Problem 112 - Introductory Chemistry Atoms First

Question

Hydrochloric acid is added to an aqueous solution of silver nitrate. (a) What precipitate forms? (b) The equilibrium concentration of \(\mathrm{Cl}^{-}(a q)\) is \(2.0 \times 10^{-3} \mathrm{M}\). What is the equilibrium concentration of \(\mathrm{Ag}^{+}(a q) ?\)

Step-by-Step Solution

Answer

(a) The precipitate formed is AgCl (silver chloride). (b) The equilibrium concentration of \(\mathrm{Ag}^{+}(a q)\) is \(9.0 \times 10^{-8} \mathrm{M}\).

Step 1: (a) Balanced chemical equation

Write the balanced chemical equation for the reaction between hydrochloric acid and silver nitrate. \[ \mathrm{HCl(aq)}+\mathrm{AgNO_{3}(aq)} \rightarrow \mathrm{AgCl(s)}+\mathrm{HNO_{3}(aq)} \] Here, AgCl is the precipitate that forms.

Step 2: (b) Solubility product constant

We will now consider the solubility product constant of AgCl, denoted by \(K_{sp}\), which represents the equilibrium between the dissolved ions and the solid: \[ \mathrm{AgCl(s)} \rightleftharpoons \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \] The solubility product constant expression can be written as: \[ K_{sp} = [\mathrm{Ag}^{+}][\mathrm{Cl}^{-}] \]

Step 3: (b) Given concentration of Cl^- ions

The problem provides the equilibrium concentration of \(\mathrm{Cl}^{-}(a q)\) as \(2.0 \times 10^{-3} \mathrm{M}\).

Step 4: (b) Finding Ksp value for AgCl

Find the \(K_{sp}\) value for AgCl from a reference table or other source. For example, the \(K_{sp}\) value for AgCl is \(1.8 \times 10^{-10}\).

Step 5: (b) Calculating equilibrium concentration of Ag+ ions

Using the \(K_{sp}\) expression and the given concentration of \(\mathrm{Cl}^{-}(a q)\), we can find the equilibrium concentration of \(\mathrm{Ag}^{+}(a q)\): \[ \begin{aligned} K_{sp}&=[\mathrm{Ag}^{+}][\mathrm{Cl}^{-}] \\ 1.8 \times 10^{-10}&=[\mathrm{Ag}^{+}](2.0 \times 10^{-3} \mathrm{M}) \\ \end{aligned} \] Now, calculate the equilibrium concentration of \(\mathrm{Ag}^{+}(a q)\): \[ \begin{aligned} [\mathrm{Ag}^{+}] &= \frac{1.8 \times 10^{-10}}{2.0 \times 10^{-3} \mathrm{M}} \\ [\mathrm{Ag}^{+}] &= 9.0 \times 10^{-8} \mathrm{M} \\ \end{aligned} \] Therefore, the equilibrium concentration of \(\mathrm{Ag}^{+}(a q)\) is \(9.0 \times 10^{-8} \mathrm{M}\).

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the concentration of reactants and products remains constant over time. This steady state occurs when the rate of the forward reaction equals the rate of the reverse reaction. Imagine a see-saw in perfect balance, where neither side tips more than the other.
At equilibrium, instead of the reaction stopping, the reactions continue to occur but with no net change in concentration. It's important to remember:

• The system must be closed, meaning no substances can enter or leave.
• Both forward and reverse reactions continue simultaneously.
• Concentrations of reactants and products remain constant.

In the case of silver chloride's solubility, the equilibrium expression is given by its solubility product constant, or \(K_{sp}\). This value gives us insight into the relationship between the solid silver chloride (\(\text{AgCl}\)) and its dissolved ions in solution. As was shown in the solution, \(K_{sp} = [\text{Ag}^+][\text{Cl}^-]\). This is a representation of the balance at the microscopic level between the dissociated ions and undissolved solid. Solving for equilibrium concentrations under given conditions helps us understand the concentration of ions present at equilibrium.

Precipitation Reactions

Precipitation reactions occur when two solutions containing soluble salts are mixed, and an insoluble solid, known as a precipitate, forms. These reactions are a common demonstration of chemical equilibrium, where a solid is produced from liquid solutions.
In our example, when hydrochloric acid (\(\text{HCl}\)) is added to a solution of silver nitrate (\(\text{AgNO}_3\)), a white solid of silver chloride (\(\text{AgCl}\)) forms as the precipitate. This results from the reaction:

• \(\text{Ag}^+ + \text{Cl}^- \rightarrow \text{AgCl} (s)\)

This shows a shift in the equilibrium towards the formation of a solid, which then settles out of the solution as the precipitate. Such reactions are useful in various applications, including the removal of ions from water, and are essential in determining the conditions under which certain compounds will form as solids. Understanding solubility and the principles of chemical equilibrium helps to predict and explain the formation of precipitates in chemical reactions.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They consist of reactants on the left side, an arrow indicating the direction of the reaction, and products on the right side. These equations must be balanced, meaning the number of atoms of each element must be the same on both sides to obey the Law of Conservation of Mass.
The equation for the reaction between hydrochloric acid and silver nitrate is: \[ \text{HCl(aq)}+\text{AgNO}_3(\text{aq}) \rightarrow \text{AgCl(s)}+\text{HNO}_3(\text{aq}) \]In this equation:

• \(\text{HCl}\) and \(\text{AgNO}_3\) are the reactants, which react together.
• \(\text{AgCl}\) is the precipitate formed, and \(\text{HNO}_3\) remains in solution.

Balancing chemical equations ensures that all atoms are accounted for and conserved through the reaction, which is critical for accurately determining the stoichiometry. It is also essential to write correct state symbols (such as (aq) for aqueous solutions or (s) for solids), which provide insights into the reaction conditions. Carefully writing and balancing chemical equations is a foundational skill in chemistry that allows scientists to communicate reactions clearly and accurately.