An organic molecule undergoes partial association in a specific solvent according to the equilibrium — Solutions and Colligative Properties Chemistry Question
Question
An organic molecule $M$ undergoes partial association in a specific solvent according to the equilibrium $nM \rightleftharpoons (M)_n$. For a given concentration, the experimental van't Hoff factor ($i$) is $0.90$ and the degree of association ($\alpha$) is exactly $0.20$. What is the precise numerical value of $n$ (the degree of polymerization)?
Answer: A
💡 Solution & Explanation
The van't Hoff factor for association is $i = 1 + \alpha(\frac{1}{n} - 1)$. Substituting the given values: $0.90 = 1 + 0.20(\frac{1}{n} - 1) \implies -0.10 = 0.20(\frac{1}{n} - 1) \implies -0.5 = \frac{1}{n} - 1 \implies \frac{1}{n} = 0.5 \implies n = 2$. Thus, the molecule forms a dimer.
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