For an arbitrary, unknown chemical electrolyte bearing the formula that undergoes partial dissociati — Solutions and Colligative Properties Chemistry Question
Question
For an arbitrary, unknown chemical electrolyte bearing the formula $A_x B_y$ that undergoes partial dissociation in an aqueous medium with a degree of dissociation defined as $\alpha$, which of the following mathematical expressions correctly define the van't Hoff factor ($i$)?
💡 Solution & Explanation
The generic dissociation is $A_x B_y \rightleftharpoons x A^{y+} + y B^{x-}$. The total number of ions produced per molecule is $n = x + y$. The formula for the van't Hoff factor is $i = 1 + \alpha(n - 1)$. Replacing $n$, we get exactly $i = 1 + \alpha(x + y - 1)$ (A). Rearranging this formula algebraically to solve for $\alpha$ gives exactly $\alpha = \frac{i - 1}{x + y - 1}$ (C). Option D is incorrect; the van't Hoff factor is inversely proportional to molar mass, so $i = \frac{\text{Normal Molar Mass}}{\text{Observed Molar Mass}}$.