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# What is the mole fraction of water in 20% w/w ethylene glycol solution?

$\begin{array}{1 1}(a)\;0.932&(b)\;0.068\\(c)\;0.102&(d)\;0.898\end{array}$

Let's start with a 100g solution that contains 20% ethylene glycol, i.e, 20g and hence 100-20 = 80g of water.
Molar mass of ethylene glycol $= 12 \times 2 + 1 \times 6 + 16 \times 2 = 62\; g\;mol^{-1}$
Number of moles of ethylene glycol $= \large\frac{20}{62} $$= 0.322\; mol Since, the molar mass of water is known to be 18\;g\;mol^{-1}, the number of moles of water = \large\frac{80}{18}$$= 4.44 \; mol$
$\Rightarrow$ Mole fraction of ethylene glycol $X_{C_2 H_6 O_2} = \large\frac{\text{moles of ethylene glycol}}{\text{moles of ethylene glycol + moles of water}}$
$\Rightarrow X_{C_2 H_6 O_2} = \large\frac{0.322}{0.322+4.44}$$= 0.068$
Hence (a) is the correct answer.
$\Rightarrow X_{H_2O} = 1 - X_{C_2 H_6 O_2} = 1- 0.068 = 0.932$
edited Jul 16, 2014