The standard enthalpy of formation `(Delta_(f)H^(@))` at `298K ` for methane `(CH_(4(g)))` is `-74.8kJ mol^(-1)`. The additional information required to determine the average energy for `C-H` bond formation would be `:`

Options

A. The dissociation energy of hydrogen molecule, `H_(2)`
B. The dissociation energy of `H _ (2)` and enthalpy of sublimation of carbon
C. Latent heat of vaporization of methane
D. The first four ionization energies of carbon and electron gain enthalpy of hydrogen

Explanation

To determine the average energy for C-H bond formation in methane (CH₄), we need to consider the enthalpy changes involved in the formation of methane from its constituent elements in their standard states. The standard enthalpy of formation (ΔfH°) for methane is given as -74.8 kJ/mol at 298 K.

### Step-by-Step Solution:

1. **Understanding the Formation Reaction**:
The standard enthalpy of formation for methane can be represented by the following reaction:
\[ C(s) + 2H_2(g) \rightarrow CH_4(g) \]
Here, carbon is in its solid state (graphite), and hydrogen is in its gaseous state.

2. **Identifying Required Enthalpy Changes**:
To find the average energy of C-H bond formation, we need to consider the enthalpy changes associated with:
- The sublimation of carbon from solid to gas.
- The dissociation of hydrogen gas into atomic hydrogen.

3. **Enthalpy of Sublimation of Carbon**:
The enthalpy of sublimation (ΔH_sub) is the energy required to convert solid carbon to gaseous carbon:
\[ C(s) \rightarrow C(g) \]
This value is necessary to account for the energy needed to convert solid carbon into gaseous form before it can bond with hydrogen.

4. **Dissociation Energy of Hydrogen**:
The dissociation energy of hydrogen (D_H-H) is the energy required to dissociate molecular hydrogen (H₂) into atomic hydrogen:
\[ H_2(g) \rightarrow 2H(g) \]
Since we need 2 moles of hydrogen to form one mole of methane, we will need the dissociation energy for 2 moles of H₂.

5. **Calculating the Average Energy of C-H Bonds**:
The average energy of C-H bond formation can be calculated using the following relationship:
\[ \Delta_fH° = \Delta H_{sub} + D_{H-H} - \text{(Energy of C-H bonds)} \]
Rearranging gives us:
\[ \text{Energy of C-H bonds} = \Delta H_{sub} + D_{H-H} + \Delta_fH° \]
By substituting the known values, we can find the average energy of the C-H bonds.

### Conclusion:
To determine the average energy for C-H bond formation, we need:
- The dissociation energy of H₂ (to account for the formation of atomic hydrogen).
- The enthalpy of sublimation of carbon (to account for the conversion of solid carbon to gaseous carbon).