Question

Write the general equation for the ionization of a weak base, \(B\), in water. Give the equilibrium law corresponding to \(K_{b}\).

Short answer

General ionization equation: \(B + H_2O \leftrightarrow BH^+ + OH^-\). Equilibrium law: \(K_b = \frac{[BH^+][OH^-]}{[B]}\).

Step-by-step solution

Write the Ionization Reaction

To write the ionization reaction of a weak base, we must show the weak base, B, reacting with water (H2O) to form its conjugate acid, BH+, and hydroxide ions, OH-. The general equation is: \(B + H_2O \leftrightarrow BH^+ + OH^-\).

Write the Equilibrium Expression

The equilibrium expression is based on the concentrations of the products and reactants when the reaction reaches equilibrium. It is expressed as: \( K_b = \frac{[BH^+][OH^-]}{[B]} \), where \(K_b\) is the base ionization constant.

Key concepts

Ionization Reaction

The ionization reaction of a weak base is fundamental to understanding acid-base chemistry. A weak base is an entity that partially dissociates in solution to produce hydroxide ions, \(OH^{-}\), which are responsible for the basic property of the solution. Unlike strong bases that dissociate completely, weak bases only ionize to a small extent. The ionization reaction for a generic weak base, \(B\), interacting with water \(\(H_2O\)\) is represented by the following reversible reaction:
\[B + H_2O \rightleftharpoons BH^{+} + OH^{-}\].
In this equilibrium process, \(B\) accepts a proton from water to form its conjugate acid \(BH^{+}\), and in the process, water acts as an acid, donating a proton and leaving behind a hydroxide ion. This reaction is essential because it determines the pH of the solution and ultimately the properties and behavior of the weak base in various chemical contexts.

To further assist students in understanding this concept, they should be encouraged to identify this reaction as an equilibrium process, which is dynamic and reversible, unlike the complete ionization seen with strong bases.

Equilibrium Expression

The concept of the equilibrium expression is crucial when dealing with reversible reactions, such as the ionization of a weak base. At equilibrium, the rate of the forward reaction, where the base and water react to form the conjugate acid and hydroxide, is equal to the rate of the reverse reaction, where the conjugate acid donates a proton back to the hydroxide ion forming water and the base again. To express this equilibrium mathematically, chemists use an equilibrium expression, which is a ratio of the concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients.

For the ionization of a weak base, the equilibrium expression, known as the base ionization constant \(K_b\), is given by: \[K_b = \frac{[BH^{+}][OH^{-}]}{[B]}\]
Here, the concentrations of the products, \(BH^{+}\) and \(OH^{-}\), are in the numerator, and the concentration of the weak base, \(B\), is in the denominator. It's important to note that liquid water isn't included in the expression as its concentration is effectively constant and does not affect the equilibrium position.

Base Ionization Constant

The base ionization constant, \(K_b\), is a quantitative measure of the strength of a weak base in solution. This value gives us insight into how far the ionization proceeds at equilibrium. A larger \(K_b\) implies a stronger base, meaning it ionizes to a greater extent, whereas a smaller \(K_b\) indicates a weaker base with a lesser degree of ionization. Understanding the \(K_b\) value is crucial for predicting the pH of the solution and the behavior of the base in chemical reactions.

To provide practical insight, exercises involving calculating \(K_b\) from known concentrations of the base and its ionized forms, or vice versa, can be invaluable. Additionally, recognizing the relationship between the base ionization constant and the acid dissociation constant (Ka) for the conjugate acid can further illuminate the interrelated nature of acidic and basic solutions.