The correct thermodynamic conditions for a non-spontaneous reaction at all temperature is

Options

A. `(delta H lt 0 and delta S gt 0)`
B. `(delta H lt 0 and delta S = 0)`
C. `(delta H gt 0 and delta S lt 0)`
D. `(delta H gt 0 and delta S gt 0)`

Answer

To determine the correct thermodynamic conditions for a non-spontaneous reaction at all temperatures, we will analyze the Gibbs free energy (ΔG) and its relationship with enthalpy (ΔH) and entropy (ΔS).

### Step-by-Step Solution:

1. **Understanding Gibbs Free Energy**:
The Gibbs free energy change (ΔG) is a crucial factor in determining the spontaneity of a reaction. The relationship is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = absolute temperature (in Kelvin)
- ΔS = change in entropy

2. **Condition for Non-Spontaneity**:
A reaction is considered non-spontaneous when ΔG is greater than zero:
\[ \Delta G > 0 \]

3. **Rearranging the Equation**:
To find the conditions for non-spontaneity, we can rearrange the Gibbs free energy equation:
\[ \Delta H - T \Delta S > 0 \]
This implies:
\[ \Delta H > T \Delta S \]

4. **Analyzing the Terms**:
- For ΔG to be greater than zero at all temperatures, we need to consider the signs of ΔH and ΔS.
- If ΔH is positive (ΔH > 0), it indicates that the reaction is endothermic.
- If ΔS is negative (ΔS < 0), it indicates that the disorder of the system is decreasing.

5. **Conclusion**:
Therefore, for a reaction to be non-spontaneous at all temperatures, the conditions must be:
- ΔH > 0 (positive enthalpy change)
- ΔS < 0 (negative entropy change)

### Final Answer:
The correct thermodynamic conditions for a non-spontaneous reaction at all temperatures are:
- ΔH > 0 (positive enthalpy change)
- ΔS < 0 (negative entropy change)