An unknown organic substance A tetramerizes in water to the extent of . A solution containing of A i — Solutions and Colligative Properties Chemistry Question
Question
An unknown organic substance A tetramerizes in water to the extent of $80\%$. A solution containing $2.5\text{ g}$ of A in $100\text{ g}$ of water lowers the freezing point by exactly $0.3^\circ\text{C}$. Calculate the molar mass of the pure monomer A ($K_f = 1.86\text{ K kg mol}^{-1}$).
Answer: D
💡 Solution & Explanation
Tetramerization means $n=4$. The association factor $i = 1 + \alpha(1/n - 1) = 1 + 0.8(0.25 - 1) = 1 - 0.6 = 0.4$. Using $\Delta T_f = i \times K_f \times m \implies 0.3 = 0.4 \times 1.86 \times \frac{2.5/M}{0.1}$. Solving for $M$: $M = \frac{0.4 \times 1.86 \times 25}{0.3} = 62\text{ g mol}^{-1}$.
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