Question

Boiling point of a 2% aqueous solution of a nonvolatile solute A is equal to the boiling point of 8% aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is.

• A. MA = 4MB
• B. MB = 4MA
• C. MA = 8MB
• D. MB = 8MA

Answer 1

Answer: (B)

MB = 4MA

Answer 2

The boiling point elevation is given by $\Delta T_b = i \cdot K_b \cdot m$. Since the boiling points are equal and the solutes are non-volatile non-electrolytes ($i=1$), the molalities must be equal: $m_A = m_B$. For a 2% solution of A: $m_A = \frac{2/M_A}{98/1000} \approx \frac{20}{M_A}$. For an 8% solution of B: $m_B = \frac{8/M_B}{92/1000} \approx \frac{80}{M_B}$. Equating molalities: $\frac{20}{M_A} = \frac{80}{M_B}$, which simplifies to $M_B = 4M_A$.