Question

Write the chemical equation and the \(K_{b}\) expression for the ionization of each of the following bases in aqueous solution: (a) dimethylamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} ;\) (b) carbonate ion, \(\mathrm{CO}_{3}{ }^{2-} ;(\mathrm{c})\) formate ion, \(\mathrm{CHO}_{2}^{-}\).

Short answer

For the ionization of each given base in aqueous solution and their corresponding \(K_{b}\) expressions, we have: a) Dimethylamine (\((\mathrm{CH}_{3})_2\mathrm{NH}\)): Ionization equation: \((\mathrm{CH}_{3})_{2} \mathrm{NH} + H_2O \rightleftharpoons (\mathrm{CH}_{3})_{2} \mathrm{NH}_2^+ + OH^-\) \(K_b\) expression: \(K_{b} = \frac{[(\mathrm{CH}_{3})_{2} \mathrm{NH}_2^+][OH^-]}{[(\mathrm{CH}_{3})_{2} \mathrm{NH}]}\) b) Carbonate ion (\(\mathrm{CO}_{3}^{2-}\)): Ionization equation: \(\mathrm{CO}_{3}^{2-} + H_2O \rightleftharpoons \mathrm{HCO}_{3}^- + OH^-\) \(K_b\) expression: \(K_{b} = \frac{[\mathrm{HCO}_{3}^-][OH^-]}{[\mathrm{CO}_{3}^{2-}]}\) c) Formate ion (\(\mathrm{CHO}_{2}^{-}\)): Ionization equation: \(\mathrm{CHO}_{2}^{-} + H_2O \rightleftharpoons \mathrm{HCHO}_{2} + OH^-\) \(K_b\) expression: \(K_{b} = \frac{[\mathrm{HCHO}_{2}][OH^-]}{[\mathrm{CHO}_{2}^{-}]}\)

Step-by-step solution

Write the chemical equation for ionization of each base in aqueous solution

For a general base B reacting with water, the ionization equation can be written as: \[ B + H_2O \rightleftharpoons BH^+ + OH^-\] Now, let's write the ionization equations for each given base in aqueous solution. a) Dimethylamine (\((\mathrm{CH}_{3})_2\mathrm{NH}\)): \[(\mathrm{CH}_{3})_{2} \mathrm{NH} + H_2O \rightleftharpoons (\mathrm{CH}_{3})_{2} \mathrm{NH}_2^+ + OH^-\] b) Carbonate ion (\(\mathrm{CO}_{3}^{2-}\)): \[ \mathrm{CO}_{3}^{2-} + H_2O \rightleftharpoons \mathrm{HCO}_{3}^- + OH^-\] c) Formate ion (\(\mathrm{CHO}_{2}^{-}\)): \[\mathrm{CHO}_{2}^{-} + H_2O \rightleftharpoons \mathrm{HCHO}_{2} + OH^-\]

Write the \(K_{b}\) expression for each chemical equation

The \(K_{b}\) expression for a chemical equation is given by the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants. For a generic base ionization chemical equation as written in Step 1, the \(K_{b}\) expression would be: \[ K_{b} = \frac{[BH^+][OH^-]}{[B]}\] Now, let's write the \(K_{b}\) expressions for each of the bases given: a) Dimethylamine (\((\mathrm{CH}_{3})_2\mathrm{NH}\)): \[K_{b} = \frac{[(\mathrm{CH}_{3})_{2} \mathrm{NH}_2^+][OH^-]}{[(\mathrm{CH}_{3})_{2} \mathrm{NH}]}\] b) Carbonate ion (\(\mathrm{CO}_{3}^{2-}\)): \[K_{b} = \frac{[\mathrm{HCO}_{3}^-][OH^-]}{[\mathrm{CO}_{3}^{2-}]}\] c) Formate ion (\(\mathrm{CHO}_{2}^{-}\)): \[K_{b} = \frac{[\mathrm{HCHO}_{2}][OH^-]}{[\mathrm{CHO}_{2}^{-}]}\] These are the chemical equations for the ionization of each base in aqueous solution and their corresponding \(K_{b}\) expressions.

Key concepts

Dimethylamine Ionization

Dimethylamine, often symbolized as \((\mathrm{CH}_3)_2\mathrm{NH}\), is an organic compound that acts as a weak base. It ionizes in water to form dimethylammonium ions and hydroxide ions. This process can be represented by the chemical equation:

\[(\mathrm{CH}_3)_2\mathrm{NH} + H_2O \rightleftharpoons (\mathrm{CH}_3)_2\mathrm{NH}_2^+ + OH^-\]

Dimethylamine is a weak base due to the moderate attraction it has for hydrogen ions (protons). This limits its ionization in water.
The equilibrium constant for this base ionization reaction, known as the base ionization constant \(K_b\), is used to quantify this weak tendency to accept protons:

\[K_{b} = \frac{[(\mathrm{CH}_3)_2\mathrm{NH}_2^+][OH^-]}{[(\mathrm{CH}_3)_2\mathrm{NH}]}\]

This expression shows the relationship between the formed ions and the remaining base, reflecting the balance of the ionization process.

Carbonate Ion Ionization

Carbonate ion, \(\mathrm{CO}_3^{2-}\), is a polyatomic ion with the ability to accept a proton, and thus classify as a base. In water, it undergoes ionization to produce bicarbonate ions \(\mathrm{HCO}_3^-\) and hydroxide ions \(OH^-\). The reaction is given by:

\[\mathrm{CO}_3^{2-} + H_2O \rightleftharpoons \mathrm{HCO}_3^- + OH^-\]

This base is significant in many natural processes, including buffering solutions. The carbonate ion’s ability to produce hydroxide ions makes it a helpful component in balancing pH in aquatic environments.
The ionization constant \(K_b\) for this reaction is:

\[K_{b} = \frac{[\mathrm{HCO}_3^-][OH^-]}{[\mathrm{CO}_3^{2-}]}\]

This formula enables the calculation of the strength of carbonate as a base, helping to predict how it will behave in aqueous solutions.

Formate Ion Ionization

The formate ion, \(\mathrm{CHO}_2^-\), derives from formic acid and acts as a weak base in water. By accepting a proton, it forms formic acid \(\mathrm{HCHO}_2\) and hydroxide ions \(OH^-\):

\[\mathrm{CHO}_2^- + H_2O \rightleftharpoons \mathrm{HCHO}_2 + OH^-\]

The formate ion's role as a base involves its participation in various chemical reactions, especially in the context of buffer solutions.
The ionization constant \(K_b\) for formate reflects its weak basic properties:

\[K_{b} = \frac{[\mathrm{HCHO}_2][OH^-]}{[\mathrm{CHO}_2^-]}\]

This expression helps in understanding the equilibrium between the ionized and non-ionized states of formate in water and predicts its behavior in solution.