`4.8 g` of `C` (diamond) on complete combustion evolves`1584 kJ` of heat. The standard heat of formation of gaseous carbon is `725 kJ//mol`. The energy required for the process
C(graphite) `rarr` C(gas)
C(diamond) `rarr` C(gas) are

Options

A. 725, 727
B. 727, 725
C. 725, 723
D. None of these

Explanation

To solve the problem, we need to calculate the energy required for the following processes:

1. \( C(\text{graphite}) \rightarrow C(\text{gas}) \)
2. \( C(\text{diamond}) \rightarrow C(\text{gas}) \)

### Step 1: Understand the Given Data
- The heat evolved during the complete combustion of 4.8 g of carbon (diamond) is 1584 kJ.
- The standard heat of formation of gaseous carbon is given as +725 kJ/mol.

### Step 2: Calculate Moles of Carbon in 4.8 g
The molar mass of carbon (C) is approximately 12 g/mol.

\[ \text{Moles of carbon} = \frac{\text{mass}}{\text{molar mass}} = \frac{4.8 \, \text{g}}{12 \, \text{g/mol}} = 0.4 \, \text{mol} \]

### Step 3: Calculate the Heat Released per Mole of Carbon
The total heat released for 0.4 moles of carbon is 1584 kJ. To find the heat released per mole:

\[ \text{Heat released per mole} = \frac{1584 \, \text{kJ}}{0.4 \, \text{mol}} = 3960 \, \text{kJ/mol} \]

### Step 4: Write the Reaction for Combustion of Diamond
The combustion of diamond can be represented as:

\[ C(\text{diamond}) + O_2 \rightarrow CO_2 + \text{heat} \]

The heat released during this reaction is 3960 kJ/mol.

### Step 5: Relate the Two Processes
1. For the process \( C(\text{graphite}) \rightarrow C(\text{gas}) \), the heat of formation is given as +725 kJ/mol.
2. For the process \( C(\text{diamond}) \rightarrow C(\text{gas}) \), we can relate it to the graphite process.

### Step 6: Calculate the Energy Required for \( C(\text{diamond}) \rightarrow C(\text{gas}) \)
Using Hess's law, we can express the energy change for the diamond to gas conversion as:

\[ \Delta H_{\text{diamond to gas}} = \Delta H_{\text{diamond to graphite}} + \Delta H_{\text{graphite to gas}} \]

Where:
- \( \Delta H_{\text{graphite to gas}} = +725 \, \text{kJ/mol} \)
- \( \Delta H_{\text{diamond to graphite}} = -3960 \, \text{kJ/mol} \) (since it is the reverse of combustion)

Thus,

\[ \Delta H_{\text{diamond to gas}} = -3960 + 725 = -3235 \, \text{kJ/mol} \]

### Step 7: Conclusion
The energy required for the process \( C(\text{diamond}) \rightarrow C(\text{gas}) \) is -3235 kJ/mol, indicating that energy is released when diamond converts to gas.

### Summary of Results
1. Energy required for \( C(\text{graphite}) \rightarrow C(\text{gas}) \) = +725 kJ/mol
2. Energy required for \( C(\text{diamond}) \rightarrow C(\text{gas}) \) = -3235 kJ/mol