium constant for a reaction is K° ß (a ) i [Eq. (11.6)]. The activity of
i,eq
i
species i is a exp[(m m°)/RT] [Eq. (11.1)], where m° is the standard-state
i
i
i
i
chemical potential of i. The choice of standard state therefore determines a and de-
i
termines the form of the equilibrium constant.
Table 11.1 summarizes the choices of standard states made in earlier sections and
lists the forms of the chemical potentials.
11.9 GIBBS ENERGY CHANGE FOR A REACTION
The term Gibbs energy change for a reaction has at least three different meanings,
which we now discuss.
1. G°. The standard molar Gibbs energy change G° for a reaction is defined by
(11.5) as G° n m°, where m° is the value of the chemical potential of
i i i i
substance i in its standard state. Since m° is an intensive quantity and n is a
i i
dimensionless number, G°isan intensive quantity with units J/mol or cal/mol.
Fora gas-phase reaction, the standard state of each gas is the hypothetical pure
ideal gas at 1 bar. For a reaction in liquid solution with use of the molality scale,
the standard state of each nonelectrolyte solute is the hypothetical state with m
i
1 mol/kg and g 1. These standard states do not correspond to the states of the
m,i
reactants in the reaction mixture. Therefore, G° (and H°, S°, etc.) refer not to