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  4. 138 g of ethyl alcohol is mixed with 72 g of water. The ratio of mole fraction of alcohol to water is

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Q. $138\, g$ of ethyl alcohol is mixed with $72\, g$ of water. The ratio of mole fraction of alcohol to water is

AIIMSAIIMS 2011

Solution:

Number of moles of ethyl alcohol
$=\frac{138}{46}=3$
Number of moles of water $ =\frac{72}{18}=4$
$X_{C_{2}H_{5}OH}=\frac{3}{3+4}$
$=\frac{3}{7}$
$X_{H_{2}O}=\frac{4}{3+4}$
$=\frac{4}{7}$
$\frac{X_{C_{2} H_{5} O H}}{X_{H_{2} O}}=\frac{3 / 7}{4 / 7}$
$=\frac{3}{4}$