The spontaneous nature of a reaction is impossible if

Options

A. `Delta H = +ve, Delta S = + ve`
B. `Delta H = -ve, Delta S = - ve`
C. `Delta H = -ve, Delta S = + ve`
D. `Delta H = +ve, Delta S = - ve`

Answer

To determine when the spontaneous nature of a reaction is impossible, we need to analyze the Gibbs free energy change (ΔG) of the reaction. The spontaneity of a reaction is indicated by the sign of ΔG:

1. **Understanding Gibbs Free Energy**:
- The equation for Gibbs free energy is given by:
\[ \Delta G = \Delta H - T \Delta S \]
- Where:
- ΔG = Change in Gibbs free energy
- ΔH = Change in enthalpy
- T = Temperature in Kelvin
- ΔS = Change in entropy

2. **Identifying Spontaneity**:
- A reaction is spontaneous if ΔG is negative (ΔG < 0).
- A reaction is non-spontaneous if ΔG is positive (ΔG > 0).

3. **Analyzing the Options**:
- We need to evaluate the conditions under which ΔG can be positive, indicating that the reaction is non-spontaneous.

**Option 1**: ΔH is positive and ΔS is positive.
- Here, ΔG could be positive or negative depending on the temperature (T). At high temperatures, the TΔS term could dominate, potentially making ΔG negative. Thus, this option does not guarantee non-spontaneity.

**Option 2**: ΔH is negative and ΔS is negative.
- In this case, ΔG could also be negative if the magnitude of ΔH is greater than the TΔS term. Thus, this option does not guarantee non-spontaneity.

**Option 3**: ΔH is negative and ΔS is positive.
- Here, both terms contribute to making ΔG negative. Thus, this option does not guarantee non-spontaneity.

**Option 4**: ΔH is positive and ΔS is negative.
- In this scenario:
- ΔG = ΔH (positive) - TΔS (negative)
- Since ΔS is negative, TΔS is also negative, making ΔG positive.
- This means that ΔG will always be positive, indicating that the reaction is non-spontaneous.

4. **Conclusion**:
- The spontaneous nature of a reaction is impossible if ΔH is positive and ΔS is negative (Option 4).