Citric acid is a tri-protic acid with a Ka1 =8.4x10-4 Ka2=1.8x10-5 and Ka3=4.0x10-6. calculate the pH at the 2nd equivalence point in the titration of 85.5 mL of a .21 M citric acid solution with .25 M NaOH. Calculate the pH, after 25.8 mL of NaOH have been added. Calculate the pH, 3.0 mL after the LAST equivalence point.
8.5
To calculate the pH at each equivalence point and beyond in the titration of citric acid with NaOH, we need to understand the reaction between citric acid and NaOH.
Citric acid (C6H8O7) is a tri-protic acid, meaning it can donate three protons (H+ ions). When it reacts with NaOH, a neutralization reaction occurs, forming water and salts. The balanced chemical equation for the reaction is:
C6H8O7 + 3NaOH → 3H2O + Na3C6H5O7
Now let's solve each part of the question.
1. pH at the 2nd equivalence point:
To find the 2nd equivalence point, we need to determine the amount of NaOH needed to reach the 2nd protonation (H+ release).
First, determine the moles of citric acid in the initial solution:
moles of citric acid = volume of citric acid solution (in L) × concentration of citric acid solution (in mol/L)
moles of citric acid = 85.5 mL × (1 L / 1000 mL) × 0.21 mol/L
Since citric acid is tri-protic, we need to determine the amount of NaOH needed to react with 2 moles of citric acid:
moles of NaOH needed = 2 × moles of citric acid
moles of NaOH needed = 2 × (85.5 mL × (1 L / 1000 mL) × 0.21 mol/L)
Now we have the moles of NaOH required to reach the 2nd equivalence point. To calculate the pH, we can use the Henderson-Hasselbalch equation:
pH = pKa + log ([salt] / [acid])
At the 2nd equivalence point, the salt formed is Na3C6H5O7, and the acid remaining is the first protonated form of citric acid, C6H7O7-. The pKa to be used is the 2nd pKa value (given as 1.8 × 10^-5).
Calculate the concentration of the salt:
[salt] = moles of salt formed / volume of the solution (in L) after adding moles of NaOH needed
Next, calculate the concentration of the remaining protonated acid:
[acid] = moles of acid remaining / volume of the solution (in L) after adding moles of NaOH needed
Finally, substitute the values into the Henderson-Hasselbalch equation to get the pH.
2. pH after 25.8 mL of NaOH have been added:
For this calculation, the approach is similar to the 2nd equivalence point. Determine the moles of NaOH added and use the Henderson-Hasselbalch equation with appropriate concentrations of salt and acid.
3. pH 3.0 mL after the LAST equivalence point:
At this point, all the citric acid has been neutralized, and we have excess NaOH. Thus, the pH should be determined by the excess NaOH. Calculate the moles of NaOH present after the last equivalence point, and use the appropriate equation to find pH.
By following these steps, you can calculate the pH at each point in the titration of citric acid with NaOH.