Problem 50 - General Chemistry

Question

Write the chemical equation for the base ionization of aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2} .\) Write the \(K_{b}\) expression for aniline.

Step-by-Step Solution

Answer

Aniline ionizes to form \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) and \(\mathrm{OH}^{-}\). The \(K_b\) expression is \(\frac{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}][\mathrm{OH}^{-}]}{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}]}\).

Step 1: Define the Base Ionization Reaction

Aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\), acts as a weak base and reacts with water in a base ionization reaction. When aniline receives a proton from water, it forms its conjugate acid and hydroxide ions:\[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2} (aq) + \mathrm{H}_{2} \mathrm{O} (l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} (aq) + \mathrm{OH}^{-} (aq)\]This equation shows the ionization of aniline in water to form hydroxide ions.

Step 2: Write the Expression for the Base Ionization Constant ( K_b )

The base ionization constant, \(K_b\), is used to measure the strength of a base in solution. It is defined in terms of the equilibrium concentrations of the products and reactants. For the reaction above, the \(K_b\) expression is:\[K_b = \frac{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}] [\mathrm{OH}^{-}]}{[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}]}\]Here, the concentrations of the products and reactants are used to express the \(K_b\) value at equilibrium.

Key Concepts

Weak Base

When you hear the term "weak base," it refers to a base that does not fully ionize in solution. Unlike strong bases that dissociate completely, weak bases only partially dissociate to form hydroxide ions in water. Aniline, represented by the chemical formula \({C}_{6} {H}_{5} {NH}_{2}\), is a great example of a weak base.
Aniline's ability to receive protons from water characterizes its behavior as a weak base. In this process, only a small fraction of aniline molecules will react with water to form its conjugate acid and hydroxide ions. This limited reaction results in a lower concentration of hydroxide ions in the solution compared to that produced by a strong base.
Understanding this concept is crucial for predicting how a substance like aniline will behave in different chemical environments. It affects the pH of the solution and plays a significant role in various chemical processes where control over the acidity or basicity is needed.

Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction where the reactants are transformed into products. It includes chemical formulas, symbols, and coefficients to represent the quantities of each substance involved. In the case of aniline's base ionization, the chemical equation helps illustrate how aniline reacts with water.
The base ionization of aniline can be represented as: \[{C}_{6} {H}_{5} {NH}_{2} (aq) + {H}_{2} {O} (l) \rightleftharpoons {C}_{6} {H}_{5} {NH}_{3}^{+} (aq) + {OH}^{-} (aq)\]
In this equation:

• \({C}_{6} {H}_{5} {NH}_{2}\) is the weak base, aniline.
• \({H}_{2} {O}\) acts as the solvent, providing protons.
• \({C}_{6} {H}_{5} {NH}_{3}^{+}\) is the conjugate acid formed.
• \({OH}^{-}\) are the hydroxide ions produced.

This equation demonstrates the equilibrium between the reactants and products. It shows how aniline gains a proton from water, leading to a reversible reaction where not all aniline molecules are ionized.

Equilibrium Constant

The equilibrium constant, specifically the base ionization constant \(K_b\), is a value that measures the strength of a base in solution. It quantifies the extent to which a base ionizes, providing insight into the equilibrium between reactants and products in a reversible reaction.
For aniline's ionization, the \(K_b\) expression is crafted from the concentrations of species present when equilibrium is reached:

• The concentration of \({C}_{6} {H}_{5} {NH}_{3}^{+}\) (conjugate acid)
• The concentration of \({OH}^{-}\) (hydroxide ions)
• The concentration of \({C}_{6} {H}_{5} {NH}_{2}\) (unreacted weak base)

The \(K_b\) expression is given by:\[K_b = \frac{[\text{C}_{6} \text{H}_{5} \text{NH}_{3}^{+}] [\text{OH}^{-}]}{[\text{C}_{6} \text{H}_{5} \text{NH}_{2}]}\]
The equilibrium constant is a crucial parameter. It helps chemists understand the degree to which a base like aniline will ionize and predict how a base will alter the pH of a solution. A low \(K_b\) value indicates a weaker base, while a higher value suggests a stronger base that ionizes more completely.