For a reaction to be spontaneous at any temperature, the conditions are

Options

A. `DeltaH=+ve, DeltaS=+ve`
B. `DeltaH=-ve, DeltaS=-ve`
C. `DeltaH=+ve, DeltaS=-ve`
D. `DeltaH=-ve, DeltaS=+ve`

Explanation

To determine the conditions for a reaction to be spontaneous at any temperature, we can analyze the Gibbs free energy equation:

### Step-by-Step Solution:

1. **Understand the Gibbs Free Energy Equation**:
The Gibbs free energy change (ΔG) for a reaction is given 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

2. **Condition for Spontaneity**:
For a reaction to be spontaneous, ΔG must be negative:
\[ \Delta G < 0 \]
This implies:
\[ \Delta H - T \Delta S < 0 \]

3. **Rearranging the Equation**:
Rearranging the inequality gives us:
\[ \Delta H < T \Delta S \]
This means that the enthalpy change must be less than the product of temperature and entropy change.

4. **Analyzing the Signs of ΔH and ΔS**:
- If ΔH is positive (endothermic reaction) and ΔS is positive (increase in disorder), the reaction can be spontaneous at high temperatures because the TΔS term can outweigh ΔH.
- If ΔH is negative (exothermic reaction) and ΔS is positive, the reaction is spontaneous at all temperatures because both terms contribute to making ΔG negative.
- If ΔH is positive and ΔS is negative, the reaction is non-spontaneous at all temperatures.
- If ΔH is negative and ΔS is negative, the reaction can be spontaneous at low temperatures.

5. **Conclusion**:
For a reaction to be spontaneous at any temperature, the necessary condition is:
- ΔH must be negative (exothermic) and ΔS must be positive (increase in disorder).

### Final Answer:
The conditions for a reaction to be spontaneous at any temperature are:
- ΔH < 0 (ΔH is negative)
- ΔS > 0 (ΔS is positive)