Match the column :-
`{:(,"Sign of" DeltaH&DeltaS"respectively",,"Nature of reaction",),(,-&-,P,"Spontaneous only at low temperture",),(,-&+,Q,"Spontaneous only at high temp.",),(,+&+,R,"Spontaneous at all temperature",),(,+&-,S,"non spontaneous at all temperature",):}`

Options

A. `AtoP,BtoR,CtoQ,DtoS`
B. `AtoR,BtoP,CtoP,DtoS`
C. `AtoQ,BtoR,CtoP,DtoS`
D. `AtoP,BtoQ,CtoR,DtoS`

Answer

To solve the problem of matching the signs of ΔH and ΔS with the nature of the reaction, we need to analyze the thermodynamic equation:

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

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

### Step-by-Step Solution:

1. **Identify the Conditions for Spontaneity:**
- A reaction is spontaneous if ΔG < 0.
- The signs of ΔH and ΔS will determine the spontaneity of the reaction at different temperatures.

2. **Case 1: ΔH < 0 (negative) and ΔS > 0 (positive)**
- Here, ΔG = ΔH - TΔS will always be negative regardless of the temperature.
- **Nature of Reaction:** Spontaneous at all temperatures.
- **Match:** A → R

3. **Case 2: ΔH > 0 (positive) and ΔS < 0 (negative)**
- Here, ΔG = ΔH - TΔS will always be positive regardless of the temperature.
- **Nature of Reaction:** Non-spontaneous at all temperatures.
- **Match:** D → S

4. **Case 3: ΔH < 0 (negative) and ΔS < 0 (negative)**
- At low temperatures, TΔS is small, so ΔG can be negative (spontaneous).
- At high temperatures, TΔS becomes significant and can make ΔG positive (non-spontaneous).
- **Nature of Reaction:** Spontaneous only at low temperature.
- **Match:** B → P

5. **Case 4: ΔH > 0 (positive) and ΔS > 0 (positive)**
- At low temperatures, ΔG can be positive (non-spontaneous).
- At high temperatures, TΔS becomes significant and can make ΔG negative (spontaneous).
- **Nature of Reaction:** Spontaneous only at high temperature.
- **Match:** C → Q

### Final Matches:
- A → R (Spontaneous at all temperatures)
- B → P (Spontaneous only at low temperature)
- C → Q (Spontaneous only at high temperature)
- D → S (Non-spontaneous at all temperatures)

### Summary of Matches:
- **A:** R (Spontaneous at all temperatures)
- **B:** P (Spontaneous only at low temperature)
- **C:** Q (Spontaneous only at high temperature)
- **D:** S (Non-spontaneous at all temperatures)