If an endothermic reaction is non - spontaneous at freezing of water and becomes feasible at its boiling point, then

Options

A. `DeltaH` is - ve, `DeltaS` is +ve
B. `DeltaH and DeltaS` both are +ve
C. `DeltaH and DeltaS` both are -ve
D. `DeltaH` is +ve, `DeltaS` is -ve

Answer

To solve the problem, we need to analyze the thermodynamic conditions of the endothermic reaction at different temperatures, specifically at the freezing point (0°C) and the boiling point (100°C) of water.

### Step-by-Step Solution:

1. **Understanding Endothermic Reactions**:
- An endothermic reaction absorbs heat from its surroundings, which means that the enthalpy change (ΔH) is positive.

2. **Gibbs Free Energy Equation**:
- The spontaneity of a reaction can be determined using the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
- Where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

3. **Condition at Freezing Point (0°C)**:
- At the freezing point of water (0°C or 273 K), the reaction is non-spontaneous. This means:
\[ \Delta G > 0 \]
- Since ΔH is positive (as it is an endothermic reaction), for ΔG to be positive, the term \(T \Delta S\) must be less than ΔH. Therefore, we can conclude:
\[ \Delta H > T \Delta S \quad \text{(at 273 K)} \]

4. **Condition at Boiling Point (100°C)**:
- At the boiling point of water (100°C or 373 K), the reaction becomes spontaneous:
\[ \Delta G < 0 \]
- Here, we can set up the inequality:
\[ \Delta H < T \Delta S \quad \text{(at 373 K)} \]

5. **Combining the Conditions**:
- From the two conditions, we have:
- At 273 K: \( \Delta H > 273 \Delta S \)
- At 373 K: \( \Delta H < 373 \Delta S \)

6. **Conclusion**:
- For the reaction to be non-spontaneous at low temperatures (freezing point) and spontaneous at high temperatures (boiling point), we can conclude that:
- ΔH is positive (endothermic),
- ΔS must also be positive (increase in disorder), since both conditions must hold true simultaneously.

### Final Answer:
The endothermic reaction is non-spontaneous at the freezing point of water and becomes feasible at its boiling point when both ΔH and ΔS are positive.

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