Question

Find out the mole fraction of $NaOH$ in solution, if the mass percent of $NaOH$ in water is $4.7\%$.

• A. $0.022$
• B. $0.321$
• C. $0.177$
• D. $1.770$

Answer 1

The correct option is A $0.022$

Let the mass of solution be $100\text{g}$
Mass % $=\frac{\text{mass of solute}}{\text{mass of solution}}\times 100$
$4.7=\frac{\text{mass of solute}}{100}\times 100$
Mass of solute $=4.7g$
Mass of solvent = $100-4.7g=95.3g$
Moles of solute $NaOH$ $=\frac{\text{given mass}}{\text{molar mass}}$
$=\frac{4.7}{40}=0.1175$
Moles of solvent $\left(H_{2}O\right)$ = $\frac{\text{given mass}}{\text{molar mass}}=\frac{95.3}{18}=5.294$
Mole fraction of $NaOH$ $x_{\text{NaOH}}=\frac{\text{moles of NaOH}}{\text{moles of NaOH + moles of}{H}_{2}O}=\frac{0.1175}{0.1175+5.294}=0.022$