The hydration energies of $$K^+$$ and $$Cl^-$$ are $$-x$$ and $$-y$$ kJ/mol respectively. If lattice energy of KCl is $$-z$$ kJ/mol, then the heat of solution of KCl is :

For an ionic solid, the heat (enthalpy) of solution, $$\Delta H_{\text{sol}}$$, is obtained in two steps:
  1. Lattice dissociation: the crystal breaks into gaseous ions. This requires the lattice dissociation energy, $$\Delta H_{\text{lattice(diss)}}$$, which is numerically equal and opposite to the lattice energy of formation.
  2. Hydration: the gaseous ions get surrounded by water molecules, releasing their hydration energies.

Given data (sign conventions):
  • Hydration energy of $$K^+ = -x$$ kJ mol$$^{-1}$$ (exothermic)
  • Hydration energy of $$Cl^- = -y$$ kJ mol$$^{-1}$$ (exothermic)
  • Lattice energy of formation of KCl $$= -z$$ kJ mol$$^{-1}$$ (exothermic for formation from gaseous ions)

Step 1: Lattice dissociation energy
Lattice energy of formation is $$-z$$, so the energy required to dissociate the lattice is the opposite sign:
$$\Delta H_{\text{lattice(diss)}} = +z \text{ kJ mol}^{-1}$$

Step 2: Hydration of the ions
$$\Delta H_{\text{hydration}} = (-x) + (-y) = -(x + y) \text{ kJ mol}^{-1}$$

Overall heat of solution
$$\Delta H_{\text{sol}} = \Delta H_{\text{lattice(diss)}} + \Delta H_{\text{hydration}}$$
$$\Delta H_{\text{sol}} = \bigl(+z\bigr) + \bigl[-(x + y)\bigr]$$
$$\Delta H_{\text{sol}} = z - (x + y)$$

Therefore the heat of solution of KCl is $$z - (x + y)$$ kJ mol$$^{-1}$$.

Hence the correct option is Option C.