1.2.4: Affinity for Spontaneous Reaction- General Differential
A given closed system is prepared using \(\mathrm{n}_{\mathrm{i}}^{0}\) moles of each chemical substance \(i\). At extent of chemical reaction \(\xi\) the ratio \((\mathrm{A}/\mathrm{T})\) where \(\mathrm{A}\) is the affinity for spontaneous chemical reaction is defined by independent variables, \(\mathrm{T}\), \(p\) and \(\xi\).
\[(\mathrm{A} / \mathrm{T})=(\mathrm{A} / \mathrm{T})[\mathrm{T}, \mathrm{p}, \xi] \nonumber \]
The general differential of this equation has the following form.[1]
\[\mathrm{d}(\mathrm{A} / \mathrm{T})=\left[\frac{\partial(\mathrm{A} / \mathrm{T})}{\partial \mathrm{T}}\right]_{\mathrm{p}, \xi} \, \mathrm{dT}+\frac{1}{\mathrm{~T}} \,\left[\frac{\partial \mathrm{A}}{\partial \mathrm{p}}\right]_{\mathrm{T}, \xi} \, \mathrm{dp}+\frac{1}{\mathrm{~T}} \,\left[\frac{\partial \mathrm{A}}{\partial \xi}\right]_{\mathrm{T}, \mathrm{p}} \, \mathrm{d} \xi \nonumber \]
Footnote
[1] Equation (b) forms the basis of equations describing the dependence of A on T at fixed p and on p at fixed T.