A reaction occurs spontanecously if `:-`

Options

A. `TDeltaS lt DeltaH` and both `DeltaH and DeltaS` are +ve
B. `TDeltaS gt DeltaH` and both `DeltaH and DeltaS` are +ve
C. `TDeltaS = DeltaH` and both `DeltaH and DeltaS` are +ve
D. `TDeltaS gt DeltaH and DeltaH` is +ve and `DeltaS` is -ve

Explanation

To determine the conditions under which a reaction occurs spontaneously, we need to analyze the Gibbs free energy (ΔG) change for the reaction. The Gibbs free energy is defined 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

A reaction is spontaneous when ΔG is negative (ΔG < 0).

### Step-by-Step Solution:

1. **Understanding the Conditions for Spontaneity:**
- For a reaction to be spontaneous, we need to analyze the signs of ΔH and ΔS.
- There are three main scenarios based on the signs of ΔH and ΔS.

2. **Case 1: ΔH < 0 and ΔS > 0**
- If ΔH is negative (exothermic reaction) and ΔS is positive (increase in entropy), then ΔG will always be negative regardless of the temperature. This means the reaction is spontaneous at all temperatures.

3. **Case 2: ΔH > 0 and ΔS > 0**
- If ΔH is positive (endothermic reaction) and ΔS is positive (increase in entropy), then for ΔG to be negative, we need:
\[ T \Delta S > \Delta H \]
- This condition is satisfied at high temperatures. Thus, the reaction will be spontaneous at high temperatures.

4. **Case 3: ΔH < 0 and ΔS < 0**
- If ΔH is negative and ΔS is negative, then for ΔG to be negative, we need:
\[ T \Delta S < \Delta H \]
- This condition is satisfied at low temperatures. Thus, the reaction will be spontaneous at low temperatures.

5. **Conclusion:**
- Based on the analysis, the correct option for the question "A reaction occurs spontaneously if" is:
- **Option B:** \( T \Delta S > \Delta H \) when both ΔH and ΔS are positive.