Untitled - Aerobib - Universidad Politécnica de Madrid

24 CHAPTER 1. THERMOCHEMISTRY
Remarks
If the reactions take place at pressure and temperature (instead of enthalpy) both constant
the conditions of equilibrium are
δp = δT = δg = 0. (1.101)
But
δg = δh − sδT − T δs. (1.102)
From Eqs. (1.95), (1.97), (1.101) and (1.102) conditions (1.99) are obtained again.
Thus conditions of equilibrium are the same for both cases, with the only difference
that here, temperature is given whilst in the previous case it must be calculated. The
computation is done by determining the conditions of equilibrium as a function of temperature,
and then looking for the value of T which satisfies the additional condition
h = h 0 .
are
Likewise, for constant volume adiabatic reactions the conditions of equilibrium
δu = δV = δs = 0, (1.103)
from which result again conditions (1.99).
1.7 Case of a mixture of ideal gases
For the case of a mixture of ideal gases the form taken by the conditions of equilibrium
is specially simple. In fact, as for (1.63) system (1.99) reduces to
∑
G i ν ij = 0, (j = 1, 2, . . . , r), (1.104)
i
or else
∑
G 0 i ν ij + RT ∑
i
i
( )
pi
ν ij ln = 0, (j = 1, 2, . . . , r), (1.105)
p 0
which together with (1.38) gives
∏
i
X ν ij
i =
( ) (
νj
p0
exp − ∆G0 j
p
RT
)
, (j = 1, 2, . . . , r), (1.106)
where
ν j = ∑ i
ν ij (1.107)