If `Delta H = +ve and Delta S = +ve`, the rection is spontaneous at ……. Temperature

Answer

To determine the temperature at which a reaction is spontaneous given that both ΔH (enthalpy change) and ΔS (entropy change) are positive, we can use the Gibbs free energy equation:

### Step-by-Step Solution:

1. **Understand the Gibbs Free Energy Equation**:
The Gibbs free energy (ΔG) is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- ΔG = Gibbs free energy change
- ΔH = change in enthalpy
- T = temperature (in Kelvin)
- ΔS = change in entropy

2. **Condition for Spontaneity**:
A reaction is spontaneous when ΔG is less than 0 (ΔG < 0).

3. **Substituting the Given Values**:
Since we know that ΔH is positive (ΔH > 0) and ΔS is also positive (ΔS > 0), we can substitute these values into the Gibbs free energy equation:
\[ \Delta G = \text{positive} - T \times \text{positive} \]

4. **Rearranging the Equation**:
For the reaction to be spontaneous (ΔG < 0), we need:
\[ \Delta H - T \Delta S < 0 \]
This can be rearranged to:
\[ \Delta H < T \Delta S \]

5. **Solving for Temperature (T)**:
To find the temperature at which this condition holds, we can rearrange the inequality:
\[ T > \frac{\Delta H}{\Delta S} \]
This means that the temperature must be greater than the ratio of ΔH to ΔS.

6. **Conclusion**:
Since both ΔH and ΔS are positive, the temperature must be sufficiently high for the reaction to be spontaneous. Therefore, the reaction is spontaneous at **high temperatures**.

### Final Answer:
The reaction is spontaneous at **high temperatures**.