Concise Physical Chemistry

c07 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

100 EQUILIBRIUM

and

lnKeq=

−
rH◦

R

(

1

T

)

+

rS◦

R

This is a “slope–intercept” problem for the linear function lnKeqvs. 1/T, where the

slope of the plot is−
rH◦/Rand the intercept is
rS◦/R. Two or more equilibrium

measurements at different temperatures yield both the enthalpy change of the reaction

and the entropy change. The resulting thermodynamic functions are only as good as

the input data, and this is a very sensitive experimental problem—especially in the


rS◦determination, which depends on what may be a long and mathematically

questionable extrapolation.

7.6 COMPUTATIONAL THERMOCHEMISTRY

Within a year of the discovery of quantum mechanics by Schrodinger and Heisenberg, ̈

Heitler and London had demonstrated that the energy of the H H chemical bond can

be approximated by a quantum mechanical calculation. The reason this calculation

isalways approximateis a reflection of one of the most profound laws of nature,

Heisenberg’s uncertainty principle. We are unable to know exactly where the moving

electrons are. Hence their Coulombic potential energy, total energy, entropy, and

Gibbs free energy are inaccessible to us in even the simplest chemical bond H H.

Nevertheless, a diverse array of approximate computational methods exists and

the results can be ranked in order of the quality of their approximations. Ranking

enables us to decide which methods are best for a given job, and it points the

way toward improved methods. Usually the quality of an approximate calculation is

measured by how well the calculated value matches well-established experimental

results. Recently, however, computed values have become so reliable that they can be

used to pick out and discard errors in the tabulated experimental results. The present

trend is from using computed results to approximate experimental results to using

them tosupplantorreplaceexperimental results, especially for reactions that occur

within hostile experimental environments (flames or explosions) or reactions that

have fleeting intermediates (free radicals). Quantum mechanical methods produce

results for molecular energy, enthalpy, entropy, Gibbs free energy, and equilibrium

constants, but they are circumscribed by limits on molecular size and they are of

varying reliability.

7.7 CHEMICAL POTENTIAL: NONIDEAL SYSTEMS

Given that the effective pressure fraction of a gas in a nonideal mixture of gases is

its fugacityfand that the effective concentration fraction of a solute in a mixture is

given by its activitya, equilibrium constants in simple A, B nonideal systems can be