In which case, a spontaneous reaction is possible at any temperature?

Options

A. `DeltaH (- ve), DeltaS (+ve)`
B. `DeltaH (- ve), DeltaS (-ve)`
C. `DeltaH (+ ve), DeltaS (+ve)`
D. None of these

Answer

To determine the conditions under which a spontaneous reaction is possible at any temperature, we need to analyze the Gibbs free energy change (ΔG) for the reaction. The relationship between ΔG, enthalpy change (ΔH), and entropy change (ΔS) is given by the equation:

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

### Step-by-Step Solution:

1. **Understand the Conditions for Spontaneity**:
- A reaction is spontaneous when ΔG < 0 (negative).

2. **Analyze the Gibbs Free Energy Equation**:
- The equation ΔG = ΔH - TΔS shows that ΔG depends on both ΔH and ΔS, as well as the temperature (T).

3. **Identify the Cases for Spontaneity**:
- For a reaction to be spontaneous at any temperature, we need to consider the signs of ΔH and ΔS:
- **Case 1**: If ΔH < 0 (exothermic reaction) and ΔS > 0 (increase in entropy), then ΔG will always be negative regardless of the temperature. This is because the negative ΔH term will outweigh the TΔS term as T increases.
- **Case 2**: If ΔH > 0 (endothermic reaction) and ΔS < 0 (decrease in entropy), then ΔG will always be positive, which means the reaction will not be spontaneous at any temperature.

4. **Conclusion**:
- The only case where a spontaneous reaction is possible at any temperature is when ΔH < 0 and ΔS > 0.

### Final Answer:
A spontaneous reaction is possible at any temperature when ΔH is negative (ΔH < 0) and ΔS is positive (ΔS > 0).