The suitable thermodynamic conditions for a spontaneous reaction at all temperature are

Options

A. `DeltaHgt0, DeltaSlt0`
B. `DeltaHlt0, DeltaSgt0`
C. `DeltaHgt0, DeltaSgt0`
D. `DeltaHlt0, DeltaSlt0`

Answer

To determine the suitable thermodynamic conditions for a spontaneous reaction at all temperatures, we need to analyze the Gibbs free energy change (ΔG) equation, which is given by:

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

Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = temperature in Kelvin
- ΔS = change in entropy

### Step-by-Step Solution:

1. **Understanding Spontaneity**:
A reaction is considered spontaneous if the change in Gibbs free energy (ΔG) is less than zero (ΔG < 0).

2. **Analyzing the Gibbs Free Energy Equation**:
From the equation ΔG = ΔH - TΔS, we can see that:
- If ΔH is negative (ΔH < 0), it indicates that the reaction is exothermic, which favors spontaneity.
- If ΔS is positive (ΔS > 0), it indicates an increase in disorder, which also favors spontaneity.

3. **Combining Conditions for All Temperatures**:
For a reaction to be spontaneous at all temperatures, we need to ensure that the conditions hold true regardless of the temperature (T):
- If ΔH < 0 (negative enthalpy change) and ΔS > 0 (positive entropy change), then:
- As T increases, the term -TΔS becomes more negative, which means ΔG will continue to remain negative.

4. **Conclusion**:
Therefore, the suitable thermodynamic conditions for a spontaneous reaction at all temperatures are:
- ΔH < 0 (enthalpy change is negative)
- ΔS > 0 (entropy change is positive)

### Final Answer:
The suitable thermodynamic conditions for a spontaneous reaction at all temperatures are:
- ΔH < 0 and ΔS > 0.