Question

Write the solubility product expression for each of the following slightly soluble ionic compounds in a saturated aqueous solution: (a) \(\mathrm{AgI}(s) \rightleftarrows \mathrm{Ag}^{+}(a q)+\mathrm{I}^{-}(a q)\) (b) \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}(\mathrm{~s}) \rightleftarrows 2 \mathrm{Ag}^{+}(a q)+\mathrm{CrO}_{4}^{2-}(a q)\) (c) \(\mathrm{Ag}_{3} \mathrm{PO}_{4}(s) \rightleftarrows 3 \mathrm{Ag}^{+}(a q)+\mathrm{PO}_{4}^{3-}(a q)\)

Short answer

Solubility products: (a) \([\mathrm{Ag}^{+}][\mathrm{I}^{-}]\), (b) \([\mathrm{Ag}^{+}]^2[\mathrm{CrO}_{4}^{2-}]\), (c) \([\mathrm{Ag}^{+}]^3[\mathrm{PO}_{4}^{3-}]\).

Step-by-step solution

Understanding Solubility Product

The solubility product constant, or Ksp, is an equilibrium constant for the dissolution of a solid substance into an aqueous solution. It describes the degree to which a compound dissolves in water. For slightly soluble compounds, Ksp is useful to predict the solubility.

Write Ksp Expression for AgI

For the dissociation: \( \mathrm{AgI}(s) \rightleftarrows \mathrm{Ag}^{+}(aq) + \mathrm{I}^{-}(aq) \), the solubility product expression is based on the concentrations of the ions in solution: \[ K_{sp} = [\mathrm{Ag}^{+}][\mathrm{I}^{-}] \] This represents the product of the concentrations of the ions in a saturated solution, with each raised to the power of its coefficient in the balanced equation, which is 1 for both.

Write Ksp Expression for Ag2CrO4

For the dissociation: \( \mathrm{Ag}_{2}\mathrm{CrO}_{4}(s) \rightleftarrows 2 \mathrm{Ag}^{+}(aq) + \mathrm{CrO}_{4}^{2-}(aq) \), the solubility product expression is: \[ K_{sp} = [\mathrm{Ag}^{+}]^2[\mathrm{CrO}_{4}^{2-}] \] Here, \([\mathrm{Ag}^{+}]\) is squared because the stoichiometric coefficient is 2 in the balanced equation.

Write Ksp Expression for Ag3PO4

For the dissociation: \( \mathrm{Ag}_{3}\mathrm{PO}_{4}(s) \rightleftarrows 3 \mathrm{Ag}^{+}(aq) + \mathrm{PO}_{4}^{3-}(aq) \), the solubility product expression is: \[ K_{sp} = [\mathrm{Ag}^{+}]^3[\mathrm{PO}_{4}^{3-}] \] In this case, \([\mathrm{Ag}^{+}]\) is raised to the power of 3 as there are three silver ions per formula unit of \(\mathrm{Ag}_{3}\mathrm{PO}_{4}\).

Key concepts

Equilibrium Constant

The Equilibrium Constant, often denoted as $K$, is a crucial concept in understanding chemical reactions. It quantifies the balance between the products and reactants in a reversible reaction at equilibrium. When considering ionic reactions in aqueous solutions, the equilibrium constant indicates the extent to which a reaction progresses before reaching equilibrium.
The value of the equilibrium constant provides insight into the position of equilibrium:

• If $K$ is large, the reaction heavily favors products at equilibrium.
• If $K$ is small, reactants are mostly present at equilibrium.

The Solubility Product Constant ($K_{sp}$) is a particular equilibrium constant used for slightly soluble ionic compounds. It applies specifically to dissolutions where a solid compound transitions to its ions in solution.

Slightly Soluble Compounds

Slightly soluble compounds are substances that do not dissolve extensively in water. They have limited solubility, meaning only a small amount of the compound will dissolve in a given quantity of water to form an equilibrium between the dissolved ions and the solid form.
These compounds are defined by their unique solubility product constants ($K_{sp}$), which are typically very small numbers. A smaller $K_{sp}$ indicates less solubility. For instance, silver iodide ($AgI$) is slightly soluble, releasing only a small concentration of $Ag^+$ and $I^-$ ions into the solution before equilibrium is reached.
These characteristics are important in fields such as environmental chemistry, where slightly soluble compounds can impact water quality and ecosystem health.

Ionic Compounds Solubility

The solubility of ionic compounds in water is governed by the interactions between the ions and water molecules. When an ionic solid dissolves, its ions are surrounded by water molecules, a process known as solvation.
The solubility depends on several factors:

• The nature of the ionic compound—larger charges and smaller ionic radii generally result in lower solubility.
• Temperature—most ionic compounds become more soluble at higher temperatures.
• Common ion effect—the presence of a common ion in the solution decreases solubility due to Le Châtelier’s principle.

The solubility product constant ($K_{sp}$) specifically helps predict whether a given ionic solution will cause the precipitate to form when the ionic product exceeds $K_{sp}$.

Aqueous Solutions

An aqueous solution is a system where water is the solvent. In chemistry, aqueous solutions are crucial as they allow reactions to take place between dissolved ions.
Characteristics of aqueous solutions include:

• The ability to dissolve various solutes due to water's polar nature.
• Conductivity—solutions containing dissolved ions can conduct electricity.
• Homogeneity—solutions are uniform mixtures at the molecular level.

When slightly soluble ionic compounds are placed in water, they reach a saturation point where the solution contains the maximum concentration of dissolved ions possible without forming a precipitate. Understanding aqueous solutions is fundamental for analyses and calculations involving solubility equilibria.

Chemical Equilibrium Expressions

In chemical reactions, equilibrium expressions describe the relationship between the concentrations of reactants and products at equilibrium. These expressions are mathematical representations that guide understanding of how systems behave when they reach a state of balance.
For slightly soluble ionic compounds, the chemical equilibrium expression is the solubility product expression ($K_{sp}$). It specifically focuses on the concentrations of the ions produced from the dissolution:

• The general form is: $K_{sp} = [ ext{Cations}]^a [ ext{Anions}]^b$, where $a$ and $b$ are stoichiometric coefficients from the balanced equation.
• This expression only involves the concentrations of dissolved ions because the concentration of the undissolved solid remains constant.

Understanding how to construct and interpret these expressions is key to solving solubility-related problems in chemistry.