Question

Which of the following would increase the solubility of \(\mathrm{Pb}(\mathrm{OH})_{2}\) : (a) Add hydrochloric acid (b) Add a solution of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) (c) Add a sólution of \(\mathrm{NaOH}\) (d) None of the above-the solubility of a compound is constant at constant temperature

Short answer

Adding hydrochloric acid (HCl) would increase the solubility of \(\mathrm{Pb}(\mathrm{OH})_{2}\) by decreasing the concentration of \(\mathrm{OH}^{-}\) through a chemical reaction, thus shifting the equilibrium and increasing solubility.

Step-by-step solution

Understanding the Effect of Common Ion

Adding a compound that provides a common ion to \(\mathrm{Pb}(\mathrm{OH})_{2}\) can decrease its solubility due to the common ion effect. In choice (b), the compound \(\mathrm{Pb}(\mathrm{NO}_{3})_{2}\) shares a common ion, \(\mathrm{Pb}^{2+}\), with \(\mathrm{Pb}(\mathrm{OH})_{2}\), and would therefore decrease the solubility of \(\mathrm{Pb}(\mathrm{OH})_{2}\).

Analyzing the Effect of Acid on Solubility

Adding hydrochloric acid (HCl) to a solution of \(\mathrm{Pb}(\mathrm{OH})_{2}\) would increase its solubility by reacting with \(\mathrm{OH}^{-}\) ions to form water and decrease their concentration in the solution. This shifts the equilibrium to the right to dissolve more \(\mathrm{Pb}(\mathrm{OH})_{2}\) to restore the \(\mathrm{OH}^{-}\) ion concentration, according to Le Chatelier's principle.

Considering the Addition of a Base

Adding \(\mathrm{NaOH}\), which contains the hydroxide ion \(\mathrm{OH}^{-}\), would increase the concentration of \(\mathrm{OH}^{-}\) in the solution. This would reduce the solubility of \(\mathrm{Pb}(\mathrm{OH})_{2}\) due to the common ion effect, as the system will shift the equilibrium to the left to try to reduce the concentration of \(\mathrm{OH}^{-}\) by forming more solid \(\mathrm{Pb}(\mathrm{OH})_{2}\).

Understanding Temperature Dependency

While the solubility of a compound is generally dependent on temperature, with an increase in temperature typically increasing solubility for solids, this is not an option provided in the question. Therefore, temperature is not a factor in this scenario.

Making the Decision

Based on the above steps, the correct choice that would increase the solubility of \(\mathrm{Pb}(\mathrm{OH})_{2}\) is to add hydrochloric acid (HCl), as it consumes the hydroxide ions in the solution and drives the dissolution of \(\mathrm{Pb}(\mathrm{OH})_{2}\) to produce more hydroxide ions, thus increasing its solubility.

Key concepts

Common Ion Effect

Understanding the common ion effect is crucial when predicting how the solubility of a compound changes upon adding different substances. In essence, the common ion effect refers to the decrease in solubility of an ionic compound when another compound containing an ion identical to one in the ionic compound is added to the solution.

Consider the solubility of lead(II) hydroxide, Pb(OH)₂. If you add lead nitrate, Pb(NO₃)₂, to the mix, you introduce more Pb²⁺ ions to the solution. These additional Pb²⁺ ions shift the solubility equilibrium of Pb(OH)₂, causing precipitation of Pb(OH)₂ and thus reducing its solubility in the solution due to the increase in concentration of the common Pb²⁺ ion.

• The equilibrium shifts to maintain a constant product of the concentrations of the ions that make up the compound, known as the solubility product.
• This effect is a direct consequence of Le Chatelier's principle, which predicts such shifts in equilibrium in response to changes in concentrations of reactants or products.

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept in chemistry that helps us to understand how a chemical system at equilibrium responds to changes in concentration, temperature, and pressure. According to this principle, if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will shift to counteract the change.

For instance, when hydrochloric acid, HCl, is added to a solution of Pb(OH)₂, it reacts with OH^- ions to form water. This reduces the concentration of OH^- ions in the solution, thereby disturbing the equilibrium. In response, the equilibrium shifts to dissolve more Pb(OH)₂ to replace the removed OH^- ions.

• The principle is an excellent tool for understanding and predicting the effects of various conditions on the solubility of a compound.
• It underscores that reactions are dynamic and reversible, adjusting to changes in their environment to maintain balance.

Effect of Acids on Solubility

Acids can significantly influence the solubility of certain compounds, particularly those containing basic anions such as OH^-. Adding an acid to such a solution often increases the solubility of the compound.

In our case of Pb(OH)₂, adding an acid like HCl increases the solubility because the acid reacts with the hydroxide ions to form water, thus lowering the OH^- ion concentration in solution. The reduced concentration of OH^- ions causes more Pb(OH)₂ to dissolve in an effort to re-establish the solubility equilibrium.

• This effect is a practical application of Le Chatelier's principle, where the acid-base reaction is used to shift the equilibrium and enhance solubility.
• The balance between solubility, pH, and ion concentration underscores the intricate nature of chemical equilibria in aqueous solutions.