$x$ grams of water is mixed in $69 \mathrm{~g}$ of ethanol. Mole fraction of ethanol in the resultant…
$x$ grams of water is mixed in $69 \mathrm{~g}$ of ethanol. Mole fraction of ethanol in the resultant solution is 0.6 . What is the value of $x$ in grams?
$54$
$36$
$180$
$18$
Solution
According to question,
$
\begin{aligned}
& w_A=x \mathrm{~g}, m_A=18, X_A=1-0.6=0.4 \\
& w_B=69 \mathrm{~g}, m_B=46, X_B=0.4
\end{aligned}
$
We know that,
$
X_A=\frac{n_A}{n_A+n_B}
$
$
\begin{gathered}
\text { or } \quad 0.4=\frac{w_A / m_A}{w_A / m_A+69 / 46} \Rightarrow 0.4=\frac{\frac{x}{18}}{\frac{x}{18}+\frac{3}{2}} \\
0.4 \times\left(\frac{2 x+54}{36}\right)=\frac{x}{18}
\end{gathered}
$
or $\quad 2 x+54=5 x$ or $3 x=54, x=18 g$