If the mole fraction of ethanol in a solution of ethanol in water is 0.050 , then find the molarity of the…
If the mole fraction of ethanol in a solution of ethanol in water is 0.050 , then find the molarity of the given solution.
$3.5 \mathrm{M}$
$2.8 \mathrm{M}$
$1.7 \mathrm{M}$
$0.95 \mathrm{M}$
Solution
Moles of ethanol $=0.050$
Moles of water $=1-0.050=0.95 \mathrm{~mol}$.
Mass of ethanol $=0.05 \times 46=2.3 \mathrm{~g}$.
Mass of $\mathrm{H}_2 \mathrm{O}=0.95 \times 18=17.1 \mathrm{~g}$
Mass of solution $=2.3+17.1 \mathrm{~g}=19.4 \mathrm{~g}$
Assuming, density of water $=1 \mathrm{~g} / \mathrm{mL}$
Volume of solution $=\frac{\text { Mass of solution }}{\text { Density }}$
$=19.4 / 1=19.4 \mathrm{~mL}=0.0194 \mathrm{~L}$
Molarity of solution $=\frac{\text { Number of moles of ethanol }}{\text { Volume of solution (L) }}$
$=\frac{0.050}{0.0194}=2.57 \cong 2.8 \mathrm{M}$