Average C – H bond energy is `416 kJ mol^(-1)` . Which of the following is correct?

Options

A. `CH_(4) (g) + 416k J rarr C(g) + 4H (g)`
B. `CH_(4)(g) rarr C(g) + 4H(g) + 416 kJ`
C. `CH_4 (g) + 1664 kJ rarr C(g) + 4H(g)`
D. `CH_(4)(g) rarr C(g) + 4H(g) + 1664 kJ`

Explanation

To solve the problem regarding the average C-H bond energy and determine which statement is correct, we can follow these steps:

### Step 1: Understand the C-H Bond Energy
The average C-H bond energy is given as 416 kJ/mol. This means that to break one C-H bond in a molecule, we need to provide 416 kJ of energy.

### Step 2: Analyze the Molecule CH4
In the molecule methane (CH4), there are four C-H bonds. To break all four C-H bonds in one mole of CH4, we need to calculate the total energy required.

### Step 3: Calculate Total Energy Required
To find the total energy required to break all four C-H bonds in CH4, we multiply the bond energy by the number of bonds:
\[ \text{Total Energy} = \text{Number of C-H bonds} \times \text{Average C-H bond energy} \]
\[ \text{Total Energy} = 4 \times 416 \text{ kJ/mol} \]
\[ \text{Total Energy} = 1664 \text{ kJ/mol} \]

### Step 4: Conclusion
The energy required to break one mole of CH4 into its constituent atoms (1 mole of carbon gas and 4 moles of hydrogen gas) is 1664 kJ. Therefore, if the question provides options, the correct option would be the one that states that breaking CH4 into C and H2 requires 1664 kJ of energy.