The heat of formation of `CO_(2)` is -407 kJ/mol. The energy required for the process `3CO_(2)(g) rarr 3C(g) + 2O_(3)(g)` is

Options

A. Less than 1221 kJ
B. More than 1221 kJ
C. Is equal to 1221 kJ
D. Cannot be predicted

Answer

To solve the problem, we need to determine the energy required for the process \(3CO_2(g) \rightarrow 3C(g) + 2O_3(g)\) given that the heat of formation of \(CO_2\) is \(-407 \, \text{kJ/mol}\).

### Step-by-Step Solution:

1. **Understanding Heat of Formation**: The heat of formation of \(CO_2\) is given as \(-407 \, \text{kJ/mol}\). This means that when 1 mole of \(CO_2\) is formed from its elements (carbon and oxygen), \(407 \, \text{kJ}\) of energy is released.

2. **Writing the Formation Reaction**: The formation reaction for \(CO_2\) from its elements can be written as:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \quad \Delta H = -407 \, \text{kJ} \]

3. **Dissociation Reaction**: The reaction we are interested in is the reverse of the formation reaction, which is the dissociation of \(CO_2\):
\[ 3CO_2(g) \rightarrow 3C(g) + 3O_2(g) \]
Since this is the reverse process, the enthalpy change will be positive:
\[ \Delta H = +3 \times 407 \, \text{kJ} = +1221 \, \text{kJ} \]

4. **Energy Required for the Given Reaction**: The energy required for the dissociation of \(3CO_2\) into \(3C\) and \(3O_2\) is therefore \(+1221 \, \text{kJ}\).

5. **Final Reaction**: However, the question asks for the process:
\[ 3CO_2(g) \rightarrow 3C(g) + 2O_3(g) \]
To find the energy required for this reaction, we need to consider the formation of \(O_3\) from \(O_2\):
- The formation of \(O_3\) from \(O_2\) can be represented as:
\[ 3O_2(g) \rightarrow 2O_3(g) \quad \Delta H = +\text{(value to be determined)} \]
The energy required for this reaction needs to be added to the energy required for the dissociation of \(3CO_2\).

6. **Calculating Total Energy**: The total energy required for the process \(3CO_2(g) \rightarrow 3C(g) + 2O_3(g)\) is:
\[ \Delta H_{total} = \Delta H_{dissociation} + \Delta H_{formation \, O_3} \]
Assuming the formation of \(O_3\) from \(O_2\) is known or can be calculated, we can add that to \(1221 \, \text{kJ}\).

### Conclusion:
The energy required for the process \(3CO_2(g) \rightarrow 3C(g) + 2O_3(g)\) is \(1221 \, \text{kJ}\) plus the energy associated with the formation of \(O_3\) from \(O_2\).