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.



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