If the bond energies are as follows (i) `C-h=413.8 KJ` (ii) Cl-Cl=238.0 KJ) (iii) C-Cl=327.2 KJ (iv) H-Cl=429.8 KJ
the enthalpy of the reaction : `CH_(4)+2Cl_(2) rarr CH_(2)Cl_(2)+2HCl` will be

Options

A. `+202.6 kJ`
B. `-202.6 KJ`
C. `+220.1 KJ`
D. `+870 KJ`

Answer

To find the enthalpy change for the reaction \( CH_4 + 2Cl_2 \rightarrow CH_2Cl_2 + 2HCl \), we will use the bond energies provided. The enthalpy change can be calculated using the formula:

\[ \Delta H = \text{(Total bond energies of reactants)} - \text{(Total bond energies of products)} \]

### Step 1: Identify the bonds in the reactants
In the reactants \( CH_4 + 2Cl_2 \):
- \( CH_4 \) has 4 C-H bonds.
- \( 2Cl_2 \) has 2 Cl-Cl bonds.

### Step 2: Calculate the total bond energy for the reactants
Using the bond energies provided:
- Bond energy of C-H = 413.8 kJ
- Bond energy of Cl-Cl = 238.0 kJ

Calculating the total bond energy for the reactants:
\[ \text{Total bond energy of reactants} = (4 \times 413.8) + (2 \times 238.0) \]
\[ = 1655.2 + 476.0 = 2131.2 \text{ kJ} \]

### Step 3: Identify the bonds in the products
In the products \( CH_2Cl_2 + 2HCl \):
- \( CH_2Cl_2 \) has 2 C-H bonds and 2 C-Cl bonds.
- \( 2HCl \) has 2 H-Cl bonds.

### Step 4: Calculate the total bond energy for the products
Using the bond energies provided:
- Bond energy of C-Cl = 327.2 kJ
- Bond energy of H-Cl = 429.8 kJ

Calculating the total bond energy for the products:
\[ \text{Total bond energy of products} = (2 \times 413.8) + (2 \times 327.2) + (2 \times 429.8) \]
\[ = 827.6 + 654.4 + 859.6 = 2341.6 \text{ kJ} \]

### Step 5: Calculate the enthalpy change
Now, we can find the enthalpy change:
\[ \Delta H = \text{Total bond energy of reactants} - \text{Total bond energy of products} \]
\[ = 2131.2 - 2341.6 = -210.4 \text{ kJ} \]

### Step 6: Conclusion
The enthalpy change for the reaction \( CH_4 + 2Cl_2 \rightarrow CH_2Cl_2 + 2HCl \) is approximately \(-210.4 \text{ kJ}\).

Since the closest option is \(-202.6 \text{ kJ}\), we conclude that the answer is:
\[ \Delta H \approx -202.6 \text{ kJ} \]