30.4 kJ of heat is required to melt 1 mol of sodium chloride.The entropy change during melting of 28.4 J `mol^(-1)K^(-1)`. Calculate the melting point of sodium chloride.

Explanation

To calculate the melting point of sodium chloride using the given data, we can follow these steps:

### Step 1: Understand the relationship between Gibbs free energy, enthalpy, and entropy
At equilibrium, the change in Gibbs free energy (ΔG) is zero. The relationship is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
Since we are at equilibrium, we can set ΔG to zero:
\[ 0 = \Delta H - T \Delta S \]

### Step 2: Rearrange the equation to solve for temperature (T)
From the equation above, we can rearrange it to find the temperature:
\[ \Delta H = T \Delta S \]
Thus,
\[ T = \frac{\Delta H}{\Delta S} \]

### Step 3: Convert the enthalpy change from kJ to J
The heat required to melt 1 mole of sodium chloride is given as 30.4 kJ. We need to convert this to joules:
\[ \Delta H = 30.4 \, \text{kJ} = 30.4 \times 1000 \, \text{J} = 30400 \, \text{J} \]

### Step 4: Use the given entropy change
The entropy change during the melting process is given as:
\[ \Delta S = 28.4 \, \text{J} \, \text{mol}^{-1} \, \text{K}^{-1} \]

### Step 5: Substitute the values into the temperature equation
Now we can substitute the values of ΔH and ΔS into the equation for T:
\[ T = \frac{30400 \, \text{J}}{28.4 \, \text{J} \, \text{mol}^{-1} \, \text{K}^{-1}} \]

### Step 6: Calculate the temperature
Perform the calculation:
\[ T = \frac{30400}{28.4} \approx 1070.4 \, \text{K} \]

### Conclusion
The melting point of sodium chloride is approximately **1070.4 K**.

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