Animated Solution for Chemistry - Chemical Thermodynamics: Lattice enthalpy and enthalpy of solution of NaCl are $788{\text{ kJ mol}}^{-1}$ and $4{\text{ kJ mol}}^{-1}$, respectively. The hydration enthalpy of NaCl is

Imagine dropping a pinch of salt into a glass of water. It vanishes almost instantly. But what is actually happening at the microscopic level? The dissolution of an ionic solid like sodium chloride ($\text{NaCl}$) is a fascinating interplay of energies that we can decode using the principles of thermodynamics.

To understand the energy changes during dissolution, we can break the process down into two hypothetical steps.

First, imagine taking the solid crystal lattice of $\text{NaCl}$ and completely shattering it into isolated, gaseous sodium (${\text{Na}}^{+}$) and chloride (${\text{Cl}}^{-}$) ions. The energy required to do this is called the Lattice Enthalpy (${\Delta }_{\text{lattice}}{H}^{\circ }$). Because we are breaking strong electrostatic bonds, this step requires a massive input of energy, making it highly endothermic.

Second, imagine these isolated gaseous ions plunging into the water. The polar water molecules immediately surround the ions, forming strong ion-dipole interactions. The energy released during this stabilization process is called the Hydration Enthalpy (${\Delta }_{\text{hyd}}{H}^{\circ }$). Because bonds are being formed, this step is highly exothermic.

According to Hess's Law, the total enthalpy change of a reaction is independent of the path taken. Therefore, the direct energy change of dissolving the solid in water—known as the Enthalpy of Solution (${\Delta }_{\text{sol}}{H}^{\circ }$)—must be exactly equal to the sum of the energies of our two hypothetical steps.

Mathematically, this is expressed as:

The problem provides us with the necessary values. The enthalpy of solution is given as $4{\text{ kJ mol}}^{-1}$, and the lattice enthalpy is $788{\text{ kJ mol}}^{-1}$.

Let's substitute these values into our master equation:

To find the hydration enthalpy, we simply rearrange the equation by moving $788$ to the other side:

Notice how highly negative the hydration enthalpy is! This massive release of energy ($-784{\text{ kJ mol}}^{-1}$) almost perfectly compensates for the huge energy required to break the solid lattice ($788{\text{ kJ mol}}^{-1}$). The slight difference of $4{\text{ kJ mol}}^{-1}$ is the net enthalpy of solution, which is slightly endothermic. This is why dissolving salt in water can cause a very tiny drop in temperature.