Page 42 - Basic physical chemistry for the atmospheric sciences

28 Basic physical chemistry

g = h - T s (2.25)
or, using Eq. (2.8),

g = u + pa - T s (2.26)
Differentiating Eqs. (2.25) and (2. 2 6)

p
u
T
dg = d h - T ds - s d = d + pda + ad - T ds - s dT (2.27)
If we now confine ourselves to transformations at constant tempera­
ture and pressure (which are common conditions for chemical reac­
tions)
dg = d h - T ds = d u + pd - T ds
a
or, using Eq. (2. 6 ) ,

dg = d h - T d = s d q - T ds (2.28)
Expressed in terms of finite changes in molar quantities for a chemical
reaction, Eq. (2.28) becomes
!J.G = !J.Hrx - T !J. S (2. 2 9)

which is called the Gibbs-Helmholtz equation.
For a system at constant pressure and temperature, we have from
s
Eq . (2. 1 6 ) and (2.28)
dg = dq - dqre v (2.30)
Now, if the transformation occurs under equilibrium conditions, and
is therefore reversible, dq = dqrev and
dg = O (2. 3 1 )
s
If, n the other hand, the transformation is spontaneou , and therefore
o
irreversible, it follows from Eq. (2. 1 9 ) that dq < dqrev· Hence, Eq.
(2.30) becomes
dg < O (2. 3 2)

Equation (2. 3 1 ) shows that at equilibrium g must have a stationary
value. We can establish whether this stationary value is a maximum or
a minimum by utilizing Eq. (2. 3 2). S i nce a spontaneous change must
move a system toward equilibrium and dg < 0, the variation of g with
the state of the system must be as shown in Figure 2 . 2 , for, in this
case, whether the system approaches the equilibrium point R from P