Freezing point of the following equilibrium, liquid solvent `hArr` solid solvent is :
(a)`(/_\H -/_\G)/(T/_\S)`
(b)`(/_\H)/(/_\S)`
(c)`(/_\G)/(/_\S)`
(d)`(/_\S)/(/_\H)`

Options

A. `(/_\H -/_\G)/(T/_\S)`
B. `(/_\H)/(/_\S)`
C. `(/_\G)/(/_\S)`
D. `(/_\S)/(/_\H)`

Answer

To solve the question regarding the freezing point of the equilibrium between liquid solvent and solid solvent, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Equilibrium**: The equilibrium in question is between the liquid solvent and the solid solvent. When a liquid solvent freezes, it transitions into a solid state, and this process can be described thermodynamically.

2. **Use Gibbs Free Energy Equation**: The Gibbs free energy change (ΔG) for a process is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = temperature (in Kelvin)
- ΔS = change in entropy

3. **Identify Conditions at Freezing Point**: At the freezing point, the system is at equilibrium, which means that the change in Gibbs free energy (ΔG) is zero:
\[ 0 = \Delta H - T \Delta S \]

4. **Rearrange the Equation**: Rearranging the equation gives:
\[ T \Delta S = \Delta H \]
or
\[ T = \frac{\Delta H}{\Delta S} \]
This equation expresses the freezing point (T) in terms of the enthalpy change (ΔH) and the entropy change (ΔS).

5. **Match with Given Options**: Now, we need to match this derived equation with the options provided in the question. The correct expression for the freezing point is:
\[ T = \frac{\Delta H}{\Delta S} \]
This corresponds to option (b).

### Final Answer:
The correct answer is **(b) \(\frac{\Delta H}{\Delta S}\)**.

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