Page 188 - Physical chemistry understanding our chemical world

THE EFFECT OF PRESSURE ON THERMODYNAMIC VARIABLES 155

Substituting for V m from Equation (4.37) into Equation (1.13) gives
dG

p = RT (4.40)
dp
And separation of the variables gives

dG 1
= RT (4.41)
dp p
so
1
dG = RT dp (4.42)
p
Integration, taking G 1 at p (initial) and G 2 at p (final) , yields

p (final)
G 2 − G 1 = RT ln (4.43)
p (initial)
Or, more conveniently, if G 2 is the final value of G and G 1 the initial value of G,then
the change in Gibbs function is

p 2
G = RT ln
p 1
i.e. Equation (4.39).

Aside

In practice, it is often found that compressing or de- The fugacity f can be
compressing a gas does not follow closely to the ideal- regarded as an ‘effec-
gas equation, particularly at high p or low T , as exem- tive’ pressure. The
plified by the need for equations such as the van der ‘fugacity coefficient’ γ
represents the devia-
Waals equation or a virial expression. The equation
tion from ideality. The
above is a good approximation, though.
value of γ tends to one
A more thorough treatment takes one of two courses:
as p tends to zero.
(1) Utilize the concept of virial coefficients; see
p. 57. The word ‘fugacity’
(2) Use fugacity instead of pressure. comes from the Latin
fugere,which means
Fugacity f is defined as ‘elusive’ or ‘difficult to
capture’. The modern
word ‘fugitive’ comes
f = p × γ (4.44)
from the same source.