A reaction is spontaneous at low temperature but non- spontaneous at high temperature. Which of the following is true for the reaction?

Options

A. `triangleH gt 0, triangleS gt 0`
B. `triangleH lt 0, triangleS gt 0`
C. `triangleH gt 0, triangleS=0`
D. `triangleH lt 0, triangleS lt 0`

Answer

To determine the correct statement regarding a reaction that is spontaneous at low temperatures but non-spontaneous at high temperatures, we can analyze the Gibbs free energy equation:

### Step-by-Step Solution:

1. **Understanding Gibbs Free Energy (ΔG)**:
The spontaneity of a reaction is determined by the Gibbs free energy change (ΔG). The relationship is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = temperature (in Kelvin)
- ΔS = change in entropy

2. **Conditions for Spontaneity**:
- A reaction is spontaneous when ΔG < 0 (negative).
- A reaction is non-spontaneous when ΔG > 0 (positive).

3. **Analyzing the Given Conditions**:
- The reaction is spontaneous at low temperatures (ΔG < 0).
- The reaction is non-spontaneous at high temperatures (ΔG > 0).

4. **Implications of the Conditions**:
- At low temperatures, the term \( -T \Delta S \) becomes less significant, allowing ΔH to dominate. This suggests that ΔH must be negative (exothermic reaction) for ΔG to be negative.
- At high temperatures, the term \( -T \Delta S \) becomes more significant. For ΔG to become positive, ΔS must also be negative (indicating a decrease in entropy).

5. **Conclusion**:
Based on the analysis:
- ΔH must be negative (exothermic reaction).
- ΔS must be negative (decrease in entropy).
Therefore, the correct option is:
**Option D: ΔH is negative and ΔS is negative.**