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 1: Write the target reaction
The enthalpy of formation of methane can be represented as:
\[ \text{C(s)} + 2\text{H}_2(g) \rightarrow \text{CH}_4(g) \]

### Step 2: Write down the given reactions and their enthalpy changes
1. \( \text{C(s)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \)
...