Page 361 - Physical Chemistry

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Chapter 11 In deriving (11.32), we used ( G°/ T) ( / T) n m° n ( m°/ T)
P
i
i
i
i
P
i
i
P
Reaction Equilibrium
in Nonideal Systems n S° S°, since ( m / T) S i [Eq. (9.30)]. When liquid or solid solutions
i i
i
P
i
are not involved, the partial derivative in (11.32) becomes an ordinary derivative. H°
¢

is equal to n H°, where the n ’s are the stoichiometric numbers and the H° ’s are the
i i i i i
standard-state molar or partial molar enthalpies. For the application of (11.32) to re-
actions in solution, see Prob. 11.41.
Figure 11.5 plots the molality-scale ionization constant K° of saturated liquid
w
water (water in equilibrium with water vapor) versus temperature. The pressure is not
constant for this plot, but below 250°C the effect of the pressure variation on K° is
w
slight. At the 220°C maximum in K°, ln K° / T is zero and H° of ionization is zero
w w
[Eq. (11.32)]. The strong temperature dependence of H° of water ionization (which
goes from 60 kJ/mol at 0°C to 100 kJ/mol at 300°C) is an example of the fact that
for many ionic reactions in aqueous solution, H° depends strongly on T (in contrast
to gas-phase reactions, where H° usually varies quite slowly with T).
Consider a reaction in which all the reactants and products are in a liquid or solid
solution. Differentiation of (11.31) with respect to P gives
0 ln K° 1 0¢G° 1 0 ¢V°
a b a b a b a n m°
i
i
0P T RT 0P T RT 0P T i RT

where ( m / P) V [Eq. (9.31)] was used. If a reaction involves species in a liquid
i T i
or solid solution and species not in a liquid or solid solution (for example, a solubility
Figure 11.5
product), then in calculating V° we consider only species in the solution. Species not
2
Ionization constant K° g m m / in solution have pressure-independent standard states and make no contribution to

w
2
(m°) for saturated liquid water G°/ P. (However, we must allow for the effect of pressure on the activity of such
versus temperature. The vertical species in K°.) Therefore for any reaction
scale is logarithmic. [Data from
H. L. Clever, J. Chem. Educ., 45, 0 ln K° ¢V° soln
231 (1968).] a b (11.33)
0P T RT
where the subscript is a reminder to include only species in solution in calculating
V° . Usually V° is small, and the pressure dependence of K° is slight unless high
soln soln
pressures are involved.
Figure 11.6 plots the ionization constant K° [Eq. (11.12)] for water at 25°C as a
w
function of pressure. An increase in P from 1 to 200 bar increases K° by 18%, and an
w
increase from 1 to 1000 bar roughly doubles K°. The effect of pressure on aqueous
w
equilibria is significant in seawater, since the typical ocean-floor depth is 4000 m
(where the pressure is 400 bar) and ocean trenches can be 10000 m deep with a
pressure of 1000 bar. (Sperm whales can dive to a depth of 2500 m in search of food.)
The effect of pressure on aqueous equilibria is reviewed in R. H. Byrne and S. H.
Laurie, Pure Appl. Chem., 71, 871 (1999).
Although K° depends only weakly on pressure, it usually depends strongly on
temperature, since H° in (11.32) is usually large. For example, the reaction N (g)
2
3H (g) ∆ 2NH (g) has H° 25 kcal/mol, and its equilibrium constant K°de-
2 3
13
creases from 3 10 at 200 K to 3 10 7 at 1000 K (Fig. 6.6).
Another example is the denaturation (unfolding) of a protein. A protein molecule
is a long-chain polymer of amino acids. Enzymes are globular proteins. In a globular
protein, certain portions of the chain are coiled into helical segments that are stabilized
Figure 11.6 by hydrogen bonds between one turn of a helix and the next. The partly coiled protein
folds on itself to give a roughly ellipsoidal overall shape. The folding is not random,
Water ionization constant K° w
versus pressure at 25°C. [Data but is determined in part by hydrogen bonds, van der Waals forces (Sec. 21.10), and
from D. A. Lown et al., Trans. SOS covalent bonds between sulfur-containing amino acids. In the denaturation re-
Faraday Soc., 64, 2073 (1968).] action, the protein unfolds into a random conformation, called a random coil.