`DeltaU^(@)` of combustion of methane is `-X kJmol^(-1)`. The value of `DeltaH^(@)` is `:`
(i) `= DeltaU^(@)` (ii) ` gt DeltaU^(@)` (iii) `lt DeltaU^(@)` (iv)` = 0`

Explanation

To solve the problem regarding the relationship between ΔU (internal energy change) and ΔH (enthalpy change) for the combustion of methane, we can follow these steps:

### Step 1: Understand the relationship between ΔH and ΔU
The relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔU) is given by the equation:

\[ \Delta H = \Delta U + RT \Delta N_G \]
...