Problem 49 - General Chemistry

Question

Write the chemical equation for the base ionization of methylamine, \(\mathrm{CH}_{3} \mathrm{NH}_{2}\). Write the \(K_{b}\) expression for methylamine.

Step-by-Step Solution

Answer

The ionization equation is \(\mathrm{CH}_3\mathrm{NH}_2 + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{CH}_3\mathrm{NH}_3^{+} + \mathrm{OH}^-\) and \(K_b = \frac{[\mathrm{CH}_3\mathrm{NH}_3^+][\mathrm{OH}^-]}{[\mathrm{CH}_3\mathrm{NH}_2]}\).

Step 1: Identify the Reactants and Products

Methylamine (\(\mathrm{CH}_3\mathrm{NH}_2\)) is a weak base. When it ionizes in water, it accepts a proton from water, forming methylammonium ion (\(\mathrm{CH}_3\mathrm{NH}_3^{+}\)) and hydroxide ion (\(\mathrm{OH}^-\)). The chemical reaction is initialized as\(\text{Base} + \text{Water} \rightarrow \text{Conjugate Acid} + \text{Hydroxide Ion}\).

Step 2: Write the Chemical Equation

Based on the reactants identified, write the chemical equation for the base ionization of methylamine:\[\mathrm{CH}_3\mathrm{NH}_2(aq) + \mathrm{H}_2\mathrm{O}(l) \rightleftharpoons \mathrm{CH}_3\mathrm{NH}_3^{+}(aq) + \mathrm{OH}^-(aq)\].

Step 3: Define the Equilibrium Expression for Base Ionization (\(K_b\))

For a base ionization, \(K_b\) describes the equilibrium constant relating to the concentration of products over reactants. The expression for methylamine is:\[K_b = \frac{[\mathrm{CH}_3\mathrm{NH}_3^+][\mathrm{OH}^-]}{[\mathrm{CH}_3\mathrm{NH}_2]}\].

Key Concepts

Chemical Equation

A chemical equation represents a chemical reaction using symbols and formulas to illustrate the substances involved. In the scenario of base ionization, the equation shows how a weak base like methylamine reacts with water. Methylamine, denoted as \(\mathrm{CH}_3\mathrm{NH}_2\), interacts with water to form a methylammonium ion \(\mathrm{CH}_3\mathrm{NH}_3^+\) and a hydroxide ion \(\mathrm{OH}^-\). This interaction is depicted as:

• \(\mathrm{CH}_3\mathrm{NH}_2(aq) + \mathrm{H}_2\mathrm{O}(l) \rightleftharpoons \mathrm{CH}_3\mathrm{NH}_3^+(aq) + \mathrm{OH}^-(aq)\)

This equation indicates that methylamine accepts a proton from water. Furthermore, the double arrow \(\rightleftharpoons\) signifies an equilibrium where the reaction progresses in both forward and backward directions.

Equilibrium Constant

The equilibrium constant, in this case \(K_b\), quantifies the state of balance between reactants and products in a reversible reaction. It provides insight into the extent of ionization for weak bases like methylamine.

• For the reaction \(\mathrm{CH}_3\mathrm{NH}_2 + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{CH}_3\mathrm{NH}_3^+ + \mathrm{OH}^-\), the constant expression is \(K_b = \frac{[\mathrm{CH}_3\mathrm{NH}_3^+][\mathrm{OH}^-]}{[\mathrm{CH}_3\mathrm{NH}_2]}\)

This formula is derived from the concentration of each species at equilibrium, where brackets \([...]\) indicate molarity. A larger \(K_b\) value implies stronger base ionization, whereas a smaller value suggests weaker ionization. This concept helps predict how much of the base has converted into its ions in solution.

Weak Base

A weak base, such as methylamine, is a base that does not completely ionize in solution. Unlike strong bases, which dissociate entirely in water, weak bases do so only partially, leading to the presence of both non-ionized and ionized forms in equilibrium.

• Methylamine's ionization is a reversible process, represented by the equation:\[\mathrm{CH}_3\mathrm{NH}_2 + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{CH}_3\mathrm{NH}_3^+ + \mathrm{OH}^-\]

This equilibrium reflects the weak ionizing nature of methylamine, where not all molecules convert to ions and a noticeable amount remains as molecules. Understanding the behavior and characteristics of weak bases helps in predicting and managing chemical reactions in solutions.

Methylamine

Methylamine, represented as \(\mathrm{CH}_3\mathrm{NH}_2\), is a simple aliphatic amine known for its characteristic fishy odor. As a weak base, it plays a significant role in organic and analytical chemistry.

• When dissolved in water, methylamine accepts a proton from water to form the methylammonium ion \(\mathrm{CH}_3\mathrm{NH}_3^+\)
• It also results in the production of hydroxide ions \(\mathrm{OH}^-\), contributing to the basicity of the solution

The reaction is an example of base ionization where equilibrium is involved, marked by:

• \(\mathrm{CH}_3\mathrm{NH}_2(aq) + \mathrm{H}_2\mathrm{O}(l) \rightleftharpoons \mathrm{CH}_3\mathrm{NH}_3^+(aq) + \mathrm{OH}^-(aq)\)

Recognizing methylamine's properties and behavior aids in various chemical applications, from synthesizing pharmaceuticals to surface coating in industrial processes.