Question

Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids. a. \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) b. \(\mathrm{Al}(\mathrm{OH})_{3}\) c. \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Short answer

a. The dissolution reaction for \(\mathrm{AgC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}\) is: \[\mathrm{AgC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}\left(s\right) \longleftrightarrow \mathrm{Ag}^{+}\left(aq\right) + \mathrm{C}_{2}\mathrm{H}_{3}\mathrm{O}_{2}^{-}\left(aq\right)\] Solubility product expression: \([K_{sp} = [\mathrm{Ag}^{+}][\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{O}_{2}^{-}]\) b. The dissolution reaction for \(\mathrm{Al}(\mathrm{OH})_{3}\) is: \[\mathrm{Al}(\mathrm{OH})_{3}\left(s\right) \longleftrightarrow \mathrm{Al}^{3+}\left(aq\right) + 3\,\mathrm{OH}^{-}\left(aq\right)\] Solubility product expression: \([K_{sp} = [\mathrm{Al}^{3+}][\mathrm{OH}^{-}]^{3}]\) c. The dissolution reaction for \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) is: \[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\left(s\right) \longleftrightarrow 3\,\mathrm{Ca}^{2+}\left(aq\right) + 2\,\mathrm{PO}_{4}^{3-}\left(aq\right)\] Solubility product expression: \([K_{sp} = [\mathrm{Ca}^{2+}]^{3}[\mathrm{PO}_{4}^{3-}]^{2}]\)

Step-by-step solution

Understand dissolution and its equations

A dissolution reaction occurs when a solid dissolves in a solvent to form a solution. In these reactions, the solid breaks into its constituent ions, which are then surrounded by solvent molecules. To write out the balanced equation for each of these reactions, we start with the solid and break it up into its individual ions.

Write the balanced equation and solubility product expression for \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)

The dissolution reaction can be written as follows: \[\mathrm{AgC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}\left(s\right) \longleftrightarrow \mathrm{Ag}^{+}\left(aq\right) + \mathrm{C}_{2}\mathrm{H}_{3}\mathrm{O}_{2}^{-}\left(aq\right)\] Now, we can write the solubility product expression: \[[K_{sp} = [\mathrm{Ag}^{+}][\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{O}_{2}^{-}]\]

Write the balanced equation and solubility product expression for \(\mathrm{Al}(\mathrm{OH})_{3}\)

The dissolution reaction can be written as follows: \[\mathrm{Al}(\mathrm{OH})_{3}\left(s\right) \longleftrightarrow \mathrm{Al}^{3+}\left(aq\right) + 3\,\mathrm{OH}^{-}\left(aq\right)\] Now, we can write the solubility product expression: \[[K_{sp} = [\mathrm{Al}^{3+}][\mathrm{OH}^{-}]^{3}]\]

Write the balanced equation and solubility product expression for \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

The dissolution reaction can be written as follows: \[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\left(s\right) \longleftrightarrow 3\,\mathrm{Ca}^{2+}\left(aq\right) + 2\,\mathrm{PO}_{4}^{3-}\left(aq\right)\] Now, we can write the solubility product expression: \[[K_{sp} = [\mathrm{Ca}^{2+}]^{3}[\mathrm{PO}_{4}^{3-}]^{2}]\] Now we have written the balanced equations for the dissolution reactions and their corresponding solubility product expressions for each of the given solids.

Key concepts

Dissolution Reactions

When a solid substance dissolves in a liquid, a dissolution reaction occurs, where the solid breaks down into its ion components within the solvent. There's an equilibrium between the undissolved solid and the ions in solution. Imagine adding salt to water; the salt crystals break apart, releasing sodium and chloride ions that mingle with the water molecules. This process is crucial for understanding solubility and the behavior of salts in various solutions.

During dissolution, the solid's particles must overcome the forces holding them together while also being stabilized by the solvent molecules. This interaction of the particles with the solvent is what causes them to disperse and become solvated or hydrated. For example, when silver acetate (AgC_{2}H_{3}O_{2}) dissolves, it separates into silver ions (Ag^+) and acetate ions (C_{2}H_{3}O_{2}^-), resulting in a homogeneous mixture, or a solution.

Balanced Chemical Equations

A balanced chemical equation represents a chemical reaction with the correct proportions of reactants and products. It adheres to the Law of Conservation of Mass, which states that mass is neither created nor destroyed in a chemical reaction. To achieve balance, one must ensure that the number of atoms for each element is the same on both sides of the equation.

For instance, the dissolution of aluminum hydroxide, Al(OH)_3, involves the solid splitting into aluminum ions, Al^{3+}, and hydroxide ions, OH^-. The balanced chemical equation is written as: Al(OH)_3 (s) Al^{3+} (aq) + 3OH^- (aq). The '3' before the OH^- indicates that three hydroxide ions are released for every aluminum ion, maintaining the balance of atoms and charge in the equation.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) quantifies the solubility of a compound under a given set of conditions and provides insight into whether a precipitate will form in a given solution. In essence, it is the equilibrium constant for the dissolution reaction. The Ksp expression for a compound is the product of the concentrations of the ionic species each raised to the power of their stoichiometric coefficients from the balanced equation.

Take calcium phosphate, Ca_3(PO_4)_2, for example, which dissociates in water to yield calcium ions, Ca^{2+}, and phosphate ions, PO_4^{3-}. The balanced dissolution reaction and corresponding Ksp expression reflect the relationship between the ions in the saturated solution: Ca_3(PO_4)_2(s) 3Ca^{2+}(aq) + 2PO_4^{3-}(aq) with K_{sp} = [Ca^{2+}]^3[PO_4^{3-}]^2. This expression signifies for every mole of calcium phosphate that dissolves, it contributes to the concentrations of the calcium and phosphate ions in the solution which are cubed and squared respectively in the Ksp formula, mirroring their stoichiometric coefficients in the balanced chemical equation.