The spontaneous nature of a reaction is impossible if

Options

A. `DeltaH " is " +ve, DeltaS` is also +ve
B. `DeltaH" is "-ve, DeltaS` is also - ve
C. `DeltaH " is " -ve, DeltaS` is + ve
D. `DeltaH " is " +ve, DeltaS` is -ve

Explanation

To determine the conditions under which the spontaneous nature of a reaction is impossible, we need to analyze the Gibbs free energy change (ΔG) using the equation:

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

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

A reaction is spontaneous when ΔG is negative. Now, let's evaluate each option provided in the question.

### Step 1: Analyze Each Option

**Option 1: ΔH is positive, ΔS is positive**
- Here, ΔG = ΔH - TΔS = positive - T(positive)
- This can be negative if TΔS is greater than ΔH. Therefore, ΔG can be negative, and the reaction can be spontaneous.

**Option 2: ΔH is negative, ΔS is negative**
- Here, ΔG = ΔH - TΔS = negative - T(negative)
- This simplifies to ΔG = negative + T(positive), which can also be negative if the magnitude of ΔH is greater than TΔS. Thus, ΔG can be negative, and the reaction can be spontaneous.

**Option 3: ΔH is negative, ΔS is positive**
- Here, ΔG = ΔH - TΔS = negative - T(positive)
- This simplifies to ΔG = negative - T(positive), which will always be negative. Therefore, the reaction is spontaneous.

**Option 4: ΔH is positive, ΔS is negative**
- Here, ΔG = ΔH - TΔS = positive - T(negative)
- This simplifies to ΔG = positive + T(positive), which will always be positive. Thus, ΔG cannot be negative, and the reaction is non-spontaneous.

### Conclusion
The spontaneous nature of a reaction is impossible if **ΔH is positive and ΔS is negative** (Option 4). In this case, ΔG will always be positive, indicating that the reaction cannot occur spontaneously.

### Final Answer
The correct option is **Option 4: ΔH is positive, ΔS is negative**.

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