Page 41 - Chemical equilibria Volume 4

By applying the same reasoning as in the previous section (see
section 1.5.1), we find: Physico-Chemical Transformations and Equilibria 17
Q = T ν k ⎜ ∑ ⎛ S ⎞ ∂ ⎟ + ∑ ν μ k [1.69]
k
V
k ⎝ n ∂ k ⎠ VT k
,, j n
However, we know that:

⎛ F ⎞ ∂
μ = ⎜ ⎟ [1.70]
i
⎝ n ∂ k ⎠ VT
,, j n
Thus:

Q = T ν k ⎜ ∑ ⎛ S ⎞ ∂ ⎟ + ν k ⎜ ∑ ⎛ F ⎞ ∂ ⎟ [1.71]
V
k ⎝ n ∂ k ⎠ VT k ⎝ n ∂ k ⎠ VT
,, j n
,, j n
and, taking account of:
F = U − TS [1.72]

the heat of transformation is:

⎛ ∂ U ⎞
∑ ⎜
Q = ν k ⎜ ⎟ ⎟ = Δ r U [1.73]
V
k ⎝ ∂ n k ⎠ V , T, n j
Thus, the heat of transformation, at constant temperature and volume, is
equal to the internal energy associated with the reaction.

1.5.3. Variations in the heat of transformation at constant
pressure with changing temperature – Kirchhoff relation

According to equation [1.66], we can write:

⎛ ∂ Q P ⎞ ⎛ H k ⎞ ∂
⎜ ⎟ = ν k ⎜∑ ⎟ [1.74]
⎝ ∂ T P ⎠ k ⎝ ∂ T j P ⎠