The value of `DeltaH_("transition")` of C (graphite) `rarr` C (diamond) is 1.9 kJ/mol at `25^(@)C`. Entropy of graphite is higher than entropy of diamond. This implies that :

Options

A. C (diamond) is more thermodynamically stable than C (graphite) at `25^(@)C`
B. C (graphite) is more thermodynamically stable than C (diamond) at `25^(@)C`
C. diamond will provide more heat on complete combustion at `25^(@)C`
D. `DeltaG_("transition")` of C (diamond) `rarr` C (graphite) is - ve

Explanation

To analyze the thermodynamic stability of graphite and diamond based on the given information, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Given Data**:
- The enthalpy change for the transition from graphite to diamond is given as ΔH_transition = 1.9 kJ/mol at 25°C.
- It is stated that the entropy of graphite is higher than that of diamond.

2. **Using the Gibbs Free Energy Equation**:
- The Gibbs Free Energy change (ΔG) for a process can be calculated using the formula:
\[ \Delta G = \Delta H - T \Delta S \]
- Here, ΔH is the enthalpy change, T is the temperature in Kelvin, and ΔS is the change in entropy.

3. **Analyzing the Entropy Change**:
- Since the entropy of graphite is higher than that of diamond, we can conclude that ΔS (entropy change) for the transition from graphite to diamond is negative (ΔS < 0).

4. **Calculating ΔG for the Transition**:
- Substituting the values into the Gibbs Free Energy equation:
\[ \Delta G = 1.9 \, \text{kJ/mol} - (298 \, \text{K}) \times (\Delta S) \]
- Since ΔS is negative, the term \(T \Delta S\) will be negative, making ΔG positive.

5. **Interpreting the Result**:
- A positive ΔG indicates that the transition from graphite to diamond is non-spontaneous at 25°C. Therefore, graphite is more thermodynamically stable than diamond at this temperature.

6. **Evaluating the Options**:
- Based on the analysis:
- **Option B**: C (graphite) is more thermodynamically stable than C (diamond) at 25°C. (True)
- **Option C**: C (diamond) is more thermodynamically stable than C (graphite) at 25°C. (False)
- **Option D**: Diamond will provide more heat on complete combustion than graphite. (True, as diamond has a higher enthalpy of combustion)

### Conclusion:
The correct implications from the given data are:
- C (graphite) is more thermodynamically stable than C (diamond) at 25°C.
- Diamond provides more heat on complete combustion than graphite.