24 cc Marsh gas $(C H_{4})$ was mixed with 106 cc oxygen and then exploded. On cooling. The volume of the mixture became 82 cc, of which 58 cc was unchanged oxygen.
Which law does this experiment support?
Explain with calculation.

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Solution

$C H_{4} (g) 1 V o l + 2 O_{2} (g) 2 V o l s ⟶ C O_{2} (g) 1 V o l s + 2 H_{2} O (l)$

Volume of $O_{2}$ unreacted - 58 cc

∴ Vol of $O_{2}$ reacted = 106 - 58 = 48 cc

Volume of $C O_{2} = 82 - 58 = 24 c c$

Vol of marsh gas $(C H_{4}) = 24 c c$

∴ 24 cc of marsh gas reacts with 48 cc of $O_{2}$ to give 24 cc of $C O_{2}$ .

Or 1 vol. of marsh gas reacts with 2 vols of $O_{2}$ to give 1 volume of $C O_{2}$ . The ratio of volumes of $C H_{4}, O_{2}$ and $C O_{2} i s 1 : 2 : 1$ .
It is a simple ratio which supports Gay Lussac's law of gaseous volumes.

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