A mixture of ethylene and excess of $H_2$ had a pressure of $600$ mm of Hg. The mixture was passed over nickel catalyst to convert ethylene to ethane. The pressure of the resultant mixture at the similar conditions of temperature and volume dropped to $400$ mm of Hg. The fraction of $C_2H_4$ by volume in the original mixture is :

Using Gay-Lussac's law of combining volumes, the reaction consumes one volume of ethylene and one volume of hydrogen to produce one volume of ethane, so the total pressure drop equals the volume of ethylene that reacted. The pressure dropped from 600 mm Hg to 400 mm Hg, giving a decrease of 200 mm Hg. The fraction of ethylene in the original mixture by volume is the initial partial pressure of ethylene divided by the total initial pressure, which is 200 divided by 600. The fraction is 1/3rd of the total volume.

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