quant chemistry

Question

Sketch to titration curve of 25.00 mL of 0.05 M citric acid with 0.100 M sodium hydroxide. Label appropriate points along the curve

Answer 1

Citric acid is triprotic. Using the values in Harris: pKa1 = 3.13, pKa2 = 4.76, pKa3 = 6.40. Substitute your book's if they differ slightly.

Step 1 - the three equivalence volumes

mmol citric acid = (25.00 mL)(0.05 M) = 1.25 mmol, and each proton needs its own mole of NaOH:

Ve1 = 1.25 / 0.100 = 12.50 mL
Ve2 = 25.00 mL
Ve3 = 37.50 mL

Every labeled point on the curve is either one of these or a half-way point between them.

Step 2 - the points to label

0 mL: weak acid alone. x^2/(0.05 - x) = Ka1 = 7.4 x 10^-4 gives [H+] = 5.7 x 10^-3, pH 2.24

6.25 mL (half of Ve1): equal H3Cit and H2Cit-, so pH = pKa1 = 3.13. This is a buffer region, and the curve is flattest here.

12.50 mL (Ve1): the solution is the amphiprotic H2Cit-, so pH = (pKa1 + pKa2)/2 = 3.95

18.75 mL: pH = pKa2 = 4.76

25.00 mL (Ve2): pH = (pKa2 + pKa3)/2 = 5.58

31.25 mL: pH = pKa3 = 6.40

37.50 mL (Ve3): only citrate3- remains. Kb = Kw/Ka3 = 2.5 x 10^-8, and [Cit3-] = 1.25 mmol / 62.50 mL = 0.0200 M, so x = sqrt((2.5 x 10^-8)(0.0200)) = 2.2 x 10^-5, pOH 4.65, pH 9.35

45.00 mL: excess strong base dominates. (7.50 mL)(0.100)/70.0 mL = 0.0107 M OH-, pH 12.03

The sketch

 pH
 13 +                                            ,-----
    |                                        ,--'
 11 +                                      ,'
    |                                      |   <-- the ONLY sharp break
  9 +                                      *   3rd eq pt: 37.50 mL, pH 9.35
    |                                     /
  7 +                            __,---''    pKa3 = 6.40 at 31.25 mL
    |                    __,--''   2nd eq pt: 25.00 mL, pH 5.58
  5 +            __,--''      pKa2 = 4.76 at 18.75 mL
    |      _,--''    1st eq pt: 12.50 mL, pH 3.95
  3 +--'''     pKa1 = 3.13 at 6.25 mL
    |  start: pH 2.24
  1 +----+----+----+----+----+----+----+----+----+
    0    5   10   15   20   25   30   35   40   45
                mL of 0.100 M NaOH added

The single most important feature - and the reason this problem gets assigned

Look at what happens at 12.50 and 25.00 mL: nothing sharp. The pKa values are only about 1.6 units apart, so each proton starts coming off before the previous one has finished. The three buffer regions overlap and the first two equivalence points show up as gentle inflections at best, not as usable endpoints.

The rule of thumb is that consecutive pKa values need to differ by roughly 4 units to give separate visible breaks. Citric acid fails that badly. Only the third equivalence point at 37.50 mL produces a real jump, because there the reaction is finally against water rather than against the next dissociation - which is why a citric acid titration is done to a single endpoint near pH 9 with phenolphthalein, and why the result is reported as total acid rather than as three separate protons.