Dluloclatlon Constants tor HsX Adds Oissocialion Constant
Phosphoric Acid
Kb K,,
K,, KdKa KdK3,
L
0
10
20
30
40
mL 0.1 M NaOH
Figure 1.Titration of an ideal solution of 25.0 mL of 0.100 M HA with 0.100 M NaOH.. = HCI, K, = large: O =aceticacid. K, = 1.80 X lo-': = HCN. K, = 6.17 X Data for V< 0.0 mL indicate shape of curve expected for reversetitration of A- with HCi, starting at V = 25.0 mL and movlng to the left. M NaOH: 0 : a M HCI with Also shown is the titratlon of 25.00 mL of sharp change in pHat the equivalencepoint is not ssm because C, is too low. The pH values at V = 0.00 mL (startof titration with NaOH) and V = 25.00 mL (eq pt 0ftitration)are.respctlveiy: 1.OOand 7.00 for 0.1 M HCI. 5.00and 7.00 for M HCI. 2.88 and 8.72 for 0.1 M HAc, 5.10 and 10.95 for 0.1 M HCN.
*
7.41 X 1.70 X 3.98 X 1.35 X 43.6 42.7
1.29 X lo-'
10.' 10.' lo-'
3.24 X lo-' 1.86 X lo-"
7.75 X 3.98 1.74 x
10"'
TO-"
10'
Figure 2 shows5the theoretical curves for the titration of 25.00 mL of the three 0.100 M H3X acids with 0.100 M NaOH. The three equivalence points are a t 25.00,50.00, and 75.00 mL NaOH. Because CsKlcb is less than for all three acids, none of these acids shows a sharp change in pH at the V equals 0.00 mL equivalence point for the reverse titration as is seen in Figure 2. Also, CaK3, is greater than only for citric acid, so that only this acid shows a sharp chance in DH a t the third equivalence point (Vb equals 75.06. ~ h i s ~ h o r acid i c shows two equivalence points, at 25 00 and 50.00 m L because its successive K, ratios exceed 10'. The successive K, ratios for citric acid are both much less than lo', and it only shows a sharp pH change at the third noint.75.00 mL. Nitrilotriaceticacid is set . - - - -eauivalence ~ ~ ~ * , another example. KlaIKzais much less than lo4, so the first equivalence point is not seen. But, K d K z a is greater than lo4,so that the second equivalence point shows a sharp pH change. ~
strong acid and illustrate the general shape of the curve if we had started with the conjugate base, A-, and titrated i t with 0.100 M HC1 (or M HC1 for the dilute curve). In this case we would begin the titration a t V = 25.00 mL and work to the left of the graph" reaching the equivalence point a t V = zero. Negative values of V correspond to titration additions of excess HC1 following the equivalence point. The e~-- the curve a t V = zero indicates if there is a ---- s h~a ~ = of sharp change in pH for the titration of the conjugate base with a strone acid and. thus. whether or not its eauivalence change can be identified. AS' is seen, the sharp exists only for titration of NaCN but not for NaCl or NaAc. This could have been predicted from the values of Kb = KwKaforthe conjugate base. For C1-, Kb is avery, very small number (because K. for HC1 is a very large number) so that For acetic acid, K b = K,/K. = 5.56 X CbKb
