Oxycodone 1C18H21NO42, a narcotic analgesic, is a weak base with pKb = 5.47. Calculate the pH and the concentrations of all species present (C18H21NO4, HC18H21NO4 + , H3O+ , and OH-) in a 0.002 50 M oxycodone solution.

검증된 단계별 안내

Identify the species in solution: Oxycodone (C18H21NO4) is a weak base, and it will partially accept protons to form its conjugate acid (HC18H21NO4+).

Use the given pKb to find the Kb (base dissociation constant) using the formula: \( K_b = 10^{-pK_b} \).

Set up the equilibrium expression for the base dissociation: \( C18H21NO4 + H_2O \rightleftharpoons HC18H21NO4^+ + OH^- \).

Write the expression for Kb: \( K_b = \frac{[HC18H21NO4^+][OH^-]}{[C18H21NO4]} \). Assume \([HC18H21NO4^+] = [OH^-] = x\) and \([C18H21NO4] = 0.00250 - x\).

Solve for x (\([OH^-]\)) using the Kb expression, then calculate \([H_3O^+]\) using \( [H_3O^+] = \frac{K_w}{[OH^-]} \), where \( K_w = 1.0 \times 10^{-14} \). Finally, calculate the pH using \( pH = -\log[H_3O^+] \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Weak Bases and pKb

A weak base is a substance that partially ionizes in solution, establishing an equilibrium between the base and its conjugate acid. The pKb value indicates the strength of the base; a higher pKb means a weaker base. In this case, oxycodone has a pKb of 5.47, which helps determine the extent of its ionization in solution and the resulting concentrations of its species.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of an acid and the ratio of the concentrations of its conjugate base and acid forms. For weak bases, it can be rearranged to find the pH based on the pKb and the concentrations of the base and its conjugate acid. This equation is essential for calculating the pH in the context of oxycodone's ionization.

Equilibrium Concentrations

In a solution, the concentrations of all species at equilibrium can be determined using the initial concentration and the extent of ionization. For oxycodone, the equilibrium involves the weak base (C18H21NO4), its conjugate acid (HC18H21NO4+), and the ions (H3O+ and OH-). Understanding how to set up and solve equilibrium expressions is crucial for calculating the concentrations of these species in the given solution.