Consider the titration of 50.0 mL of a 0.100 M solution of the protonated form of the amino acid alanine (H₂A⁺: K_a1 = 4.6 × 10^–3, K_a2 = 2.0 × 10^–10) with 0.100 M NaOH. Calculate the pH after the addition of each of the following volumes of base. (d) 75.0 mL

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Determine the initial moles of the protonated form of alanine (H2A+) using the initial concentration and volume: \( \text{moles of } H_2A^+ = 0.100 \text{ M} \times 0.050 \text{ L} \).

Calculate the moles of NaOH added using its concentration and the volume added: \( \text{moles of NaOH} = 0.100 \text{ M} \times 0.075 \text{ L} \).

Determine the limiting reactant by comparing the initial moles of H2A+ and the moles of NaOH added.

Identify the species present after the reaction and their concentrations. If NaOH is in excess, calculate the concentration of OH- ions.

Use the concentration of OH- ions to calculate the pOH, and then find the pH using the relation \( \text{pH} = 14 - \text{pOH} \).

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주요 개념

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

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (in this case, NaOH) to a solution containing the analyte (the protonated form of alanine) until the reaction reaches its equivalence point. The pH changes during this process can be monitored to understand the acid-base behavior of the solution.

Acid-Base Equilibria

Acid-base equilibria describe the balance between protonated and deprotonated forms of a substance in solution. For alanine, the two dissociation constants (Ka1 and Ka2) indicate how readily it donates protons. Understanding these constants is crucial for calculating the pH at various stages of the titration, especially when determining the pH after adding specific volumes of NaOH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a way to calculate the pH of a buffer solution based on the concentrations of the acid and its conjugate base. It is expressed as pH = pKa + log([A-]/[HA]). This equation is particularly useful in titration scenarios, as it allows for the determination of pH at points where the solution contains both the protonated and deprotonated forms of the amino acid.

Consider the titration of 50.0 mL of a 0.100 M solution of the protonated form of the amino acid alanine (H2A+: Ka1 = 4.6 × 10–3, Ka2 = 2.0 × 10–10) with 0.100 M NaOH. Calculate the pH after the addition of each of the following volumes of base. (d) 75.0 mL