Solutions and Colligative PropertieshardNUMERICAL

A aqueous solution of a theoretical electrolyte with the chemical formula is experimentally found toSolutions and Colligative Properties Chemistry Question

Question

A $1.0\text{ molal}$ aqueous solution of a theoretical electrolyte with the chemical formula $X_3Y_2$ is experimentally found to be exactly $25\%$ ionized. Calculate the theoretical van't Hoff factor ($i$) for this solution.

Answer: 2

💡 Solution & Explanation

The electrolyte $X_3Y_2$ dissociates according to $X_3Y_2 \rightleftharpoons 3X^{2+} + 2Y^{3-}$. The total number of ions produced is $n = 3 + 2 = 5$. The degree of ionization is given as $\alpha = 25\% = 0.25$. Using the van't Hoff equation: $i = 1 + \alpha(n-1) = 1 + 0.25(5-1) = 1 + 0.25(4) = 1 + 1.0 = 2$.

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