1.a. Potentiometric determination of dissociation constant of
weak acid
The dissociation constant of weak 𝐻𝐻𝐻𝐻 is
HA
AH
A
a
aa
K
−+ ⋅
=
(1.1.)
where HAa , +
H
a and −
A
a are activity of undissociated weak acid and activity of
dissociation products respectively. By the mathematical rearrangement of the
equation (1.1.), we obtain the Henderson-Hasselbalch equation:
−
+==−
A
HA
AA
a
a
pHpKK loglog (1.2.)
Activities can be replaced with molarities (𝑎𝑎𝐻𝐻𝐻𝐻 = [𝐻𝐻𝐻𝐻], 𝑎𝑎𝐴𝐴− = [𝐴𝐴−]) in the case of
dilute solutions below approx. 10 2−
M in this case.
The dissociation constant 𝑝𝑝𝑝𝑝𝑎𝑎 can be determined by titration of weak acid using a
strong base or acid. Measurement of 𝑝𝑝𝑝𝑝 changes during titration allows evaluating
the molarity of the dissociated and undissociated form of weak acid. Titration may be
done in two ways, depending on the 𝑝𝑝𝑝𝑝𝑎𝑎 value. The way depends whether 𝑝𝑝𝑝𝑝𝑎𝑎 of
weak acid is below or above value 7.
TITRATION OF VERY WEAK ACID WITH STRONG HYDROXIDE.
Boric acid (𝐻𝐻𝐻𝐻) represents a very weak acid 𝑝𝑝𝑝𝑝𝑎𝑎 > 7. The first degree dissociation
constant 𝑝𝑝𝑝𝑝𝑎𝑎 can be determined from the titration results of boric acid with strong
potassium hydroxide (optionally sodium hydroxide).
Electroneutrality and mass conservation law of weak acid are respected at any
addition of strong 𝐾𝐾𝐾𝐾𝐾𝐾 hydroxide to to the weak 𝐻𝐻𝐴𝐴 solution:
[ ] [ ] [ ] [ ]A OH K H− − + +
+ = +
(1.3.)
[ ] [ ]−
+= AHAcHA (1.4.)
where 𝑐𝑐𝐻𝐻 𝐻𝐻 means analytical concentration of 𝐻𝐻𝐻𝐻. Potassium cation remains
dissociated during titration and its concentration [ ]K+
is equal to the total analytical
concentration of strong hydroxide KOHc . Then the eqn (1.3.) gives:
[ ] [ ] [ ]−+−
−+= OHHcA KOH (1.5.)
We obtain for the undissociated acid concentration [𝐻𝐻𝐻𝐻] following if we insert the
relation (1.5.) in the equation (1.4.) and then mathematically rearrange the result:
[ ] [ ] [ ]−+
+−−= OHHccHA KOHHA (1.6.)
The obtained concentrations [ ]A−
and [ ]HA can be used in the HendersonHasselbalch
equation (1.2.).
TITRATION OF SALT OF WEAK ACID WITH STRONG ACID.
Acetic acid (𝐻𝐻𝐻𝐻) represents a weak acid 𝑝𝑝𝑝𝑝𝑎𝑎 < 7. The dissociation constant 𝑝𝑝𝑝𝑝𝑎𝑎 can
be determined from the titration results of salt 𝐾𝐾𝐾𝐾 (where 𝐾𝐾 means sodium or
potasium) of weak acid with strong acid 𝐻𝐻𝐻𝐻 (for example with hydrochloric acid 𝐻𝐻𝐻𝐻𝐻𝐻).
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The mixed solution of 𝐾𝐾𝐾𝐾 and 𝐻𝐻𝐻𝐻 keep electroneutrality and the mass conservation
law of salt of weak acid:
[ ] [ ] [ ] [ ] [ ]A OH X K H− − − + +
+ + = + (1.7.)
[ ] [ ]HAAcKA += −
(1.8.)
The salt 𝐾𝐾𝐾𝐾 is completely dissociated, so the concentration [ ]K+
during the titration
is always equal to the total analytical salt concentration KAc . For the same reason,
the strong acid anion concentration [ ]−
X is equal to the total analytical concentration
HXc of strong acid.
If we replace the concentrations [ ]K+
a [ ]−
X in eqn (1.7.) by analytical
concentrations, we get:
[ ] [ ] [ ] HXKA cOHHcA −−+= −+−
(1.9.)
We can insert this relation in eqn (1.8.), mathematically rearrange and to obtain:
[ ] [ ] [ ]+−
−+= HOHcHA HCl (1.10.)
The concentrations [ ]A−
and [ ]HA we use in the Henderson-Hasselbalch eqn (1.2.).
TASK: Determine pKa of acetic acid and boric acid to the first stage. Compare
the result with the values from literature.
LABORATORY AIDS AND CHEMICALS: automatic titrator equipped by 𝑝𝑝𝑝𝑝 detection,
weighing boat, 2 volumetric flasks (50ml), 0,1M KOH or NaOH, 0,1M HCl, boric
acid, sodium acetate, titration beaker (100ml).
INSTRUCTIONS: Get study how to operate the automatic titrator and how to
measure the 𝑝𝑝𝑝𝑝, switch titrator on and prepare the device for measurement.
Check 𝑝𝑝𝑝𝑝 measurements with calibration solutions (use buffers).
• Weigh 5.10
-4
moles of boric acid (or sodium acetate) with maximum accuracy.
Transfer the weight to a 50 ml volumetric flask and dissolve in distilled water up to
volume marking. Pour the solution into a dry titration beaker.
• Titrate with solution agent 0,1M KOH (or 0,1M HCl) by 0.5ml dose to total dose
5ml. Record the 𝑝𝑝𝑝𝑝 after stabilization.
DATA ANALYSIS: The ratio of the concentration of the dissociated and nondissociated
form [𝐻𝐻𝐻𝐻]/[𝐴𝐴−] of acid 𝐻𝐻𝐻𝐻 changes after each dose. The
concentrations [𝐻𝐻+] and [𝑂𝑂𝑂𝑂−] can be omitted in the data evaluation if they are
significantly lower than other concentrations in eqns (1.5.), (1.6.), (1.9.) or (1.10.).
REPORT: For both very weak and weak acid: weight in mg, TABULE 1: for zero
and each consequent titration dose: volume of added agent, total volume,
analytical concentration of boric acid (or sodium acetate), experimental pH,
[𝐻𝐻+], [𝑂𝑂𝑂𝑂−], [𝐴𝐴−], and [𝐻𝐻𝐻𝐻] concentrations, expression 𝑙𝑙𝑙𝑙𝑙𝑙[𝐻𝐻𝐻𝐻]/[𝐴𝐴−], pKA
calculated using eqn (1.2.). NEXT: mean value of pKA
and confidence interval using
Student’s t-distribution.
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