10mL of gaseous hydrocarbon was mixed with 100mL of oxygen and exploded in a eudiometer tube. The volume of the residual gases was 95mL out of which 20mL was absorbed by caustic soda the remaining by pyrogallol. The molecular formula of the gas is

C₂H₂

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C₂H₆

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C₃H₆

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C₄H₈

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Solution

The correct option is A
C₂H₂

volume left after explosion and cooling i.e volume of $C O_{2}$ formed + unused $O_{2}$ = 95mL

volume after introducing $K O H$ , i.e volume of $C O_{2}$ formed = 20mL

volume absorbed by alkaline pyrogallol i.e volume of unused $O_{2}$ = 95-20 = 75mL

$∴$ volume of $O_{2}$ used = 100-75 = 25mL

Applying the combustion equation

$C_{x} H_{y} + (x + \frac{y}{4}) O_{2} \to x C O_{2} + \frac{y}{2} H_{2} O$

$10 m L 10 (x + \frac{y}{4}) m L 10 x m L$ Negligible volume

Equating theoretical and experimented values

$10 x = 20$ and $10 + \frac{x + y}{4} = 25$

$x = 2$ $10 + \frac{2 + y}{4} = 25$

$y = 2$ .

Thus the hydrocarbon is $C_{2} H_{2}$

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