Assertion.The bond enthalpy of C-H bondin `CH_(4)` is nearly 416 k J `mol^(-1)`
Reason . First , second, third and fourth C-H bonds in `CH_(4)` have same bond enthalpy.

Options

A. If both A and R are true,andR is the true explanation of A.
B. If both A and R are true,but R is not the true explanation of A.
C. If A is true, but R is false
D. If both A and R are false.

Answer

To solve the given question, we need to analyze the assertion and reason statements regarding the bond enthalpy of C-H bonds in methane (CH₄).

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the bond enthalpy of the C-H bond in CH₄ is nearly 416 kJ/mol.
- To verify this, we need to calculate the average bond enthalpy of the C-H bonds in CH₄.

2. **Bond Dissociation Enthalpy**:
- The bond dissociation enthalpy is the energy required to break a bond in a molecule.
- For CH₄, we can consider the following bond dissociation steps:
- CH₄ → CH₃ + H (ΔH = +427 kJ/mol)
- CH₃ → CH₂ + H (ΔH = +439 kJ/mol)
- CH₂ → CH + H (ΔH = +452 kJ/mol)
- CH → C + H (ΔH = +347 kJ/mol)

3. **Calculating Total Bond Enthalpy**:
- Now, we sum these bond dissociation enthalpies:
\[ \text{Total } ΔH = 427 + 439 + 452 + 347 = 1665 \text{ kJ/mol} \]

4. **Calculating Average Bond Enthalpy**:
- Since there are 4 C-H bonds in CH₄, we can find the average bond enthalpy by dividing the total bond enthalpy by 4:
\[ \text{Average bond enthalpy} = \frac{1665 \text{ kJ/mol}}{4} \approx 416.25 \text{ kJ/mol} \]
- This confirms that the bond enthalpy of the C-H bond in CH₄ is indeed approximately 416 kJ/mol.

5. **Understanding the Reason**:
- The reason states that the first, second, third, and fourth C-H bonds in CH₄ have the same bond enthalpy.
- From our calculations, we see that the bond enthalpies are not identical; they vary for each bond.

6. **Conclusion**:
- The assertion is true as the bond enthalpy is approximately 416 kJ/mol.
- The reason is false as the bond enthalpies of the C-H bonds are not the same.
- Therefore, the correct answer is that the assertion is true but the reason is false.

### Final Answer:
Assertion is true, but the reason is false.

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