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

(a) The ionization of Dimethylamine: \((\mathrm{CH}_{3})_{2}\mathrm{NH} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons (\mathrm{CH}_{3})_{2}\mathrm{NH}_{2}^{+} + \mathrm{OH}^{-}\), \(K_{b} = \dfrac{[ (\mathrm{CH}_{3})_{2}\mathrm{NH}_{2}^{+} ][\mathrm{OH}^{-}]}{[(\mathrm{CH}_{3})_{2}\mathrm{NH}]}\) (b) The ionization of Carbonate ion: \(\mathrm{CO}_{3}^{2-} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{HCO}_{3}^{-} + \mathrm{OH}^{-}\), \(K_{b} = \dfrac{[\mathrm{HCO}_{3}^{-}][\mathrm{OH}^{-}]}{[\mathrm{CO}_{3}^{2-}]}\) (c) The ionization of Formate ion: \(\mathrm{CHO}_{2}^{-} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{HCHO}_{2} + \mathrm{OH}^{-}\), \(K_{b} = \dfrac{[\mathrm{HCHO}_{2}][\mathrm{OH}^{-}]}{[\mathrm{CHO}_{2}^{-}]}\)

Step-by-step solution

(a) Dimethylamine: Write the chemical equation for ionization

To write the chemical equation for the ionization of dimethylamine in the aqueous solution, we have: \((\mathrm{CH}_{3})_{2}\mathrm{NH} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons (\mathrm{CH}_{3})_{2}\mathrm{NH}_{2}^{+} + \mathrm{OH}^{-}\)

(a) Dimethylamine: Write the \(K_b\) expression

The \(K_{b}\) expression for the ionization of dimethylamine is: \(K_{b} = \dfrac{[ (\mathrm{CH}_{3})_{2}\mathrm{NH}_{2}^{+} ][\mathrm{OH}^{-}]}{[(\mathrm{CH}_{3})_{2}\mathrm{NH}]}\)

(b) Carbonate ion: Write the chemical equation for ionization

To write the chemical equation for the ionization of carbonate ion in the aqueous solution, we have: \(\mathrm{CO}_{3}^{2-} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{HCO}_{3}^{-} + \mathrm{OH}^{-}\)

(b) Carbonate ion: Write the \(K_b\) expression

The \(K_{b}\) expression for the ionization of carbonate ion is: \(K_{b} = \dfrac{[\mathrm{HCO}_{3}^{-}][\mathrm{OH}^{-}]}{[\mathrm{CO}_{3}^{2-}]}\)

(c) Formate ion: Write the chemical equation for ionization

To write the chemical equation for the ionization of formate ion in the aqueous solution, we have: \(\mathrm{CHO}_{2}^{-} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{HCHO}_{2} + \mathrm{OH}^{-}\)

(c) Formate ion: Write the \(K_b\) expression

The \(K_{b}\) expression for the ionization of formate ion is: \(K_{b} = \dfrac{[\mathrm{HCHO}_{2}][\mathrm{OH}^{-}]}{[\mathrm{CHO}_{2}^{-}]}\)

Key concepts

Ionization Constants

Ionization constants are crucial in understanding how bases and acids behave in water. In an aqueous solution, a base will partially ionize, forming hydroxide ions (\(\text{OH}^-\)). The equilibrium reached during this process is represented by the base dissociation constant, denoted as (K_b). This value helps us determine the strength of a base:

• If (K_b) is high, the base ionizes more completely, making it a strong base.
• If (K_b) is low, ionization is less complete, indicating a weak base.

Understanding (K_b) helps in predicting the behavior of bases in various chemical reactions. For instance, calculations involving (K_b) are essential when evaluating the concentrations of ions in a solution, providing insights into the solution's pH and reactivity.

Chemical Equations

Chemical equations depict the substances involved and the changes they undergo during a chemical reaction. When writing the ionization of bases, the equation shows how the base and water react to form conjugate acids and bases. Consider dimethylamine (\((\text{CH}_3)_2\text{NH}\)):

• Reactant side: Dimethylamine and water.
• Product side: Dimethylammonium ion \((\text{CH}_3)_2\text{NH}_2^+\) and hydroxide ion \(\text{OH}^-\).

These equations help us understand:

• How bases interact with water.
• The formation of conjugate acid-base pairs.

By balancing these equations, chemists ensure that the number of atoms and charges are equal on both sides, reflecting the law of conservation of mass. This understanding allows us to predict reaction outcomes accurately in chemical processes.

Aqueous Solutions

Aqueous solutions, where water acts as the solvent, are a common medium for many chemical reactions. The ionization process often occurs here because water has unique properties:

• It can stabilize ions through hydrogen bonding.
• Its polar nature helps dissolve ionic compounds.

In the case of bases like carbonate ion (\(\text{CO}_3^{2-}\)), their behavior in water determines how they react and affect the pH. As bases ionize:

• They increase hydroxide ion concentration, raising the solution's pH.
• The degree of ionization impacts the solution's basicity, influenced by temperature and concentration.

Aqueous solutions also facilitate various experiments and analytical techniques, making understanding their dynamics essential for a wide range of scientific and industrial applications.