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Forming Inequalities from statement

A 20 ml mixtu...

Question

A 20 ml mixture of $C_{4} H_{4}$ and $C_{2} H_{2}$ undergoes sparking in gas eudiometer with just sufficient amount of $O_{2}$ and shows contraction of $37.5 m l$ . What is the volume (in ml) of $C_{2} H_{2}$ in mixture?

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Solution

$\frac{2}{π} H_{3} + \frac{5}{2} O_{2} \to 2 C O_{2} + H_{2} O$
$\frac{5}{2} x \to 2 x x$
$C_{4} H_{4} + 50_{2} \to 4 C O_{2} + 2 H_{2} O (l)$
$y 5 y \to 4 y 2 y$
Decrese in volume in $x n - - - (i)$
$= 2 x - x - \frac{5}{2} x = \frac{- 3}{2} x$
Decrease in volume in $x n - - - (i i)$
$- 4 y - y - 5 y = - 2 y$
$∴ \frac{3}{2} + 2 y = 37.5 - - - (i i i)$
$x + y = 20 - - - - (i v)$
solving equation $(i i i)$ & $(i v)$
$\Rightarrow x = 5 \Rightarrow b o l u m e o f C_{2} H_{2} = 5 m l$

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