Question

What mass of ethanol $C_2{H}_{5}OH$ needs to be added to $1.0kg$ water so that the mole fraction of ethanol becomes $0.20?$

• A. 93.5 g
• B. 8.3 g
• C. 638.89 g
• D. 800 g

Answer 1

The correct option is C 638.89 g

$\chi =\frac{\text{No. of moles of Ethanol}}{\text{No. of moles of ethanol + No. of moles of water}}$
$0.2=\frac{\left(m/46gmo{l}^{-1}\right)}{\left(m/46gmo{l}^{-1}\right)+\left(1000g/18gmo{l}^{-1}\right)}$
$\Rightarrow 0.2\times \left(\right(m/46gmo{l}^{-1})+(1000g/18gmo{l}^{-1}\left)\right)=\left(m/46gmo{l}^{-1}\right)\Rightarrow \frac{m}{46}=\frac{0.2\times 1000}{18}\times \frac{1}{0.8}\frac{m}{46}=13.89$
$\Rightarrow m=13.89\times 46g=638.89g$