Page 42 - Chemical equilibria Volume 4

18 Chemical Equilibria
However, the differential of the partial molar enthalpy can be expressed
in the form:
d H = T d S + V k d P + ∑ μ k d n k [1.75]
k
k
k
Thus, at a given pressure and extent, we obtain:
⎛ H k ⎞ ∂ ⎛ k S ⎞ ∂
⎜ ⎟ = T ⎜ ⎟ = C k P [1.76]
⎝ ∂ T j P ⎠ ⎝ ∂ T j P ⎠

By substituting that equation back into relation [1.74], we find:

⎛ ∂ Q P ⎞
⎜ ⎟ = ∑ν k C P = Δ r C P [1.77]
⎝ ∂ T P ⎠ k k

This relation constitutes what we call the Kirchhoff relation. An
equivalent relation would give the variation of the heat of transformation at
constant volume with the temperature as a function of the molar specific heat
capacity at constant volume associated with the transformation.

1.6. Set of points representing the equilibrium states of a
transformation

Consider a transformation at thermodynamic equilibrium for given values
of the variables of state. Its affinity is null. If we vary one or more of the
variables of state by an infinitesimal amount, the affinity takes on a new
value A + d A . In order for that new state to also be a state of equilibrium of
transformation, it is necessary for that new value of the affinity to be null,
so:

A + d A = 0 [1.78]

This leads us to:

d A = 0 [1.79]