Calculate enthalpy of formation of methane `(CH_4)` from the following data :
(i) `C(s) + O_(2)(g) to CO_(2) (g) , Delta_rH^(@) = -393.5 KJ mol^(-1)`
(ii) `H_2(g) + 1/2 O_(2)(g) to H_(2)O(l) , Deta_r H^(@) = -285.5 kJ mol^(-1)`
(iii) `CH_(4)(g) + 2O_(2)(g) to CO_(2)(g) + 2H_(2)O(l), Delta_(r)H^(@) = -890.3 kJ mol^(-1)`.

Explanation

To calculate the enthalpy of formation of methane (CH₄) from the given data, we can use Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction.

### Step-by-Step Solution:

1. **Write down the reactions and their enthalpy changes:**
- Reaction 1: \( C(s) + O_2(g) \rightarrow CO_2(g) \)
- \( \Delta_rH^\circ = -393.5 \, \text{kJ/mol} \)
- Reaction 2: \( H_2(g) + \frac{1}{2} O_2(g) \rightarrow H_2O(l) \)
...