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

To find the heat of solution for \( \text{KCl} \), we need to understand the relationship between hydration energy, lattice energy, and the enthalpy of solution. This relationship is governed by the Born-Haber cycle, which is expressed as:

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

In the given problem, we have:

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

Substitute these values into the formula:

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

Simplifying the expression, we get:

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

Thus, the correct option is:

\( z - (x + y) \)

Therefore, the heat of solution of KCl is calculated as the lattice energy minus the sum of the hydration energies of \( K^+ \) and \( Cl^- \).

Answer 2

Step 1: Understand the process of dissolution and the associated energy changes.
The dissolution of an ionic compound like KCl in water involves two main steps:
1. Breaking the lattice: The ionic lattice of KCl must be broken down into individual gaseous ions \( K^+(g) \) and \( Cl^-(g) \). The energy required for this process is the lattice energy, \( \Delta H_{lattice} \). Since lattice energy is defined as the energy released when gaseous ions combine to form one mole of a solid ionic compound, the energy required to break the lattice is the negative of the lattice energy given. \[ KCl(s) \rightarrow K^+(g) + Cl^-(g) \quad \Delta H_1 = -(-z) = +z \, kJ/mol \] 
2. Hydration of ions: The gaseous ions then get hydrated by water molecules, forming aqueous ions \( K^+(aq) \) and \( Cl^-(aq) \). The energy released in this process is the hydration energy, \( \Delta H_{hydration} \). The hydration energy of \( K^+ \) is \( -x \) kJ/mol, and the hydration energy of \( Cl^- \) is \( -y \) kJ/mol. The total hydration energy is the sum of the hydration energies of the individual ions. \[ K^+(g) + H_2O \rightarrow K^+(aq) \quad \Delta H_{hyd}(K^+) = -x \, kJ/mol \] \[ Cl^-(g) + H_2O \rightarrow Cl^-(aq) \quad \Delta H_{hyd}(Cl^-) = -y \, kJ/mol \] The overall hydration energy is: \[ K^+(g) + Cl^-(g) \rightarrow K^+(aq) + Cl^-(aq) \quad \Delta H_2 = -x + (-y) = -(x + y) \, kJ/mol \] 
Step 2: Apply Hess's Law to find the heat of solution.
The heat of solution \( \Delta H_{sol} \) is the enthalpy change when one mole of a substance dissolves in a specified amount of solvent. According to Hess's Law, the overall enthalpy change for a reaction is independent of the path taken. Therefore, the heat of solution of KCl can be found by summing the enthalpy changes of the two steps mentioned above: \[ \Delta H_{sol} = \Delta H_1 + \Delta H_2 \] \[ \Delta H_{sol} = (+z) + (-(x + y)) \] \[ \Delta H_{sol} = z - (x + y) \, kJ/mol \] 
Step 3: Match the result with the given options.
The heat of solution of KCl is \( z - (x + y) \) kJ/mol, which matches option (3).