A researcher synthesizes a aqueous solution of a theoretical, hypothetical electrolyte designated em — Solutions and Colligative Properties Chemistry Question
Question
A researcher synthesizes a $1.0\text{ molal}$ aqueous solution of a theoretical, hypothetical electrolyte designated empirically as $A_2B_3$. Electrical conductivity measurements confirm that the salt is exactly $60\%$ ionized at this temperature. What is the theoretical numerical value of the van't Hoff factor ($i$) for this specific solution?
💡 Solution & Explanation
The hypothetical salt dissociates according to $A_2B_3 \rightleftharpoons 2A^{3+} + 3B^{2-}$. This dissociation yields a total of $n = 2 + 3 = 5$ ions per intact formula unit. The mathematical relationship for the van't Hoff factor is $i = 1 + \alpha(n - 1)$. We are given the degree of dissociation $\alpha = 60\% = 0.60$. Substituting the values into the equation gives $i = 1 + 0.60(5 - 1) = 1 + 0.60(4) = 1 + 2.4 = 3.4$.