One mole mixture of C $H_{4}$ & air (containing 80% $N_{2}$ , 20% $O_{2}$ by volume) of a composition such that when underwent combustion gave maximum heat (assume combustion of only ${C H}_{4}$ ). Then which of the statements are correct? regarding the composition of the initial mixture. (X presents mole fraction)

X_{{C H}_{4}} = \frac{1}{11}, X_{O_{2}} = \frac{2}{11}, X_{N_{2}} = \frac{8}{11}

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X_{{C H}_{4}} = \frac{3}{8}, X_{O_{2}} = \frac{1}{8}, X_{N_{2}} = \frac{1}{2}

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X_{{C H}_{4}} = \frac{1}{6}, X_{O_{2}} = \frac{1}{6}, X_{N_{2}} = \frac{2}{3}

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Solution

The correct option is D $X_{{C H}_{4}} = \frac{1}{11}, X_{O_{2}} = \frac{2}{11}, X_{N_{2}} = \frac{8}{11}$
Let $x$ $m o l e$ of $C H_{4}$ b present.
$C H_{4} + 2 O_{2} ⟶ C O_{2} + 2 H_{2} O$
$x$ $2 x$
$x$ $m o l e$ $C H_{4}$ reacts with $2 x$ $m o l e$ $O_{2}$
Let $y$ $m o l e$ of air be present.
$y \times 0.2 = 2 x$
$⟹ x = 10 x$
$x + 10 x = 1$
$⟹ x = \frac{1}{11} = x_{C H_{4}}$
$x_{O_{2}} = 2 x = \frac{2}{11}$
$x_{N_{2}} = 8 x = \frac{8}{11}$

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One mole of mixture of $C H_{4}$ and air (containing 80% $N_{2}$ 20% $O_{2}$ by volume) of a composition such that when underwent combustion gave maximum heat (assume combustion of only $C H_{4}$ . Then which of the statements are correct, regarding composition of initial mixture. (X presents mole fraction)