---
title: "A student investigates the common-ion effect by measuring the equilibrium concentration of \\(\\text{Ba}^{2+}\\text{(aq)}\\) in several saturated solutions of \\(\\text{BaSO}_4\\text{(s)}\\) containing different initial concentrations of dissolved \\(\\text{Na}_2\\text{SO}_4\\text{(aq)}\\) at \\(298 \\text{ K}\\).  \\[ \\text{BaSO}_4\\text{(s)} \\rightleftharpoons \\text{Ba}^{2+}\\text{(aq)} + \\text{SO}_4^{2-}\\text{(aq)} \\quad K_{sp} = 1.1 \\times 10^{-10} \\text{ at } 298 \\text{ K} \\]  The student’s results are shown in the graph below.  Which of the following best explains why the equilibrium concentration of \\(\\text{Ba}^{2+}\\text{(aq)}\\) decreases non-linearly and approaches the horizontal axis asymptotically as the concentration of added \\(\\text{SO}_4^{2-}\\text{(aq)}\\) increases?"
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url: "https://nerd-notes.com/ubq/123869/"
date_modified: "2026-09-28T12:30:41+00:00"
---

# A student investigates the common-ion effect by measuring the equilibrium concentration of \(\text{Ba}^{2+}\text{(aq)}\) in several saturated solutions of \(\text{BaSO}_4\text{(s)}\) containing different initial concentrations of dissolved \(\text{Na}_2\text{SO}_4\text{(aq)}\) at \(298 \text{ K}\).

\[ \text{BaSO}_4\text{(s)} \rightleftharpoons \text{Ba}^{2+}\text{(aq)} + \text{SO}_4^{2-}\text{(aq)} \quad K_{sp} = 1.1 \times 10^{-10} \text{ at } 298 \text{ K} \]

The student’s results are shown in the graph below.

Which of the following best explains why the equilibrium concentration of \(\text{Ba}^{2+}\text{(aq)}\) decreases non-linearly and approaches the horizontal axis asymptotically as the concentration of added \(\text{SO}_4^{2-}\text{(aq)}\) increases?

A student investigates the common-ion effect by measuring the equilibrium concentration of \(\text{Ba}^{2+}\text{(aq)}\) in several saturated solutions of \(\text{BaSO}_4\text{(s)}\) containing different initial concentrations of dissolved \(\text{Na}_2\text{SO}_4\text{(aq)}\) at \(298 \text{ K}\).

\[ \text{BaSO}_4\text{(s)} \rightleftharpoons \text{Ba}^{2+}\text{(aq)} + \text{SO}_4^{2-}\text{(aq)} \quad K_{sp} = 1.1 \times 10^{-10} \text{ at } 298 \text{ K} \]

The student's results are shown in the graph below.

Which of the following best explains why the equilibrium concentration of \(\text{Ba}^{2+}\text{(aq)}\) decreases non-linearly and approaches the horizontal axis asymptotically as the concentration of added \(\text{SO}_4^{2-}\text{(aq)}\) increases?

![A line graph with bare axes and no gridlines. The horizontal axis is labeled 'Concentration of Added \(\text{SO}_4^{2-}\) (M)' and begins at 0. The vertical axis is labeled 'Equilibrium \([\text{Ba}^{2+}]\) (M)' and begins at 0. A single smooth, solid black curve starts at a point on the vertical axis above zero, curves downward steeply toward the right, and flattens to approach the horizontal axis asymptotically without touching or crossing it. No other lines, data points, legends, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790598641-fJBTXi.jpg)

- **A.** The equilibrium expression requires that \([\text{Ba}^{2+}][\text{SO}_4^{2-}] = K_{sp}\), so \([\text{Ba}^{2+}]\) is inversely proportional to \([\text{SO}_4^{2-}]\); it approaches zero asymptotically because \([\text{Ba}^{2+}]\) must remain greater than zero to satisfy \(K_{sp}\).
- **B.** The value of \(K_{sp}\) decreases continuously as more \(\text{SO}_4^{2-}\text{(aq)}\) is added, causing the molar solubility of \(\text{BaSO}_4\text{(s)}\) to decrease until the salt becomes completely insoluble.
- **C.** The rate of the forward dissolution reaction decreases to zero as \([\text{SO}_4^{2-}]\) increases, preventing any \(\text{BaSO}_4\text{(s)}\) from dissolving once the common-ion concentration is sufficiently large.
- **D.** The concentration of \(\text{Ba}^{2+}\text{(aq)}\) decreases linearly because the \(1:1\) stoichiometric ratio of the salt requires that one mole of \(\text{Ba}^{2+}\text{(aq)}\) precipitates for every mole of \(\text{SO}_4^{2-}\text{(aq)}\) added.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123869/*