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Question: The hydration energies of $K^+$ and $Cl^-$ are $-x$ and $-y$ kJ/mol respectively. If the lattice ene...

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

A

z - (x + y)

B

z + (x + y)

C

x + y - z

D

x + y + z

Answer

z - (x + y) kJ/mol

Explanation

Solution

The heat of solution (ΔHsol\Delta H_{sol}) is the sum of the energy required to break the ionic lattice and the energy released during hydration of the ions. Energy to break the lattice of KCl = −- (Lattice energy of KCl) = −(−z)=+z-(-z) = +z kJ/mol. Total energy released during hydration = (Hydration energy of K+K^+) + (Hydration energy of Cl−Cl^-) = (−x)+(−y)=−(x+y)(-x) + (-y) = -(x+y) kJ/mol. Therefore, ΔHsol=(Energy to break lattice)+(Total hydration energy)\Delta H_{sol} = (\text{Energy to break lattice}) + (\text{Total hydration energy}) ΔHsol=z+(−(x+y))=z−(x+y)\Delta H_{sol} = z + (-(x+y)) = z - (x+y) kJ/mol.