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Sodium acetate trihydrate dissolves in water to its constituent ions:

$$\ce{NaOAc.3H2O (s) ->[H2O] Na+ (aq) + OAc- (aq) + 3H2O (l)}$$

The crystallisation of sodium acetate from a supersaturated solution is well-known to be exothermic. Since dissolution is the reverse of crystallisation, should the enthalpy of dissolution be positive (i.e. an endothermic process)?

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  • $\begingroup$ I don't particularly like calling the melting of a hydrate salt dissolving. $\endgroup$ – A.K. Oct 26 '18 at 4:09
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The process of dissolving sodium acetate trihydrate $(\ce{NaC2H3O2.3H2O})$ in water is endothermic. The molar enthalpy of solution at $T=25\ \mathrm{^\circ C}$ is $\Delta_\text{sol}H^\circ=19.66\ \mathrm{kJ\ mol^{-1}}$.*

Accordingly, since crystallization is the reverse process of dissolution, the crystallization of sodium acetate trihydrate from aqueous solutions is exothermic. For practical purposes, the enthalpy of solution with a reverse sign is taken as enthalpy of crystallization.

The enthalpy of solution mainly depends on two energy contributions: lattice energy and hydration energy. Lattice energy is the energy released when the crystal lattice of an ionic compounds is formed. Conversely, energy equal to the lattice energy has to be supplied to break up the crystal lattice; i.e. this process is endothermic. Hydration energy is released when water molecules hydrate the ions; i.e. when water molecules surround the ions and new attractions form between water molecules and ions. This process is exothermic.

Therefore, whether the process of dissolving a salt in water is exothermic or endothermic depends on the relative sizes of the lattice energy and the hydration energy. If the lattice energy is greater than the hydration energy, the process of dissolving the salt in water is endothermic. Conversely, if the lattice energy is smaller than the hydration energy, the process of dissolving the salt in water is exothermic.

For anhydrous sodium acetate $(\ce{NaC2H3O2})$, the lattice energy is actually smaller than the hydration energy. The molar enthalpy of solution is negative; at $T=25\ \mathrm{^\circ C}$ it is $\Delta_\text{sol}H^\circ=-17.32\ \mathrm{kJ\ mol^{-1}}$.* Thus, the process of dissolving anhydrous sodium acetate in water is exothermic.

However, hydration of ions can also occur in crystalline solids. Sodium acetate trihydrate $(\ce{NaC2H3O2.3H2O})$ contains three water molecules for each $\ce{NaC2H3O2}$ unit in the crystal. The corresponding amount of hydration energy is already released when crystalline anhydrous sodium acetate absorbs water and is converted to crystalline sodium acetate trihydrate. Therefore, the additional amount of hydration energy that is released when sodium acetate trihydrate is dissolved in water and completely hydrated is smaller than the total hydration energy that is released when anhydrous sodium acetate is dissolved in water. Hence, the resulting value for the molar enthalpy of solution is larger for sodium acetate trihydrate than for anhydrous sodium acetate.

* “Enthalpy of Solution of Electrolytes”, in CRC Handbook of Chemistry and Physics, 90th Edition (CD-ROM Version 2010), David R. Lide, ed., CRC Press/Taylor and Francis, Boca Raton, FL.

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