The magniutudes of lattice and hydration energies of salt AB are found to be 764 and 755 kJ respectively. If entropy of dissolution of AB in water is `40 JK^(-1) mol^(-1)` at 298 K. Gibb's energy change for the dissolution of AB will be

Options

A. 9 kJ
B. `-20.92 kJ`
C. `-11.2 kJ`
D. `-9 KJ`

Answer

To solve the problem, we need to calculate the Gibbs free energy change (ΔG) for the dissolution of salt AB using the provided lattice energy, hydration energy, and entropy of dissolution. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Lattice energy (U) = 764 kJ/mol
- Hydration energy (H) = 755 kJ/mol
- Entropy of dissolution (ΔS) = 40 J/K·mol
- Temperature (T) = 298 K

### Step 2: Calculate the enthalpy change (ΔH) for the dissolution
The enthalpy change for the dissolution of AB can be calculated using the formula:
\[ \Delta H = \text{Hydration energy} - \text{Lattice energy} \]
Substituting the values:
\[ \Delta H = 755 \text{ kJ/mol} - 764 \text{ kJ/mol} = -9 \text{ kJ/mol} \]
To convert this to joules:
\[ \Delta H = -9000 \text{ J/mol} \]

### Step 3: Calculate the Gibbs free energy change (ΔG)
The Gibbs free energy change can be calculated using the formula:
\[ \Delta G = \Delta H - T \Delta S \]
Substituting the values:
\[ \Delta G = -9000 \text{ J/mol} - (298 \text{ K} \times 40 \text{ J/K·mol}) \]
Calculating the second term:
\[ T \Delta S = 298 \times 40 = 11920 \text{ J/mol} \]
Now substituting back into the ΔG equation:
\[ \Delta G = -9000 \text{ J/mol} - 11920 \text{ J/mol} = -20920 \text{ J/mol} \]
To convert this to kJ:
\[ \Delta G = -20.92 \text{ kJ/mol} \]

### Final Answer
The Gibbs free energy change for the dissolution of AB is:
\[ \Delta G = -20.92 \text{ kJ/mol} \]

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