A 70.0 mL solution of 0.165 M potassium alaninate (H2NC2H5CO2K) is titrated with 0.165 M HCl. The pKa values for the amino acid alanine are 2.344 (pKa1) and 9.868 (pKa2), which correspond to the carboxylic acid and amino groups, respectively.
Calculate pH of second equivalence point.
To calculate the pH of the second equivalence point in this titration, we need to determine the components of the solution at that point. The second equivalence point occurs when all the alanine has reacted with the HCl, resulting in the formation of the second protonated form of alanine (H3NC2H5CO2H), which has a pKa value of 9.868 (pKa2).
To calculate the pH, we can use the Henderson-Hasselbalch equation:
pH = pKa2 + log([A-]/[HA])
Where:
pKa2 = 9.868
[A-] = concentration of the alanine anion (H2NC2H5CO2-) at the second equivalence point
[HA] = concentration of the protonated alanine (H3NC2H5CO2H) at the second equivalence point
To find the concentrations of [A-] and [HA], we need to calculate the moles of each compound at the second equivalence point.
We know that the initial volume of the solution is 70.0 mL, and the molarity of the potassium alaninate solution is 0.165 M. So, the initial moles of potassium alaninate is:
moles of H2NC2H5CO2K = volume × concentration
= 70.0 mL × 0.165 M
= 11.55 mmol (millimoles)
Since HCl and potassium alaninate have a 1:1 stoichiometric ratio, at the second equivalence point, all the moles of potassium alaninate have reacted with HCl resulting in the formation of H3NC2H5CO2H. Therefore, the moles of H3NC2H5CO2H at the second equivalence point is also 11.55 mmol.
Now, we can calculate the concentrations of [A-] and [HA] at the second equivalence point:
[A-] = moles of H2NC2H5CO2- / volume
= 11.55 mmol / 70.0 mL
= 0.1647 M
[HA] = moles of H3NC2H5CO2H / volume
= 11.55 mmol / 70.0 mL
= 0.1647 M
Finally, we can substitute the values into the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa2 + log([A-]/[HA])
= 9.868 + log(0.1647/0.1647)
= 9.868 + log(1)
= 9.868 + 0
= 9.868
Therefore, the pH of the second equivalence point in this titration is approximately 9.868.