One of the parts in a question I'm trying to solve for an assignment goes like this:
A key issue in the Hydrogen Economy is Hydrogen Storage. This can be restored if a substance $X$ can bind to $H_2$. The binding should be strong enough so that $XH_2$ is a liquid or solid. Necessarily, $X$ must also be a liquid or solid. Consider the chemical reaction at constant pressure:
$ X(l) + H_2(g) \rightarrow XH_2 (l) $
Write a relation between $\Delta G^{\circ}(T)$ and $\Delta S^{\circ}$ for this reaction. Take $\Delta S^{\circ}(T)$ to be a constant of temperature, equal to $ -85 kJ/mol $. Justify this approximation.
(and then there are more parts)
I know how to write the relation ($\Delta G^{\circ}(T)$ = $\Delta H^{\circ}(T)$ - T$\Delta S^{\circ}$ since $S$ is constant), but how do I justify the approximation?
I'm confused, because the value given seems to be the one given by Trouton's rule - but if you use Trouton's rule, then entropy of $X$ and $XH_2$ are both approximately equal, so $\Delta S^{\circ}(T) \approx -S_{H_2}$. But entropy of $H_2$, being a gas, would massively change with temperature, and would definitely not be $-85 kJ/mol.$
Does that mean the approximation is wrong, or am I thinking in the wrong direction?
