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One mole mixture of ${CH}_{4}$ and air (containing $N_{2}$ 20% $O_{2}$ by volume) of a composition such tna when underwent combustion gave maximum hea (assume combustion of only ${CH}_{4}$ ). Then which o the statements are correct. regarading composition of initial mixture? (X presents mole fraction).

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$X_{{CH}_{4}} = \frac{1}{11}, X_{O_{2}} = \frac{2}{11}, X_{N_{2}} = \frac{8}{11}$

$X_{{CH}_{4}} = \frac{3}{8}, X_{O_{2}} = \frac{1}{8}, X_{N_{2}} = \frac{1}{2}$

$X_{{CH}_{4}} = \frac{1}{6}, X_{O_{2}} = \frac{1}{6}, X_{N_{2}} = \frac{2}{3}$

Data insufficient

answer is A.

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Detailed Solution

${CH}_{4} + 2 O_{2} ⟶ {CO}_{2} + 2 H_{2} O \underset{x}{1} \underset{2 x}{2}$

$x + 2 x + 8 x = 1$

or $11 x = 1$

or $x = \frac{1}{11}$

$X_{{CH}_{4}} = \frac{1}{11}, X_{O_{2}} = \frac{2}{11}, X_{N_{2}} = \frac{8}{11}$

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