Which of the following is correct ?

Options

A. `{:(DeltaH , DeltaS, " Nature of reaction ") , ((+),(-), "Nonspontaneous regardless of temperature "):}`
B. `{:(DeltaH , DeltaS, " Nature of reaction ") ,( (-),(+), "Spontaneous only at high temperature"):}`
C. `{:(DeltaH , DeltaS, " Nature of reaction "),((+),(+),"Spontaneous only at low temperature"):}`
D. `{:(DeltaH , DeltaS, " Nature of reaction ") ,((+),(-),"Spontaneous at all temperatures "):}`

Answer

To determine which of the given statements about the thermodynamic properties of reactions is correct, we will analyze each option based on the relationship between Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS). The key equation we will use is:

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

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

### Step-by-Step Solution:

1. **Analyze Option 1:**
- Given: ΔH is positive, ΔS is negative.
- According to the equation, if ΔH is positive and ΔS is negative, then:
\[ \Delta G = \Delta H - T \Delta S > 0 \quad (\text{for all } T) \]
- This means the reaction is non-spontaneous at all temperatures.
- **Conclusion:** This option is correct.

2. **Analyze Option 2:**
- Given: ΔH is negative, ΔS is positive.
- In this case:
\[ \Delta G = \Delta H - T \Delta S < 0 \quad (\text{for all } T) \]
- This indicates that the reaction is spontaneous at all temperatures, not just at high temperatures.
- **Conclusion:** This option is incorrect.

3. **Analyze Option 3:**
- Given: ΔH is positive, ΔS is positive.
- Here:
\[ \Delta G = \Delta H - T \Delta S \]
- For spontaneity, we need:
\[ T \Delta S > \Delta H \]
- This means the reaction can be spontaneous at high temperatures, but not at low temperatures.
- **Conclusion:** This option is incorrect.

4. **Analyze Option 4:**
- Given: ΔH is positive, ΔS is negative.
- Similar to Option 1:
\[ \Delta G = \Delta H - T \Delta S > 0 \quad (\text{for all } T) \]
- This indicates that the reaction is non-spontaneous at all temperatures.
- **Conclusion:** This option is incorrect.

### Final Conclusion:
The only correct statement is from **Option 1**: ΔH is positive, ΔS is negative, indicating the reaction is non-spontaneous at all temperatures.