Question

Calculate the molarity and molality of $20\%$ aqueous ethanol $\left(C_2{H}_{5}OH\right)$ solution by volume. (Density of solution $=0.96$ g/mL)

• A. Molarity $=3.48$, Molality $=4.35$
• B. Molarity $=4.35$, Molality $=3.48$
• C. Molarity $=4.48$, Molality $=3.35$
• D. None of the above

Answer 1

The correct option is A Molarity $=3.48$, Molality $=4.35$

$C_2{H}_{5}OH$ is $20\%$ by volume i.e. $20$ mL of $C_2{H}_{5}OH$ is dissolved in $100$ mL of solution.

Volume of $H_{2}O=100-20=80$ mL
Weight of $H_{2}O=80\times 1=80$ g ($d_{H_{2}O}=1$ g/cc)
Weight of solution $=100\times 0.96=96$ g
Weight of $C_2{H}_{5}OH=96-80=16$ g
Molecular weight of $C_2{H}_{5}OH=12\times 2+5+16+1=46$ g/mol

$M=\frac{W_2\times 1000}{M{w}_2\times V_{sol}}=\frac{16\times 1000}{46\times 100}=3.48M$

$m=\frac{W_2\times 1000}{M{w}_2\times W_1}=\frac{16\times 1000}{46\times 80}=4.35m$

Hence, option B is correct.