Question

Write equations showing how each weak base ionizes water to form \(\mathrm{OH}^{-}\). Also write the corresponding expression for \(K_{\mathrm{b}}\). a. \(\mathrm{NH}_{3}\) b. \(\mathrm{HCO}_{3}^{-}\) c. \(\mathrm{CH}_{3} \mathrm{NH}_{2}\)

Short answer

The ionization equations and corresponding \textrm{K}_b expressions are: (a) \textrm{NH}_3 + \textrm{H}_2O \rightleftharpoons \textrm{NH}_4^+ + \textrm{OH}^-, \textrm{K}_b = \frac{[\textrm{NH}_4^+][\textrm{OH}^-]}{[\textrm{NH}_3]}(b) \textrm{HCO}_3^- + \textrm{H}_2O \rightleftharpoons \textrm{H}_2\textrm{CO}_3 + \textrm{OH}^-, \textrm{K}_b = \frac{[\textrm{H}_2\textrm{CO}_3][\textrm{OH}^-]}{[\textrm{HCO}_3^-]}(c) \textrm{CH}_3\textrm{NH}_2 + \textrm{H}_2O \rightleftharpoons \textrm{CH}_3\textrm{NH}_3^+ + \textrm{OH}^-, \textrm{K}_b = \frac{[\textrm{CH}_3\textrm{NH}_3^+][\textrm{OH}^-]}{[\textrm{CH}_3\textrm{NH}_2]}

Step-by-step solution

- Write the Ionization Equation for \textrm{NH}_3

A weak base ionizes in water by accepting a proton (\textrm{H}^+) from a water molecule, resulting in the production of hydroxide ions (\textrm{OH}^-). For ammonia (\textrm{NH}_3), the ionization reaction would be: \[\textrm{NH}_3 (aq) + \textrm{H}_2\textrm{O} (l) \rightleftharpoons \textrm{NH}_4^+ (aq) + \textrm{OH}^- (aq)\]

- Write the Expression for \textrm{K}_b for \textrm{NH}_3

The base ionization constant expression (\textrm{K}_b) is written using the concentrations of the products over the reactants, excluding water as it is a pure liquid. For ammonia, the expression is: \[K_{b} = \frac{[NH_{4}^{+}][OH^{-}]}{[NH_{3}]}\]

- Write the Ionization Equation for \textrm{HCO}_3^-

Bicarbonate ion (\textrm{HCO}_3^-) also acts as a weak base in water: \[\textrm{HCO}_3^- (aq) + \textrm{H}_2\textrm{O} (l) \rightleftharpoons \textrm{H}_2\textrm{CO}_3 (aq) + \textrm{OH}^- (aq)\]

- Write the Expression for \textrm{K}_b for \textrm{HCO}_3^-

The expression for the base ionization constant of bicarbonate ion is: \[K_{b} = \frac{[H_2CO_3][OH^{-}]}{[HCO_3^{-}]}\]

- Write the Ionization Equation for \textrm{CH}_3\textrm{NH}_2

Methylamine (\textrm{CH}_3\textrm{NH}_2) is another weak base and its ionization can be represented by the following equation: \[\textrm{CH}_3\textrm{NH}_2 (aq) + \textrm{H}_2\textrm{O} (l) \rightleftharpoons \textrm{CH}_3\textrm{NH}_3^+ (aq) + \textrm{OH}^- (aq)\]

- Write the Expression for \textrm{K}_b for \textrm{CH}_3\textrm{NH}_2

The base ionization constant for methylamine is given by: \[K_{b} = \frac{[CH_3NH_3^{+}][OH^{-}]}{[CH_3NH_2]}\]

Key concepts

Base Ionization Constant

When discussing weak bases and their affinity to interact with water, we introduce the concept of a base ionization constant, usually represented by the symbol \(K_b\). It quantifies the extent to which a base can ionize in an aqueous solution. This ionization process usually involves the base accepting a proton \(\textrm{H}^+\) from a water molecule, which leads to the production of hydroxide ions \(\textrm{OH}^-\).

The value of \(K_b\) can tell us a lot about the strength of a base: the higher the \(K_b\), the stronger the base, meaning it ionizes more completely in water. Calculating \(K_b\) involves setting up an equilibrium expression that relates the concentrations of the products to the reactants. In the case of ammonia \(\textrm{NH}_3\), for example, the expression is \[K_{b} = \frac{[NH_{4}^{+}][OH^{-}]}{[NH_{3}]}\]where each concentration term is raised to the power of the coefficient in the balanced equation. It’s important to note that the concentration of water is not included in the expression because it’s the solvent and its concentration remains relatively constant.

Hydroxide Ion Production

The production of hydroxide ions \(\textrm{OH}^-\) is a key aspect of the ionization of weak bases in water. Once \(\textrm{OH}^-\) ions are generated, they increase the pH of the solution, making it more basic. The degree of ionization and thus the number of hydroxide ions produced depends on the strength of the base and the environmental conditions, such as temperature and the concentration of the base.

Weak bases like ammonia \(\textrm{NH}_3\), bicarbonate ion \(\textrm{HCO}_3^-\), and methylamine \(\textrm{CH}_3\textrm{NH}_2\), partially ionize in water, releasing fewer hydroxide ions compared to strong bases, which ionize completely. Thus, understanding how much \(\textrm{OH}^-\) is produced helps determine the base's ability to shift the pH, a concept crucial in fields like chemistry, biology, and environmental science.

Acid-Base Equilibrium

Acid-base equilibrium is a particular type of chemical equilibrium that occurs in solutions of acids and bases. It represents the point at which the rates of the forward reaction (where a weak base picks up a proton from water to produce \(\textrm{OH}^-\) and a conjugate acid) and the reverse reaction (where the conjugate acid donates a proton back to \(\textrm{OH}^-\)) are equal, leading to no net change in the concentrations of the reactants and products.

This dynamic balance is described by the equilibrium constant, for bases known as \(K_b\). A weak base’s incomplete ionization in water is a good illustration of such an equilibrium. The position of the equilibrium (favoring reactants or products) will depict the base's strength and, in turn, will impact the pH of the solution. Environmental factors can shift the equilibrium, thereby changing the concentration of \(\textrm{OH}^-\) ions present and affecting the solution's basicity.

Chemical Equilibrium Expressions

Chemical equilibrium expressions mathematically represent the state of equilibrium in a chemical reaction. For acid-base reactions, we use expressions like \(K_a\) for acids and \(K_b\) for bases. These constants express the ratio of the product concentrations to the reactant concentrations at equilibrium, excluding any pure solids or liquids (like water in dilute aqueous solutions).

The generic form of an equilibrium constant expression is \[K = \frac{\text{Products}}{\text{Reactants}}\]where the products and reactants are raised to the power of their respective coefficients in the balanced chemical equation. In the context of weak base ionization, these expressions help us understand how a particular base will behave in a water solution, the extent to which it will form hydroxide ions, and ultimately, its basic strength. These expressions are foundational when predicting the outcome of chemical reactions and calculating the pH of solutions in chemistry.