50 ml of gaseous mixture of acetylene and ethylene if taken in a ratio of a : b requires 700 ml of air containing 20% by volume $O_{2}$ for complete combustion. Calculate the volume of air required for complete combustion of a mixture having ratio b:a.

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675 ml

135 ml

700 ml

140 ml

answer is B.

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Detailed Solution

In the reaction we have,

$\begin{aligned} C_{2} H_{2} + \frac{5}{2} O_{2} \to 2 {CO}_{2} + H_{2} O \\ C_{2} H_{4} + 3 O_{2} \to 2 {CO}_{2} + 2 H_{2} O \end{aligned}$

Initially,

$\frac{5 a}{2} + 3 b = 700 \times 0.2$ and $a + b = 5$

$\Rightarrow a = 20$ and $b = 30$

Finally,

$\frac{5 b}{2} + 3 a = V \times 0.2$ and $a + b = 50$

$\Rightarrow V = 675 ml$ .

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