Following data is known about melting of a compound AB`.DeltaH=9.2kJmol^(-1),DeltaS=0.008kJK^(-1)mol^(-1)` Its melting point is

Options

A. 736 K
B. 1050 K
C. 1150 K
D. `1150^(@)C`

Answer

To find the melting point of the compound AB, we can use the relationship between enthalpy change (ΔH), entropy change (ΔS), and temperature (T) at the melting point. The equation we will use is derived from the Gibbs free energy equation for phase changes:

\[ \Delta G = \Delta H - T \Delta S \]

At the melting point, the process is at equilibrium, which means that the change in Gibbs free energy (ΔG) is zero. Therefore, we can set up the equation as follows:

\[ 0 = \Delta H - T \Delta S \]

Rearranging this equation gives us:

\[ T = \frac{\Delta H}{\Delta S} \]

Now, we can plug in the values given in the problem:

- ΔH = 9.2 kJ/mol
- ΔS = 0.008 kJ/K·mol

Before substituting these values into the equation, we need to ensure that they are in compatible units. Since both ΔH and ΔS are in kJ, we can directly substitute them.

Now substituting the values:

\[ T = \frac{9.2 \text{ kJ/mol}}{0.008 \text{ kJ/K·mol}} \]

Calculating this gives:

\[ T = \frac{9.2}{0.008} = 1150 \text{ K} \]

Thus, the melting point of the compound AB is **1150 K**.

### Summary of the Steps:
1. Write down the Gibbs free energy equation for phase changes.
2. Set ΔG to zero at the melting point.
3. Rearrange the equation to solve for temperature (T).
4. Substitute the values of ΔH and ΔS into the equation.
5. Calculate the melting point.