A reaction occurs spontaneously if

Options

A. `TDeltaS lt Delta H` and both `Delta H and Delta S are +ve`
B. `TDeltaS gt Delta H` and both `Delta H and Delta S are +ve`
C. `TDeltaS = Delta H` and both `Delta H and Delta S are +ve`
D. `TDeltaS gt Delta H and Delta H is +ve and Delta S is -ve`

Answer

To determine the conditions under which a reaction occurs spontaneously, we will analyze the Gibbs free energy change (ΔG) using the equation:

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

Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = absolute temperature (in Kelvin)
- ΔS = change in entropy

### Step-by-Step Solution:

1. **Understanding Spontaneity**:
- A reaction is spontaneous if ΔG is negative (ΔG < 0). This indicates that the process can occur without external energy input.

2. **Analyzing Different Cases**:
- We will consider four scenarios based on the signs of ΔH and ΔS.

3. **Case 1**: ΔH > TΔS and both ΔH and ΔS are positive.
- Here, ΔG = ΔH - TΔS will be positive because ΔH is greater than TΔS.
- **Conclusion**: Not spontaneous.

4. **Case 2**: TΔS > ΔH and both ΔH and ΔS are positive.
- In this case, ΔG = ΔH - TΔS will be negative because TΔS is greater than ΔH.
- **Conclusion**: Spontaneous.

5. **Case 3**: ΔH = TΔS (both are equal).
- Here, ΔG = ΔH - TΔS = 0.
- **Conclusion**: The reaction is at equilibrium, not spontaneous.

6. **Case 4**: TΔS > ΔH, ΔH is positive, and ΔS is negative.
- In this scenario, ΔG = ΔH - TΔS will be positive because TΔS is negative (since ΔS is negative) and ΔH is positive.
- **Conclusion**: Not spontaneous.

### Summary of Results:
- **Case 1**: ΔG > 0 (Not spontaneous)
- **Case 2**: ΔG < 0 (Spontaneous)
- **Case 3**: ΔG = 0 (Equilibrium)
- **Case 4**: ΔG > 0 (Not spontaneous)

### Final Conclusion:
A reaction occurs spontaneously if ΔG is negative, which happens in Case 2 where TΔS > ΔH and both ΔH and ΔS are positive.