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. (a) 10.0 mL

검증된 단계별 안내

Step 1: Determine the initial moles of the protonated form of alanine (H2A+). Use the formula: moles = concentration × volume. Here, the initial concentration is 0.100 M and the volume is 50.0 mL.

Step 2: Calculate the moles of NaOH added. Use the formula: moles = concentration × volume. The concentration of NaOH is 0.100 M and the volume added is 10.0 mL.

Step 3: Determine the reaction between H2A+ and NaOH. The reaction is: H2A+ + OH- → HA + H2O. Calculate the moles of H2A+ and OH- after the reaction.

Step 4: Identify the species present in the solution after the reaction. Since NaOH is a strong base, it will react completely with H2A+. Determine the remaining moles of H2A+ and the moles of HA formed.

Step 5: Calculate the pH of the solution. Since HA is a weak acid, use the Henderson-Hasselbalch equation: pH = pKa1 + log([A-]/[HA]) to find the pH, where pKa1 corresponds to the first dissociation constant of H2A+.

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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 points during the titration, particularly before and after the equivalence point.

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 both the acid and its conjugate base are present, such as after the addition of a specific volume of NaOH.

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. (a) 10.0 mL