A reaction occurs spontaneously in forward direction if

Options

A. (A) `T Delta S gt Delta H` where `Delta H` is positive and `Delta S` is negative.
B. (B) `T Delta S = Delta H` where both `Delta H and Delta S` are positive
C. (C) `T Delta S lt Delta H` where both `Delta H and Delta S` are positive
D. (D)`T Delta S gt Delta H` where both `Delta H and Delta S` are positive

Answer

To determine the condition under which a reaction occurs spontaneously in the forward direction, we can analyze the relationship between Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) using the equation:

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

### Step-by-Step Solution:

1. **Understanding the Gibbs Free Energy Equation**:
- The Gibbs free energy change (ΔG) indicates the spontaneity of a reaction. A reaction is spontaneous in the forward direction if ΔG < 0.

2. **Condition for Spontaneity**:
- Rearranging the Gibbs free energy equation gives us:
\[ \Delta G < 0 \implies \Delta H - T \Delta S < 0 \implies \Delta H < T \Delta S \]
- This means that for a reaction to be spontaneous, the term \(T \Delta S\) must be greater than ΔH.

3. **Analyzing the Options**:
- **Option A**: \(T \Delta S > \Delta H\) with ΔH positive and ΔS negative.
- Here, ΔG would be positive, making the reaction non-spontaneous. **Incorrect**.

- **Option B**: \(T \Delta S = \Delta H\).
- In this case, ΔG = 0, indicating equilibrium. The reaction is neither spontaneous nor non-spontaneous. **Incorrect**.

- **Option C**: \(T \Delta S < \Delta H\) with both ΔH and ΔS positive.
- Here, ΔG would also be positive since ΔH is greater than \(T \Delta S\). This means the reaction is non-spontaneous. **Incorrect**.

- **Option D**: \(T \Delta S > \Delta H\) with both ΔH and ΔS positive.
- In this case, ΔG would be negative because \(T \Delta S\) is greater than ΔH. This indicates that the reaction is spontaneous in the forward direction. **Correct**.

### Conclusion:
The correct condition for a reaction to occur spontaneously in the forward direction is:
\[ T \Delta S > \Delta H \]