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) Dissolution reaction of \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\): \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2(s)} \rightleftharpoons \mathrm{Ag}^{+} _{\mathrm{(aq)}} + \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-} _{\mathrm{(aq)}}\); Solubility product expression: \(K_\mathrm{sp} = [\mathrm{Ag}^{+}] [\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}]\) b) Dissolution reaction of \(\mathrm{Al}(\mathrm{OH})_{3}\): \(\mathrm{Al}(\mathrm{OH})_{3(s)} \rightleftharpoons \mathrm{Al}^{3+}_{\mathrm{(aq)}} + 3\mathrm{OH}^{-}_{\mathrm{(aq)}}\); Solubility product expression: \(K_\mathrm{sp} = [\mathrm{Al}^{3+}][\mathrm{OH}^{-}]^{3}\) c) Dissolution reaction of \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\): \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2(s)} \rightleftharpoons 3\mathrm{Ca}^{2+}_{\mathrm{(aq)}} + 2\mathrm{PO}_{4}^{3-}_{\mathrm{(aq)}}\); Solubility product expression: \(K_\mathrm{sp} = [\mathrm{Ca}^{2+}]^{3}[\mathrm{PO}_{4}^{3-}]^{2}\)

Step-by-step solution

a) Dissolution reaction of \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)#

To write the balanced equation for the dissolution of silver acetate \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), we can dissociate the solid into its ionic species: \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2(s)} \rightleftharpoons \mathrm{Ag}^{+} _{\mathrm{(aq)}} + \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-} _{\mathrm{(aq)}}\)

a) Solubility product expression of \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)#

For the solubility product (\(K_\mathrm{sp}\)) expression, we can define the equilibrium constant for the dissolution reaction by multiplying the concentrations of the ions in their aqueous state: \(K_\mathrm{sp} = [\mathrm{Ag}^{+}] [\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}]\)

b) Dissolution reaction of \(\mathrm{Al}(\mathrm{OH})_{3}\)#

To write the balanced equation for the dissolution of aluminium hydroxide \(\mathrm{Al}(\mathrm{OH})_{3}\), we can dissociate the solid into its ionic species: \(\mathrm{Al}(\mathrm{OH})_{3(s)} \rightleftharpoons \mathrm{Al}^{3+}_{\mathrm{(aq)}} + 3\mathrm{OH}^{-}_{\mathrm{(aq)}}\)

b) Solubility product expression of \(\mathrm{Al}(\mathrm{OH})_{3}\)#

For the solubility product (\(K_\mathrm{sp}\)) expression, we can define the equilibrium constant for the dissolution reaction by multiplying the concentrations of the ions in their aqueous state: \(K_\mathrm{sp} = [\mathrm{Al}^{3+}][\mathrm{OH}^{-}]^{3}\)

c) Dissolution reaction of \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)#

To write the balanced equation for the dissolution of calcium phosphate \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\), we can dissociate the solid into its ionic species: \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2(s)} \rightleftharpoons 3\mathrm{Ca}^{2+}_{\mathrm{(aq)}} + 2\mathrm{PO}_{4}^{3-}_{\mathrm{(aq)}}\)

c) Solubility product expression of \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)#

For the solubility product (\(K_\mathrm{sp}\)) expression, we can define the equilibrium constant for the dissolution reaction by multiplying the concentrations of the ions in their aqueous state: \(K_\mathrm{sp} = [\mathrm{Ca}^{2+}]^{3}[\mathrm{PO}_{4}^{3-}]^{2}\)