Question

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 :

• A. \( +x - y - z \)
• B. \( x + y + z \)
• C. \( z - (x + y) \)
• D. \( -z - (x + y) \)

Hint:

The heat of solution is the net energy change during the dissolution process. It can be thought of as the energy required to break the lattice minus the energy released during the hydration of the ions. Remember the sign conventions for lattice energy (usually negative) and hydration energy (usually negative).

Answer 1

The Correct Option is C

The heat of solution for \( \text{KCl} \) is determined by the interplay of hydration energy and lattice energy, as described by the Born-Haber cycle equation:

\[\text{Heat of Solution} = \text{Lattice Energy} - (\text{Hydration Energy of } K^+ + \text{Hydration Energy of } Cl^-)\]

Given values are:

• \(\text{Hydration energy of } K^+ = -x \, \text{kJ/mol}\)
• \(\text{Hydration energy of } Cl^- = -y \, \text{kJ/mol}\)
• \(\text{Lattice energy of KCl} = -z \, \text{kJ/mol}\)

Substituting these into the formula yields:

\[\text{Heat of Solution} = -z - (-x + -y) = -z + (x + y)\]

This simplifies to:

\[\text{Heat of Solution} = z - (x + y)\]

The correct option is:

\( z - (x + y) \)

Consequently, the heat of solution for KCl is calculated by subtracting the combined hydration energies of \( K^+ \) and \( Cl^- \) from the lattice energy.