Is it true that according to gibbs free energy equation, insoluble salts such as AgCl don't dissolve because the process would be too endothermic? The right side of the equation, TΔS, would have to be positive because entropy increases when salts dissolve, which means that ΔH would have to be high enough to make the equation positive. Is this correct?
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$\begingroup$ G = H - TS. Let G = 0. It is known empirically that H is -127 and S is .0963, therefore T must be -1318.8 K. This means the reaction occurs at all temperatures, and therefore insoluble salts must not dissolve for some other reason. Correct me if I'm wrong, but that's my understanding of it. $\endgroup$– Christopher MarleyOct 9, 2018 at 4:44
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1$\begingroup$ @ChristopherMarley aren't those numbers the standard enthalpy of formation of AgCl from the elements in their standard states, and the standard entropy of AgCl? Not related to solubility? $\endgroup$– user64968Oct 9, 2018 at 5:00
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$\begingroup$ It is incorrect to say that "entropy increases when salts dissolve" as a general truth. That is sometimes correct, but it can also happen that the solvent becomes more ordered in order to create a solvation shell, for example, which can overcome the gain in entropy of breaking up the salt lattice, so the $\Delta S$ is negative. Such salts are only soluble if the $\Delta H$ is negative and greater in magnitude than the positive $-T\Delta S$ term. $\endgroup$– AndrewJan 24, 2019 at 13:19
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Yes, this is correct. Assuming that you are talking about solubility in water, it is discussed by JF Liebman, Structural Chemistry, 15, 165 (2004) which needs a subscription to read in full, but much of the key information is given on the first couple of pages which are available as a preview. The relevant thermodynamic quantities (in kJ mol$^{-1}$) for dissolution of one mole in water are given as a table, with AgCl compared with NaCl and KCl:
$$ \begin{array}{cccc} & \Delta H & \Delta G & T\Delta S \\ \hline \text{NaCl} & +4 & -9 & +13 \\ \text{KCl} & +17 & -5 & +22 \\ \text{AgCl} & +45 & +37 & +8 \end{array} $$
The author got the original data from NBS Tables of Chemical Thermodynamic Properties. All the entropy terms are favourable. All the enthalpy terms are unfavourable, but the AgCl has a much more unfavourable enthalpy of solution than the alkali metal chlorides, and the entropy cannot compensate for this. The Ag$^+$ ion is poorly hydrated in solution compared with Na$^+$ and K$^+$.