A solution has a 1:4 mole ratio of pentane to hexane. The vapour pressures of the pure hydrocarbons at 20 °C are 440 mm Hg for pentane and 120 mm Hg for hexane. The mole fraction of pentane in the vapour phase would be:
A
0.200
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B
0.786
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C
0.549
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D
0.478
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Solution
The correct option is D 0.478 nC5H12nC6H14=14 ⇒xC5H12=15
and xC6H14=45 poC5H12=440mmHg,poC6H14=120mmHg Ptotal=poC5H12xC5H12+poC6H14xC6H14 =440×15+120×45=88+96=184mmHg
By Raoult's law, pC5H12=poC5H12xC5H12...(i) xC5H12- mole fraction of pentane in solution
By Dalton's law PC5H12=x′C5H12Ptotal...(ii) x′C5H12-Mole fraction of pentane above the solution
From (i) and (ii) pC5H12=440×15=88mmHg ⇒88=x′C5H12×184 x′C5H12=88184=0.478