Bond enthalpies in kJ/mol: C-H in methane 439; Br₂ 193, H-Br 366, CH₃-Br 293; I₂ 151, H-I 299…

Step 1. Bromine, step 1. $439 - 366 = +73\ \text{kJ/mol}$.

Step 2. Bromine, step 2. $193 - 293 = -100\ \text{kJ/mol}$.

Step 3. Iodine, overall. Step 1: $439\ \text{kJ/mol} - 299\ \text{kJ/mol} = +140\ \text{kJ/mol}$. Step 2: $151\ \text{kJ/mol} - 234\ \text{kJ/mol} = -83\ \text{kJ/mol}$. The sum is $+57\ \text{kJ/mol}$. The reaction takes in energy overall.

Step 4. Chlorine. Step 1: $439\ \text{kJ/mol} - 431\ \text{kJ/mol} = +8\ \text{kJ/mol}$. Step 2: $243\ \text{kJ/mol} - 351\ \text{kJ/mol} = -108\ \text{kJ/mol}$. The overall change is $-100\ \text{kJ/mol}$ of methane.

Step 5. Heat released. $\dfrac{8.00\ \text{g}}{16.0\ \text{g/mol}} = 0.500\ \text{mol}$, so $0.500\ \text{mol} \times 100\ \text{kJ/mol} = 50.0\ \text{kJ}$ is released.