Question

At \(25^{\circ} \mathrm{C}\), a \(0.20 \mathrm{M}\) solution of methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) is \(5.0 \%\) ionized. What is \(K_{b}\) for methylamine?

Short answer

Answer: The Kb value for the methylamine solution is approximately 5.26 x 10^(-4).

Step-by-step solution

Understand the Ionization Reaction

Methylamine (CH3NH2) is a weak base. When it undergoes ionization, it reacts with water (H2O) to produce a hydroxide ion (OH-) and a methylammonium ion (CH3NH3+). The ionization equation is: CH3NH2 + H2O ↔ CH3NH3+ + OH-

Calculate Initial Ionized Species Concentrations

Since the solution is initially 5.0% ionized, we can calculate the concentration of CH3NH2 that has ionized: 0.05 * 0.20 M CH3NH2 = 0.01 M CH3NH2 ionized The ion concentrations will be the same for CH3NH3+ and OH- since they are produced in a 1:1 ratio: [CH3NH3+] = [OH-] = 0.01 M

Calculate the Remaining CH3NH2 Concentration

Subtract the ionized CH3NH2 concentration from the initial concentration to find the remaining CH3NH2 concentration: 0.20 M - 0.01 M = 0.19 M CH3NH2

Calculate Kb using Ion Concentrations and Base Equation

Now, we can use the calculated concentrations and the base-dissociation constant equation to find Kb: Kb = ([CH3NH3+] [OH-]) / [CH3NH2] Kb = (0.01 M * 0.01 M) / 0.19 M Kb ≈ 5.26 x 10^(-4) The Kb value for methylamine is approximately 5.26 x 10^(-4).

Key concepts

Methylamine

Methylamine (CH₃NH₂) is a simple amine that acts as a weak base. In chemistry, methylamine is fascinating due to its ability to accept protons. It has a single -NH₂ group attached to a methyl group (CH₃-), giving it basic properties. In water, methylamine does not fully dissociate. Instead, only a portion of the molecules reacts to form ions. Methylamine is used in various industrial applications and is important in organic reactions as a building block. Its behavior under ionization conditions is crucial for understanding its role in chemical reactions.

Weak Bases

Weak bases, such as methylamine, do not fully ionize in solution. They only partially accept protons when dissolved in water, which results in a relatively low concentration of hydroxide ions (OH⁻).
Characteristics of Weak Bases:

• Low degree of ionization.
• Intermediate pH values, typically between 8 and 10.
• The amount of base that ionizes is often expressed as a percentage.

The inability of weak bases to completely ionize is a key reason why their related equilibrium constant, the base dissociation constant (Kₚ), is a relatively small number. Understanding this concept is essential in calculating equilibrium concentrations for reactions involving weak bases.

Ionization

Ionization refers to the process where molecules split into ions in solution. For weak bases like methylamine, ionization occurs when they interact with water molecules. During this process, methylamine gains a proton from water, forming hydroxide ions (OH⁻) and methylammonium ions (CH₃NH₃⁺).
Key Points of Ionization in Weak Bases:

• Ionization is partial, leading to equilibrium.
• Affects the pH of the solution.
• Ionization percentage helps in calculating dissociation constants like Kₚ.

In the example of methylamine at 25°C, only 5% of the solution ionizes. This means that out of every 100 molecules, 5 molecules will form ions in the solution, significant for calculating Kₚ and understanding the base's reactivity.