Question

A solution containing $0.1g$ of a non-volatile organic substance $P$ (molecular mass $100$) in $100g$ of benzene raises the boiling point of benzene by $0.2^{∘}C$, while a solution containing $0.1g$ of another non-volatile substance $Q$ in the same amount of benzene raises the boiling point of benzene by $0.4^{∘}C$. What is the ratio of molecular masses of $P$ and $Q$ ?

• A. $1:2$
• B. $4:1$
• C. $1:4$
• D. $2:1$

Answer 1

Answer: (D)

$\frac{(ΔT{)}_P}{(ΔT{)}_Q}=\frac{K_b×{\left(\frac{w_B×1000}{m_B×w_A}\right)}_P}{K_b×{\left(\frac{w_B×1000}{m_B×w_A}\right)}_Q}$
$\frac{0.2}{0.4}=\frac{{\left(\frac{0.1×1000}{100×100}\right)}_P}{{\left(\frac{0.1×1000}{100×w_B}\right)}_Q}$
$\frac{1}{2}=\frac{{\left(m_B\right)}_Q}{100}{m}_B=50$
$∴{\left(m_B\right)}_P:{\left(m_B\right)}_Q$
$=100:50=2:1$