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I'm fine with doing these questions, such as:

For ammonia, enthalpy of fusion is 5.65 kJ/mol, and entropy of fusion is 28.9 J/K.mol

Hence find an approximate melting point: Well $\Delta G = \Delta H - T\Delta S = 5.65*10^3 - T(28.9)=0$ Which yields $T=196K$. This is quite close to Google's value.

What I'm thinking, though, is that we shouldn't be able (in real life) to determine a melting point so easily, because $\Delta_r H$ and $\Delta_r S$ both vary with temperature, so in reality this isn't as simple as solving a linear equation for T?

I'd just like some confirmation here, as my textbook isn't giving much away on this point :)

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  • $\begingroup$ Enthalpy and entropy of fusion cannot vary with temperature really. They can vary with pressure, in which case the melting point changes. ;) $\endgroup$ – Karl Apr 24 '16 at 17:47
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In real life the melting point is determined by measuring the temperature. The entropy of fusion is usually determined by dividing the enthalpy of fusion by the melting temperature.

$$\Delta S_f = \Delta H_f / T_f$$

Your text book calculation just solves this equation for $T_f$ to recover the temperature that probably had been measured before.

Note that for constant pressure the temperature is constant $T_f$ as long as the phase transition takes place.

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  • $\begingroup$ Ok, I think there's something I left out from my question: I don't know what conditions the thermodynamic data is quoted at. For instance, the entropy and enthalpy of fusion could have been at 298K, quite different from reality. If they were quoted at melting point, then I'd have no problem with solving for T. But what if they aren't? $\endgroup$ – zaddy Apr 24 '16 at 21:11
  • $\begingroup$ By 'enthalpy of fusion at 298K', I mean hypothetical values for 298K (although the process can't occur at 298K) - values achieved by applying Hess's law $\endgroup$ – zaddy Apr 24 '16 at 21:33
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What the respective free energies of the solid and liquid are doing away from the melting point is irrelevant - you know they aren't equal. At the melting point, the two must be equal, so the enthalpy and entropy of fusion must balance each other out in the manner you describe. There is nothing magic about it. Now, determining them experimentally is the hard part, but once determined the melting point is implicitly defined by them.

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