Question

Consider the following system at equilibrium: $$ \mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q) $$ Even small quantities of lead ion in drinking water can be toxic. Indicate whether or not the addition of each of the following would reduce the concentration of dissolved lead ion. Explain your reasoning for each. (a) \(\mathrm{PbI}_{2}\) (b) \(\mathrm{KI}\) (c) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\)

Short answer

Adding PbI2 would not reduce the concentration of dissolved lead ion, adding KI would reduce it, and adding Pb(NO3)2 would not reduce it.

Step-by-step solution

Analyzing change due to PbI2

Adding \(\mathrm{PbI}_{2}\) to the system would not shift the equilibrium at all because it is a solid and does not appear in the equilibrium expression. According to Le Chatelier's principle, adding a solid to an equilibrium would not change the concentrations of the reacting species in the solution. Thus, it will not reduce the concentration of dissolved lead ions.

Analyzing change due to KI

Adding \(\mathrm{KI}\) to the system would increase the concentration of \(\mathrm{I}^{-}\) ions. According to Le Chatelier's principle, this extra stress would cause the system to adjust to reduce the increase, shifting the equilibrium to the left. This means PbI2 would increase and the concentration of \(\mathrm{Pb^{2+}}\) ions, i.e., dissolved lead ion, would decrease.

Analyzing change due to Pb(NO3)2

Adding \(\mathrm{Pb(NO3)}_{2}\) to the system would increase the concentration of \(\mathrm{Pb^{2+}}\) ions because \(\mathrm{Pb(NO3)}_{2}\) is a soluble salt that fully dissociates into its ions in water. According to Le Chatelier's principle, this would cause the equilibrium to shift to the left to counteract this increase, hence the concentration of \(\mathrm{Pb^{2+}}\) would increase, not decrease. So, addition of \(\mathrm{Pb(NO3)}_{2}\) would not reduce the concentration of dissolved lead ions.

Key concepts

Le Chatelier's principle

Le Chatelier's principle is a fundamental concept in chemical equilibrium that describes how a system at equilibrium responds to external changes. It asserts that if a dynamic equilibrium is disturbed by changing the conditions, such as concentration, temperature, or pressure, the system adjusts itself to counteract the imposed change and a new equilibrium is established.

For instance, if the concentration of a reactant is increased, the system tends to produce more products to reduce this surplus. Conversely, if a product is removed from the system, it will produce more of that product to fill the gap. This principle helps us understand how different changes can affect chemical reactions and is a valuable tool in predicting the direction of the shift in equilibrium.

Equilibrium concentration

Equilibrium concentration refers to the concentrations of reactants and products in a chemical reaction that has reached equilibrium. At this point, the rate of the forward reaction equals the rate of the reverse reaction, so the concentration of the reactants and products remains constant over time.

Understanding equilibrium concentrations is critical when it comes to controlling a reaction. For example, in water treatment processes, maintaining low equilibrium concentrations of toxic ions is essential for safety. Equilibrium concentrations can be altered by changing the reaction conditions, and this is often done in industrial processes to maximize product yields.

Dissociation of salts

The dissociation of salts into their constituent ions in a solution is a key concept in understanding ionic reactions in aqueous environments. When a salt like potassium iodide (KI) dissolves in water, it separates into potassium (K+) and iodide (I-) ions.

This dissociation is crucial when considering the solubility equilibrium of slightly soluble salts such as lead iodide (PbI2). The addition of a salt containing a common ion, like KI providing additional I- ions, can shift the equilibrium according to Le Chatelier's principle and reduce the solubility of the slightly soluble salt by causing it to precipitate out of the solution.

Toxicity of lead ions

Toxicity of lead ions, particularly Pb2+ in drinking water, is a significant health concern due to their harmful effects on the human body. Even in small concentrations, lead ions can lead to serious health conditions including neurological damage and delayed development in children.

Understanding chemical equilibrium is important for mitigating the risks associated with the presence of lead ions in water. For instance, to decrease the concentration of dissolved lead ions, compounds that remove lead from the water by causing it to become less soluble can be added. This process ties directly into Le Chatelier's principle, where the addition of certain substances would shift the equilibrium and reduce the concentration of toxic lead ions.