A 0.135 M solution of a weak base has a pH of 11.23. Determine Kb for the base.

Verified step by step guidance

Identify the relationship between pH and pOH: \( \text{pH} + \text{pOH} = 14 \). Use this to find pOH from the given pH.

Calculate the hydroxide ion concentration \([\text{OH}^-]\) using the formula \([\text{OH}^-] = 10^{-\text{pOH}}\).

Set up the expression for the base dissociation constant \(K_b\) using the formula \(K_b = \frac{[\text{OH}^-]^2}{[\text{Base}] - [\text{OH}^-]}\).

Assume that \([\text{Base}] - [\text{OH}^-] \approx [\text{Base}]\) if \([\text{OH}^-]\) is much smaller than the initial concentration of the base.

Substitute the values into the \(K_b\) expression and solve for \(K_b\).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Weak Base and pH

A weak base is a substance that partially ionizes in solution, establishing an equilibrium between the base and its ions. The pH of a solution indicates its acidity or basicity, with values above 7 being basic. In this case, a pH of 11.23 suggests that the solution is basic, and the concentration of hydroxide ions can be derived from the pH to help calculate the base's dissociation constant.

Equilibrium Constant (Kb)

The base dissociation constant (Kb) quantifies the strength of a weak base in solution. It is defined as the ratio of the concentration of the products (the ions formed) to the concentration of the reactants (the un-ionized base) at equilibrium. For a weak base, Kb can be calculated using the concentrations of the base and its ions at equilibrium, which can be derived from the pH and initial concentration.

Relationship Between pH and pOH

The pH and pOH of a solution are related through the equation pH + pOH = 14 at 25°C. This relationship allows us to convert pH values into pOH values, which can then be used to find the concentration of hydroxide ions (OH-) in the solution. Knowing the concentration of OH- is essential for calculating Kb, as it directly relates to the degree of ionization of the weak base.

Recommended video:

Guided course

02:09

pH and pOH Calculations

Related Practice

Textbook Question

Caffeine (C₈H₁₀N₄O₂) is a weak base with a pK_b of 10.4. Calculate the pH of a solution containing a caffeine concentration of 455 mg/L.

views

Textbook Question

Amphetamine (C₉H₁₃N) is a weak base with a pK_b of 4.2. Calculate the pH of a solution containing an amphetamine concentration of 225 mg/L.

Textbook Question

Morphine is a weak base. A 0.150 M solution of morphine has a pH of 10.7. What is K_b for morphine?

views

Textbook Question

Determine if each anion acts as a weak base in solution. For those anions that are basic, write an equation that shows how the anion acts as a base. a. Br^– b. ClO^– c. CN^– d. Cl^–

views

Textbook Question

Determine whether each anion is basic or neutral. For those anions that are basic, write an equation that shows how the anion acts as a base. c. NO₃^–

Textbook Question

Determine the [OH^–] and pH of a solution that is 0.140 M in F^–.