The number of moles of methane required to produce $$11$$ g $$CO_2(g)$$ after complete combustion is : (Given molar mass of methane in $$g mol^{-1} : 16$$)

We need to find the number of moles of methane required to produce 11 g of $$CO_2$$ after complete combustion.

Write the balanced equation for the complete combustion of methane

$$CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$$

From the balanced equation, 1 mole of $$CH_4$$ produces 1 mole of $$CO_2$$. This is a 1:1 molar ratio.

Calculate the moles of $$CO_2$$ produced

The molar mass of $$CO_2 = 12 + 2(16) = 44$$ g/mol.

$$\text{Moles of } CO_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{11}{44} = 0.25 \text{ mol}$$

Use the stoichiometric ratio to find moles of $$CH_4$$

Since the molar ratio of $$CH_4$$ to $$CO_2$$ is 1:1:

$$\text{Moles of } CH_4 = \text{Moles of } CO_2 = 0.25 \text{ mol}$$

Verification: 0.25 mol of $$CH_4 = 0.25 \times 16 = 4$$ g of methane, which upon complete combustion produces 0.25 mol of $$CO_2 = 0.25 \times 44 = 11$$ g. This matches the given data.

The correct answer is Option (4): 0.25.