I am trying to understand what is isosteric heat of adsorption. Based on van't Hoff equation:
$$ \left(\frac{\partial \ln K}{\partial T}\right)_θ = \frac{ΔH^\circ}{RT^2} $$
and $ΔH^\circ$ is defined as the isosteric enthalpy of adsorption. The equilibrium constant for adsorption is:
$$K = \frac{a_{ads}}{a_g \cdot a_s}$$
and it is given by:
$$K = \exp\left(-\frac{ΔG^\circ}{RT}\right)$$
What is the point of differentiating with respect to temperature while keeping surface coverage $θ$ constant. I mean equilibrium constant depends only on $T$, that is $K=f(T)$.
I can't understand even how we are able to force surface coverage to have a constant value.
