# Justifying that Standard Entropy of a Reaction is a Constant of Temperature

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?

• 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. Commented Nov 11, 2023 at 13:17
• 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? Commented Nov 11, 2023 at 13:32