Write the dissociation reaction and the corresponding \(K_{\mathrm{a}}\) equilibrium expression for each of the following acids in water. a. \(\mathrm{HCN}\) b. \(\mathrm{HOC}_{6} \mathrm{H}_{5}\) c. \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}\)

Short Answer

Expert verified
The dissociation reactions and equilibrium expressions for each of the given acids in water are: a. HCN: Reaction: \(\mathrm{HCN} \, (aq) + \mathrm{H_2O} \, (l) \rightleftharpoons \mathrm{H_3O^+} \, (aq) + \mathrm{CN^-} \, (aq)\) Equilibrium expression: \(K_{\mathrm{a}} = \frac{[\mathrm{H_3O^+}][\mathrm{CN^-}]}{[\mathrm{HCN}]}\) b. HOC\(_{6}\)H\(_{5}\): Reaction: \(\mathrm{HOC}_{6} \mathrm{H}_{5} \, (aq) + \mathrm{H_2O} \, (l) \rightleftharpoons \mathrm{H_3O^+} \, (aq) + \mathrm{OC}_{6} \mathrm{H}_{5}^- \, (aq) \) Equilibrium expression: \(K_{\mathrm{a}} = \frac{[\mathrm{H_3O^+}][\mathrm{OC}_{6} \mathrm{H}_{5}^{-}]}{[\mathrm{HOC}_{6} \mathrm{H}_{5}]}\) c. C\(_{6}\)H\(_{5}\)NH\(_{3}^{+}\): Reaction: \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+} \, (aq) + \mathrm{H_2O} \, (l) \rightleftharpoons \mathrm{H_3O^+} \, (aq) + \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2} \, (aq) \) Equilibrium expression: \(K_{\mathrm{a}} = \frac{[\mathrm{H_3O^+}][\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}]}{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}]} \)

Step by step solution

01

Dissociation Reaction of HCN#a Acid#

The acid dissociation reaction of hydrogen cyanide (HCN) in water can be represented as: \[ \mathrm{HCN} \, (aq) + \mathrm{H_2O} \, (l) \rightleftharpoons \mathrm{H_3O^+} \, (aq) + \mathrm{CN^-} \, (aq) \]
02

Equilibrium Expression for HCN#a Acid#

Based on the dissociation reaction, the equilibrium expression for the acid dissociation constant \(K_a\) of HCN is: \[ K_{\mathrm{a}} = \frac{[\mathrm{H_3O^+}][\mathrm{CN^-}]}{[\mathrm{HCN}]} \]
03

Dissociation Reaction of HOC\(_{6}\)H\(_{5}\) Acid#

The acid dissociation reaction of phenol (HOC\(_{6}\)H\(_{5}\)) in water can be represented as: \[ \mathrm{HOC}_{6} \mathrm{H}_{5} \, (aq) + \mathrm{H_2O} \, (l) \rightleftharpoons \mathrm{H_3O^+} \, (aq) + \mathrm{OC}_{6} \mathrm{H}_{5}^- \, (aq) \]
04

Equilibrium Expression for HOC\(_{6}\)H\(_{5}\) Acid#

Based on the dissociation reaction, the equilibrium expression for the acid dissociation constant \(K_a\) of HOC\(_{6}\)H\(_{5}\) is: \[ K_{\mathrm{a}} = \frac{[\mathrm{H_3O^+}][\mathrm{OC}_{6} \mathrm{H}_{5}^{-}]}{[\mathrm{HOC}_{6} \mathrm{H}_{5}]} \]
05

Dissociation Reaction of C\(_{6}\)H\(_{5}\)NH\(_{3}^{+}\) Acid#

The acid dissociation reaction of the anilinium ion (C\(_{6}\)H\(_{5}\)NH\(_{3}^{+}\)) in water can be represented as: \[ \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+} \, (aq) + \mathrm{H_2O} \, (l) \rightleftharpoons \mathrm{H_3O^+} \, (aq) + \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2} \, (aq) \]
06

Equilibrium Expression for C\(_{6}\)H\(_{5}\)NH\(_{3}^{+}\) Acid#

Based on the dissociation reaction, the equilibrium expression for the acid dissociation constant \(K_a\) of C\(_{6}\)H\(_{5}\)NH\(_{3}^{+}\) is: \[ K_{\mathrm{a}} = \frac{[\mathrm{H_3O^+}][\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}]}{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}]} \]

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