Page 366 - Physical Chemistry

lev38627_ch11.qxd 3/14/08 1:10 PM Page 347

347
discuss the details of biochemical processes, one uses chemical reaction equations, Further Reading and Data Sources

such as ATP 4 H O ∆ ADP 3 HPO 2 H , in which atoms and charges are
2
4
balanced. The relation between equilibrium constants for biochemical reactions and
those for chemical reactions is discussed in R. A. Alberty and A. Cornish-Bowden,
Trends Biochem. Sci., 18, 288 (1993); R. N. Goldberg et al., J. Phys. Chem. Ref. Data,
22, 515 (1993); R. A. Alberty, Pure Appl. Chem., 66, 1641 (1994); R. A. Alberty,
Thermodynamics of Biochemical Reactions, Wiley-Interscience, 2003.
One must use caution in applying thermodynamics to living organisms. Organisms and the
cells that compose them are open (rather than closed) systems and are not at equilibrium.
The rates of the chemical reactions may thus be more relevant than the values of the equi-
librium constants. For discussion on these and related points, see B. E. C. Banks, Chem.
Brit., 5, 514 (1969); L. Pauling, ibid., 6, 468 (1970); D. Wilkie, ibid., 6, 472; A. F. Huxley,
ibid., 6, 477; R. A. Ross and C. A. Vernon, ibid., 6, 541; B. E. C. Banks and C. A. Vernon,
J. Theor. Biol., 29, 301 (1970). For a formulation of nonequilibrium thermodynamics de-
vised to apply to biological systems, see H. Qian and D. A. Beard, Biophys. Chem., 114,
213 (2005).

11.11 SUMMARY
The activity a of species i in a system is defined to satisfy m m° RT ln a .
i
i
i
i
Substitution into the reaction-equilibrium condition n m 0 leads to G°
i
i
i
RT ln K°, which relates the standard Gibbs energy change G° to the equilibrium
n
constant K° ß (a i,eq ) i . For reactions in solution, the mole-fraction scale is used for
i
the solvent (A) and the molality scale is most commonly used for each solute (i); we
x and a g
have a g x,A A i m,i m /m°, where the g’s are activity coefficients. In dilute
A
i
solutions, it is reasonable to approximate a as 1 and g m,i as 1 for nonelectrolytes. For
A
ions, the Davies equation can be used to estimate g . The activity of a pure solid or
m
pure liquid not at high pressure can be approximated as 1. Calculations for ionization
of weak acids and for solubility-product equilibria of salts were discussed. For gases,
a f /P° f x P/P°. The Lewis–Randall rule f f*(T, P) or an equation of state
i i
i
i
i
i
can be used to estimate fugacity coefficients in gas mixtures. The temperature and
pressure dependences of K° are given by (11.32) and (11.33).
Important kinds of calculations discussed in this chapter include:
• Calculation of equilibrium constants for nonideal systems from G° data using
f
G° RT ln K°.
• Calculation of equilibrium molalities in electrolyte equilibria (e.g., weak-acid
ionization, solubility product) with use of the Davies equation to estimate activ-
ity coefficients.
• Calculation of nonideal-gas equilibria.
• Calculation of changes in K° with temperature and pressure changes.
FURTHER READING AND DATA SOURCES
Denbigh, secs. 4.5, 4.9, chap. 10; McGlashan, secs. 12.13, 12.14, 12.15, 18.10,
20.9–20.11; J. E. Ricci, Hydrogen Ion Concentration, Princeton, 1952; J. N. Butler
and D. R. Cogley, Ionic Equilibrium, Wiley, 1998.
Equilibrium constants in water (including ionization constants of acids and bases,
solubility products, stability constants of complex ions, and constants for ion-pair for-
mation): A. E. Martell and R. M. Smith, Critical Stability Constants, vols. 1–6,
Plenum, 1974–1989.