For an endothermic reaction to be spontaneous

Options

A. `Delta G = 0`
B. `Delta G 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 need to analyze the relationship between Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS).

### Step-by-Step Solution:

1. **Understanding Endothermic Reactions**:
- An endothermic reaction is one that absorbs heat from the surroundings. This means that the change in enthalpy (ΔH) for the reaction is positive (ΔH > 0).

2. **Gibbs Free Energy Equation**:
- The spontaneity of a reaction can be determined using the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
- Here, 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 for Spontaneity**:
- For a reaction to be spontaneous, ΔG must be less than 0 (ΔG < 0).
- Rearranging the Gibbs free energy equation gives us:
\[ \Delta G < 0 \implies \Delta H - T \Delta S < 0 \]
- This can be rearranged to:
\[ \Delta H < T \Delta S \]
- This means that for an endothermic reaction (where ΔH is positive), the term \(T \Delta S\) must be greater than ΔH for the reaction to be spontaneous.

4. **Role of Entropy**:
- Since ΔH is positive for endothermic reactions, we need a sufficiently high value of TΔS (where ΔS is the change in entropy) to ensure that the reaction can still be spontaneous.
- Therefore, if ΔS is positive (indicating an increase in disorder), at high temperatures, the term \(T \Delta S\) can outweigh the positive ΔH, making ΔG negative.

5. **Conclusion**:
- Thus, for an endothermic reaction to be spontaneous, it is necessary that ΔG < 0, which can occur when TΔS is sufficiently large to overcome the positive ΔH.

### Final Answer:
The correct option is **C: ΔG < 0**.