When exactly of a non-volatile, non-electrolyte organic substance is dissolved into of pure ether, t — Solutions and Colligative Properties Chemistry Question
Question
When exactly $10.6\text{ g}$ of a non-volatile, non-electrolyte organic substance is dissolved into $740\text{ g}$ of pure ether, the normal boiling point of the resulting solution is raised by exactly $0.284^\circ\text{C}$. Using the molal boiling point elevation constant for ether ($K_b = 2.11^\circ\text{C kg mol}^{-1}$), calculate the molecular weight of the substance (in $\text{g mol}^{-1}$). (Round your final answer to the nearest integer).
💡 Solution & Explanation
The elevation in boiling point formula is $\Delta T_b = K_b \times m = K_b \times \frac{w_{solute} \times 1000}{M_{solute} \times W_{solvent}(\text{in g})}$. We rearrange to solve for the molecular mass: $M_{solute} = \frac{1000 \times K_b \times w_{solute}}{\Delta T_b \times W_{solvent}}$. Substituting the given values: $M_{solute} = \frac{1000 \times 2.11 \times 10.6}{0.284 \times 740} = \frac{22366}{210.16} = 106.42\text{ g mol}^{-1}$. Rounding to the nearest integer yields $106$.