Assertion : If both `DeltaH^(@) and DeltaS^(@)` are positive then reaction will be spontaneous at high temperature.
Reason : All processes with positive entropy chang are spontaneous.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that if both ΔH (enthalpy change) and ΔS (entropy change) are positive, then the reaction will be spontaneous at high temperatures.

### Step 2: Analyze the Gibbs Free Energy Equation
The spontaneity of a reaction is determined by the Gibbs Free Energy change (ΔG), which is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- ΔG = Gibbs Free Energy change
- ΔH = Enthalpy change
- T = Temperature (in Kelvin)
- ΔS = Entropy change

### Step 3: Substitute the Values
Since both ΔH and ΔS are positive:
- ΔH > 0
- ΔS > 0

At high temperatures (T is large), the term \( T \Delta S \) will also be positive and can become larger than ΔH.

### Step 4: Determine the Sign of ΔG
As temperature increases, the \( T \Delta S \) term will dominate, leading to:
\[ \Delta G = \Delta H - T \Delta S \]
Since both ΔH and \( T \Delta S \) are positive, at sufficiently high temperatures, \( T \Delta S \) can exceed ΔH, making ΔG negative:
\[ \Delta G < 0 \]
This indicates that the reaction is spontaneous at high temperatures.

### Step 5: Understand the Reason
The reason states that all processes with a positive entropy change are spontaneous. While it is true that an increase in entropy (positive ΔS) contributes to spontaneity, it is not the sole factor. The overall spontaneity also depends on the enthalpy change and temperature.

### Step 6: Conclusion
- The assertion is true: If both ΔH and ΔS are positive, the reaction can be spontaneous at high temperatures.
- The reason is false: Not all processes with positive entropy change are spontaneous; it also depends on ΔH and temperature.

### Final Answer
The correct answer is that the assertion is true, but the reason is false. Therefore, the answer is option C.

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