For an endothermic reaction to be spontaneous

Options

A. `Delta G = 0`
B. `Delta gt 0`
C. `Delta G lt 0`
D. `Delta G may be +ve or -ve`

Answer

To determine the conditions under which an endothermic reaction can be spontaneous, we can analyze the relationship between Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) using the Gibbs free energy equation:

### Step-by-Step Solution:

1. **Understand the Gibbs Free Energy Equation**:
The Gibbs free energy change (ΔG) is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- ΔG = Gibbs free energy change
- ΔH = Enthalpy change
- T = Temperature in Kelvin
- ΔS = Entropy change

2. **Identify the Nature of the Reaction**:
For an endothermic reaction, the enthalpy change (ΔH) is positive (ΔH > 0). This means that the reaction absorbs heat from the surroundings.

3. **Determine the Conditions for Spontaneity**:
For the reaction to be spontaneous, ΔG must be negative (ΔG < 0). Therefore, we need to analyze the equation:
\[ \Delta G = \Delta H - T \Delta S < 0 \]
Rearranging this gives:
\[ \Delta H < T \Delta S \]

4. **Analyze the Entropy Change**:
For an endothermic reaction to be spontaneous, the entropy change (ΔS) must be positive (ΔS > 0). This indicates that the disorder of the system increases.

5. **Establish Temperature Conditions**:
From the inequality ΔH < TΔS, we can deduce that:
\[ T > \frac{\Delta H}{\Delta S} \]
This means that at higher temperatures, the term \(T \Delta S\) can outweigh the positive ΔH, making ΔG negative and thus the reaction spontaneous.

### Conclusion:
For an endothermic reaction to be spontaneous, it is necessary that:
- The reaction has a positive entropy change (ΔS > 0).
- The temperature (T) must be sufficiently high such that \(T > \frac{\Delta H}{\Delta S}\).