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In a question, I was asked to integrate the Gibbs-Helmholtz equation to derive some formula. Then the next question asked:

Identify one assumption that you have made in deriving the above equation and identify one scenario where it is a very bad assumption, and explain why the assumption fails

Now the assumption that was made was the $\Delta H_{\mathrm{fus}}$ is constant over the change in temperature. However, could someone please explain when and why this assumption fails.

Thanks.

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The G-H equation describes the effect of T on $\Delta G$ at constant pressure. But, along the fusion contour of T vs P, T is a unique function of P. So, along this contour, P is changing. So the G-H equation is not valid to use for a change of phase such as fusion. The G-H equation was developed to describe the effect of T on $\Delta G$ for chemical reactions at constant pressure, usually for the change from separate pure reactants to separate pure products at the standard pressure of 1 bar.

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  • $\begingroup$ Thanks for your great answer. Out curiosity, would assuming the enthalpy of fusion being constant also be a bad assumption in certain scenarios? $\endgroup$ – Nanoputian Feb 4 '16 at 12:38
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    $\begingroup$ If both the temperature and the pressure change (i.e., in tandum along the equilibrium contour), the change in enthalpy between the solid and the liquid in equilibrium with one another also changes. But usually, the effect of pressure on the heat of fusion is going to be very weak. $\endgroup$ – Chet Miller Feb 4 '16 at 12:47

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