Page 162 - Modern physical chemistry

154 Relationships among Reactants

Let us consider the unit of partial pressure Pi to be the standard-state pressure Pia'
Then integrating (7.39) at constant temperature leads to

[7.40]

If the ideal gaseous solution were at equilibrium with another phase, the chemical
potentials in the two phases would be equal by condition (6.102). Furthermore, the activ-
ity ai of the ith constituent in the new phase is measured by the partial pressure in the
gas phase. By definition, we take them to be proportional:

Pi _ k. ~ [7.41]
P.o - t a 9
t t
Substituting the new Pi and expression (7.41) into equation (7.40) gives us

Pi = (p? )gas + RTlnki + RT( ai I a?) = p? + RTlnai [7.42]
for the new phase. In the final form, quantity Pia has replaced the sum (t.tiO)gas + RT In ki
and the unit of activity has been taken to be the standard-state activity at Expression
p/ is now the standard chemical potential of the ith constituent in the given phase.

Z 11 Gibbs Energy of Reaction

A common problem in chemistry is whether a particular reaction can proceed at a
given temperature and pressure with a certain set of concentrations or activities. But
from section 5.14, the net tendency for a reaction to go is measured by the pertinent neg-
ative Gibbs free energy change.
Let us consider a homogeneous system in which the reaction

aA+bB~lL+mM [7.43]
moves forward by dA. unit at a given temperature and pressure. The changes in moles of
A, B, L, Mare
dnA = -a dA, dnB = -b dA, dnL = l dA, dnM = m dA. [7.44]

Applying formula (5.97) to the process gives us

dG = lPL dA + mpM dA - apA dA - bPB dA [7.45]
l aG) =lPL +mpM -apA -bpB' [7.46]
whence

aA T,P
Derivative (dGldA.. )T. P is the increase in Gibbs energy per unit of reaction when only
an infinitesimal amount of reaction occurs. If the reacting system were of infinite extent,
it would be the Gibbs energy change when a moles A reacted with b moles B to produce
l moles L and m moles M. Thus it is called the Gibbs energy of reaction i1G:

[7.47]

Consider the reacting mixture to be gaseous and introduce formula (7.40) for each
chemical potential:

i1G=l~ +mG~ -aGi -b~ +LRTlnP L + mRT In PM -aRTlnP A -bRTlnP B. [7.48]