Which of the following conditions reagarding a chemical process ensures its spontaneity at all temperature?

Options

A. `Delta H gt 0, DeltaS lt 0`
B. `Delta H lt 0, DeltaS gt 0`
C. `Delta H lt 0, DeltaS lt 0`
D. `Delta H gt 0, DeltaS lt 0`

Explanation

To determine the conditions that ensure the spontaneity of a chemical process at all temperatures, we can analyze the Gibbs free energy change (ΔG) of the process. The spontaneity of a process is indicated by the sign of ΔG:

1. **Understanding Gibbs Free Energy**:
The Gibbs free energy change 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 process to be spontaneous, ΔG must be negative (ΔG < 0).

3. **Analyzing the Equation**:
- If ΔH is negative (ΔH < 0), it indicates that the reaction is exothermic.
- If ΔS is positive (ΔS > 0), it indicates an increase in disorder or randomness in the system.

4. **Combining Conditions**:
- If ΔH is negative and ΔS is positive, we can analyze the equation:
\[ \Delta G = \Delta H - T \Delta S \]
- As T increases, the term \( -T \Delta S \) becomes more negative (since ΔS is positive), which will ensure that ΔG remains negative.
- Therefore, under these conditions (ΔH < 0 and ΔS > 0), ΔG will be negative at all temperatures.

5. **Conclusion**:
The conditions that ensure spontaneity at all temperatures are:
- ΔH must be less than 0 (ΔH < 0)
- ΔS must be greater than 0 (ΔS > 0)

Now, we can identify the correct option from the given choices based on these conditions.

**Final Answer**: The correct option is that ΔH < 0 and ΔS > 0 ensures spontaneity at all temperatures.

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