Question

What is the quantity of water that should be added to 16 g, methanol to make the mole fraction of methanol as 0.25 ?

• A. 27 g
• B. 12 g
• C. 18 g
• D. 36 g

Answer 1

The correct option is A 27 g

Moles = $\frac{Mass}{Molarmass}$
Moles of methanol = $\frac{16}{32}=0.5$
Let us consider moles of water added is $n_{H_{2}O}$
Mole fraction $\chi$ of methanol = $\frac{Molesofmethanol}{Totalmoles}$
${\chi }_{methanol}=\frac{n_{C{H}_{2}OH}}{n_{C{H}_{2}OH}+n_{H_{2}O}}$
$0.25=\frac{0.5}{0.5+n_{H_{2}O}}$
$\Rightarrow n_{H_{2}O}=2-0.5=1.5$ Hence Weight of water = $Moles\times 18=1.5\times 18=27g$