Question

Calculate \(\left[\mathrm{OH}^{-}\right],\left[\mathrm{H}^{+}\right],\) and the \(\mathrm{pH}\) of \(0.20 M\) solutions of each of the following amines. a. triethylamine \(\left[\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{3} \mathrm{N}, K_{\mathrm{b}}=4.0 \times 10^{-4}\right]\) b. hydroxylamine (HONH \(\left._{2}, K_{\mathrm{b}}=1.1 \times 10^{-8}\right)\)

Short answer

a. For the triethylamine solution: - [OH-] = 2.0 * 10^-2 M - [H+] = 5.0 * 10^-13 M - pH = 12.3 b. For the hydroxylamine solution: - [OH-] = 4.7 * 10^-4 M - [H+] = 2.1 * 10^-11 M - pH = 10.7

Step-by-step solution

Write the base-dissociation reaction and Kb expression for each amine

First, we need to write the base dissociation reaction and the Kb expression for each amine. a. For triethylamine, (C2H5)3N: Base dissociation reaction: (C2H5)3N + H2O -> (C2H5)3NH+ + OH- Kb expression: \(K_{b} = \frac{[(C_{2}H_{5})_{3}NH^{+}][OH^{-}]}{(C_{2}H_{5})_{3}N}\) b. For hydroxylamine, HONH2: Base dissociation reaction: HONH2 + H2O -> HONH3+ + OH- Kb expression: \(K_{b} = \frac{[HONH_{3}^{+}][OH^{-}]}{HONH_{2}}\)

Calculate the initial concentration of amine and dissociation

Initial concentration of each amine is given as 0.20 M. a. For triethylamine, let the dissociation per mole be x. Then, the concentration of (C2H5)3NH+ will be x, and the concentration of (C2H5)3N will be (0.20 - x) after dissociation. b. For hydroxylamine, let the dissociation per mole be x. Then, the concentration of HONH3+ will be x, and the concentration of HONH2 will be (0.20 - x) after dissociation.

Substitute the known values in Kb expressions and solve for x

Substitute the values in the Kb expression for each amine, and solve for x. a. For triethylamine: \(4.0 \times 10^{-4} = \frac{x^2}{0.20 - x}\) Assuming x << 0.20, we can approximate: \(4.0 \times 10^{-4} \approx \frac{x^2}{0.20}\) b. For hydroxylamine: \(1.1 \times 10^{-8} = \frac{x^2}{0.20 - x}\) Assuming x << 0.20, we can approximate: \(1.1 \times 10^{-8} \approx \frac{x^2}{0.20}\)

Find [OH-], [H+], and pH for each amine solution

Find [OH-], [H+], and pH for each amine solution using the calculated x values. a. For triethylamine, [OH-] = x: 1. x = 0.20 * sqrt(4.0 * 10^-4) = 2.0 * 10^-2 M 2. [H+] = Kw (10^-14) / [OH-] = 10^-14 / 2.0 * 10^-2 = 5.0 * 10^-13 M 3. pH = -log10(5.0 * 10^-13) = 12.3 b. For hydroxylamine, [OH-] = x: 1. x = 0.20 * sqrt(1.1 * 10^-8) = 4.7 * 10^-4 M 2. [H+] = Kw (10^-14) / [OH-] = 10^-14 / 4.7 * 10^-4 = 2.1 * 10^-11 M 3. pH = -log10(2.1 * 10^-11) = 10.7 So, the final answers are: a. [OH-] = 2.0 * 10^-2 M, [H+] = 5.0 * 10^-13 M, pH = 12.3 for the triethylamine solution. b. [OH-] = 4.7 * 10^-4 M, [H+] = 2.1 * 10^-11 M, pH = 10.7 for the hydroxylamine solution.

Key concepts

Base Dissociation

In chemistry, base dissociation is a crucial concept when discussing amines. Amines are organic compounds derived from ammonia by replacement of one or more hydrogen atoms with organic groups. They act as bases when they accept protons from acids in a reaction known as dissociation.
A base dissociation reaction involves an amine interacting with water to form a positively charged amine ion and a hydroxide ion (OH-). This process is important for understanding how basicity operates in solution. For instance, triethylamine ((C2H5)3N) dissociates into (C2H5)3NH+ and OH-. Similarly, hydroxylamine (HONH2) dissociates into HONH3+ and OH-. Understanding these reactions helps us calculate important chemical properties like pH.

Kb Expression

The concept of Kb, or base dissociation constant, reflects a base's strength in water. This constant is specific to each base and is derived from the equilibrium concentrations of the reactants and products in a base dissociation reaction.
For triethylamine, the Kb expression is given by: \[ K_b = \frac{[(C_{2}H_{5})_{3}NH^{+}][OH^{-}]}{(C_{2}H_{5})_{3}N} \] The Kb for triethylamine is 4.0 x 10^-4, indicating its ability to produce OH- ions in water.
For hydroxylamine, the Kb expression is: \[ K_b = \frac{[HONH_{3}^{+}][OH^{-}]}{HONH_{2}} \] With a much smaller Kb of 1.1 x 10^-8, hydroxylamine is a weaker base compared to triethylamine. By solving these expressions, you can determine how much of the base will dissociate in solution, a crucial step for pH calculation.

pH Calculation

The pH of a solution is a measure of its acidity or basicity. For a basic solution, such as those containing amines, the pH is calculated indirectly from the hydroxide ion concentration ([OH-]).
To find [OH-], insert the Kb and initial concentration values into the Kb expression and solve for x, which represents the [OH-]. In the cases of triethylamine and hydroxylamine, it's often assumed x is small, simplifying the calculation.
Once [OH-] is known, calculate [H+] using the relation: \[ [H^+] = \frac{10^{-14}}{[OH^-]} \]Finally, determine the pH using: \[ pH = -\log_{10}([H^+]) \] This series of calculations permits us to determine the specific pH of different amine solutions, such as triethylamine with a pH of 12.3 and hydroxylamine with a pH of 10.7, corresponding to their distinct basic strengths.

Hydroxylamine

Hydroxylamine (HONH2) is a weak base and a derivative of ammonia with an -OH group replacing one hydrogen atom. It reacts with water to form hydroxylammonium ions (HONH3+), contributing a smaller amount of OH- compared to stronger bases.
The Kb for hydroxylamine is quite low at 1.1 x 10^-8, signifying limited dissociation in water. This affects the pH of its solutions, resulting in a relatively lower basicity, with a pH of about 10.7 in a 0.20 M solution. Despite its weak base nature, hydroxylamine is crucial in various chemical reactions, particularly in organic synthesis and as a reducing agent.

Triethylamine

Triethylamine ((C2H5)3N) is a stronger base than hydroxylamine, characterized by three ethyl groups attached to a nitrogen atom. These alkyl groups donate electron density to the nitrogen, enhancing its ability to accept protons.
Triethylamine readily dissociates in water, forming triethylammonium ions and OH- ions, with a Kb of 4.0 x 10^-4, indicating a higher tendency to produce hydroxide ions in the solution.
Its 0.20 M aqueous solution has a high pH of 12.3, reflecting its strong basicity. Triethylamine is often used in industrial applications, such as in the production of quaternary ammonium compounds and as a catalyst due to its effective basic properties.