Under which of the following sets of conditions, `triangleG` is always negative ?

Options

A. `triangleH=-ve and triangleS=+ve`
B. `triangleH=-ve and triangleS=-ve`
C. `triangleH=+ve and triangleS=+ve`
D. `triangleH=+ve and triangleS=-ve`

Answer

To determine under which set of conditions ΔG (Gibbs free energy change) is always negative, we will analyze the four options provided based on the relationship:

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

Where:
- ΔG = Change in Gibbs free energy
- ΔH = Change in enthalpy
- T = Temperature (in Kelvin)
- ΔS = Change in entropy

### Step-by-Step Solution:

1. **Identify the Conditions:**
We need to evaluate the four sets of conditions (not provided in the question, but we will analyze them generally).

2. **Analyze Each Condition:**
- **Condition A:** ΔH < 0 (negative) and ΔS > 0 (positive)
- Here, ΔG = ΔH - TΔS
- Since ΔH is negative and ΔS is positive, TΔS will also be positive.
- Therefore, ΔG will always be negative because it is the subtraction of a positive value from a negative value.
- **Conclusion:** ΔG is always negative in this case.

- **Condition B:** ΔH < 0 (negative) and ΔS < 0 (negative)
- Here, ΔG = ΔH - TΔS
- ΔH is negative and ΔS is negative, which means TΔS will also be negative.
- The sign of ΔG will depend on the temperature (T). At low temperatures, ΔG could be negative, but at high temperatures, TΔS could dominate, making ΔG positive.
- **Conclusion:** ΔG is not always negative.

- **Condition C:** ΔH > 0 (positive) and ΔS > 0 (positive)
- Here, ΔG = ΔH - TΔS
- Both ΔH and TΔS are positive, thus ΔG will be positive for low temperatures and could be negative at high temperatures.
- **Conclusion:** ΔG is not always negative.

- **Condition D:** ΔH > 0 (positive) and ΔS < 0 (negative)
- Here, ΔG = ΔH - TΔS
- ΔH is positive and TΔS is negative, thus ΔG will be positive.
- **Conclusion:** ΔG is not always negative.

3. **Final Conclusion:**
The only condition under which ΔG is always negative is **Condition A** (ΔH < 0 and ΔS > 0).

### Summary:
- **Condition A:** ΔG is always negative.
- **Condition B:** ΔG is not always negative.
- **Condition C:** ΔG is not always negative.
- **Condition D:** ΔG is not always negative.