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?

  • $\begingroup$ Entropy must have unit J/K, respectively molar entropy J/K/mol. Additionally, respective Delta S and delta H are either both functions of T, either considered both constant, as they are linked by the difference of heat capacity of reactants and products. $\endgroup$
    – Poutnik
    Commented Nov 11, 2023 at 13:17
  • $\begingroup$ Further parts of the question require calculation of delta H at different temperatures, so they don't expect us to take that as a constant. How, then, do I justify the constant delta S? $\endgroup$
    – poirot_06
    Commented Nov 11, 2023 at 13:32


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