Calculate the Gibbs energy change on dissolving one mole of sodium chloride at `25^(@)C`.
Lattice energy = `+ 777.8 kJ "mol"^(-1)`
Hydration of `NaCI = -774.1 kJ "mol"^(-1)`
`DeltaS at 25^(@)C = 43 JK^(-1) "mol"^(-1)`.

Explanation

To calculate the Gibbs energy change (ΔG) when dissolving one mole of sodium chloride (NaCl) at 25°C, we will follow these steps:

### Step 1: Gather Given Data
We have the following data:
- Lattice energy (ΔH_lattice) = +777.8 kJ/mol
- Hydration energy (ΔH_hydration) = -774.1 kJ/mol
- Temperature (T) = 25°C = 298 K
- Entropy change (ΔS) = 43 J/K·mol = 0.043 kJ/K·mol (converted to kJ)

### Step 2: Calculate the Enthalpy Change (ΔH)
The enthalpy change (ΔH) for the dissolution process can be calculated using the formula:
\[ \Delta H = \Delta H_{\text{lattice}} + \Delta H_{\text{hydration}} \]
Substituting the values:
\[ \Delta H = 777.8 \text{ kJ/mol} + (-774.1 \text{ kJ/mol}) = 777.8 - 774.1 = 3.7 \text{ kJ/mol} \]

### Step 3: Calculate ΔG Using the Gibbs Free Energy Equation
The Gibbs free energy change (ΔG) can be calculated using the equation:
\[ \Delta G = \Delta H - T \Delta S \]
Substituting the values:
\[ \Delta G = 3.7 \text{ kJ/mol} - (298 \text{ K} \times 0.043 \text{ kJ/K·mol}) \]

### Step 4: Calculate TΔS
Now, we calculate \(T \Delta S\):
\[ T \Delta S = 298 \text{ K} \times 0.043 \text{ kJ/K·mol} = 12.814 \text{ kJ/mol} \]

### Step 5: Substitute Back to Find ΔG
Now substitute \(T \Delta S\) back into the ΔG equation:
\[ \Delta G = 3.7 \text{ kJ/mol} - 12.814 \text{ kJ/mol} \]
Calculating this gives:
\[ \Delta G = 3.7 - 12.814 = -9.114 \text{ kJ/mol} \]

### Final Answer
The Gibbs energy change (ΔG) on dissolving one mole of sodium chloride at 25°C is:
\[ \Delta G = -9.114 \text{ kJ/mol} \]

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