Ephedrine, a central nervous system stimulant, is used in nasal sprays as a decongestant. This compound is a weak organic base: C10H15ON1aq2 + H2O1l2 Δ C10H15ONH+1aq2 + OH-1aq2 A 0.035 M solution of ephedrine has a pH of 11.33. (b) Calculate Kb for ephedrine.

Verified step by step guidance

1. Step 1: Understand the problem. We are given a weak base, ephedrine, with a concentration of 0.035 M and a pH of 11.33. We need to calculate the base dissociation constant, K_b.
2. Step 2: Calculate the concentration of OH^- ions. Use the pH to find the pOH: \( \text{pOH} = 14 - \text{pH} \). Then, calculate the concentration of OH^- using \( [\text{OH}^-] = 10^{-\text{pOH}} \).
3. Step 3: Set up the equilibrium expression for the dissociation of ephedrine. The reaction is: \( \text{C}_{10}\text{H}_{15}\text{ON} + \text{H}_2\text{O} \rightleftharpoons \text{C}_{10}\text{H}_{15}\text{ONH}^+ + \text{OH}^- \).
4. Step 4: Write the expression for K_b. The base dissociation constant is given by \( K_b = \frac{[\text{C}_{10}\text{H}_{15}\text{ONH}^+][\text{OH}^-]}{[\text{C}_{10}\text{H}_{15}\text{ON}]} \).
5. Step 5: Substitute the known values into the K_b expression. Use the initial concentration of ephedrine and the calculated concentration of OH^- to find K_b.

Key Concepts

Weak Bases and Kb

Weak bases are substances that partially ionize in solution, establishing an equilibrium between the un-ionized base and its ions. The base dissociation constant (Kb) quantifies the strength of a weak base, indicating the extent to which it can accept protons from water. A higher Kb value signifies a stronger base, while a lower value indicates a weaker base.

pH and pOH Relationship

pH is a measure of the hydrogen ion concentration in a solution, while pOH measures the hydroxide ion concentration. The relationship between pH and pOH is defined by the equation pH + pOH = 14 at 25°C. In the context of weak bases, knowing the pH allows for the calculation of pOH, which is essential for determining the concentration of hydroxide ions in the solution.

Equilibrium Expressions

Equilibrium expressions describe the ratio of the concentrations of products to reactants at equilibrium for a given reaction. For the dissociation of a weak base, the Kb expression is formulated as Kb = [BH+][OH-] / [B], where [B] is the concentration of the un-ionized base, [BH+] is the concentration of the conjugate acid, and [OH-] is the concentration of hydroxide ions. This expression is crucial for calculating Kb from the concentrations at equilibrium.