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  4. The vapour pressures of ethanol and methanol are 44.5 mmHg and 88.7 mmHg respectively at the same temperature. An ideal solution is formed by mixing 60 g of ethanol and 40 g of methanol. The mole fraction of methanol in the vapour phase is

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Q. The vapour pressures of ethanol and methanol are $44.5\, mmHg$ and $88.7\, mmHg$ respectively at the same temperature. An ideal solution is formed by mixing $60\, g$ of ethanol and $40\, g$ of methanol. The mole fraction of methanol in the vapour phase is

Solutions

Solution:

Mole of $CH_{3}OH =\frac{40}{32}=1.25$
Mole of $CH_{3}CH_{2}OH=\frac{60}{46}=1.304$
Let $CH_{3}OH \to A, C_{2}H_{5}OH \to B$
$X_{A}=\frac{n_{A}}{n_{A}+n_{B}}=\frac{1.25}{1.25+1.304}=0.49$
$\therefore X_{B}=0.51$
$\therefore P_{T}=P_{A}^{o}X_{A}+P_{B}^{o}X_{B}=88.7\times0.49+44.5\times0.51$
$P_{T}=43.480+2.695=66.175$
$\therefore P_{A}=43.48$ ;
$\therefore X_{A}=\frac{P_{A}}{P_{T}}$
$=\frac{43.48}{66.175}$
$=0.66$