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. (a) What are the equilibrium concentrations of C10H15ON, C10H15ONH+, and OH-?

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 find the equilibrium concentrations of C_{10}H_{15}ON, C_{10}H_{15}ONH^+, and OH^-.
2. <Step 2: Calculate the concentration of OH^-.> 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.> Write the equilibrium expression for the dissociation of the weak base: \( C_{10}H_{15}ON + H_2O \rightleftharpoons C_{10}H_{15}ONH^+ + OH^- \).
4. <Step 4: Use the ICE table.> Set up an ICE (Initial, Change, Equilibrium) table to express the changes in concentrations. Initially, [C_{10}H_{15}ON] = 0.035 M, and [C_{10}H_{15}ONH^+] and [OH^-] are 0. At equilibrium, [C_{10}H_{15}ON] = 0.035 - x, [C_{10}H_{15}ONH^+] = x, and [OH^-] = x.
5. <Step 5: Solve for x.> Use the equilibrium expression and the calculated [OH^-] to solve for x, which represents the change in concentration. This will give you the equilibrium concentrations of C_{10}H_{15}ON, C_{10}H_{15}ONH^+, and OH^-.

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium involves the balance between acids and bases in a solution, characterized by the transfer of protons (H+ ions). In this context, ephedrine acts as a weak base, accepting protons from water to form its conjugate acid, C10H15ONH+. Understanding this equilibrium is crucial for calculating the concentrations of the species involved.

pH and pOH

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. In a basic solution, pOH can also be calculated, which is the negative logarithm of the hydroxide ion concentration. The relationship between pH and pOH is given by the equation pH + pOH = 14, which is essential for determining the concentrations of hydroxide ions in this problem.

Concentration Calculations

Concentration calculations involve determining the molarity of different species in a solution at equilibrium. Given the initial concentration of ephedrine and the pH, one can use the equilibrium expression and the known values to find the concentrations of C10H15ON, C10H15ONH+, and OH-. This requires an understanding of stoichiometry and the principles of chemical equilibrium.