If `Delta H gt 0` and `Delta S gt 0`, the reaction proceeds spontaneously when :-

Options

A. `Delta H gt 0`
B. `Delta H lt T Delta S`
C. `Delta H = T Delta S`
D. None

Answer

To determine when a reaction with \(\Delta H > 0\) and \(\Delta S > 0\) proceeds spontaneously, we can use the Gibbs free energy equation:

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

### Step-by-Step Solution:

1. **Understand the Gibbs Free Energy Equation**:
The Gibbs free energy change (\(\Delta G\)) determines the spontaneity of a reaction. A reaction is spontaneous when \(\Delta G < 0\).

2. **Identify the Conditions**:
We are given that \(\Delta H > 0\) (the reaction is endothermic) and \(\Delta S > 0\) (the disorder of the system increases).

3. **Set Up the Inequality for Spontaneity**:
For the reaction to be spontaneous, we need:
\[ \Delta G < 0 \]
Substituting the Gibbs free energy equation:
\[ \Delta H - T \Delta S < 0 \]

4. **Rearranging the Inequality**:
Rearranging the equation gives:
\[ \Delta H < T \Delta S \]

5. **Determine the Temperature Condition**:
Since \(\Delta H\) is positive, for the inequality \(\Delta H < T \Delta S\) to hold true, the temperature \(T\) must be sufficiently high. Therefore, the reaction will be spontaneous at high temperatures.

6. **Conclusion**:
The reaction proceeds spontaneously when the temperature \(T\) is greater than \(\frac{\Delta H}{\Delta S}\).

### Final Answer:
The reaction proceeds spontaneously when \(T > \frac{\Delta H}{\Delta S}\).