Alternate Method for Determination of pKa
The Method of Albert and Serjeant
Background:
In the pharmaceutical industry pKa is an important factor is drug design and development. It is important
in drug ligand interactions (how the drug works) and is also important in the partitioning behavior of the
potential drug candidate (how the drug gets into the body). As you are now aware there are several way to
go about this determination. In this lab you will be introduced to the current method employed by most
companies to make this experimental determination. Selection of the pKa at 1/2 V e has been not been
adopted due to lack of precision and the Gran method and not gained widespread acceptance. The Albert
and Serjeant Method is a variation on the former method and allows for multiple determinations in a single
titration and allows the scientist to more readily detect deviations that would not be possible just making
the determination at Ve/2.
As you have already discovered these determinations can be tedious and the development of new methods
to automate and speed up such analyses is an active area of current research. Companies that are active in
this area are Sirius (http://www.cix.co.uk/~sirius/ ) in Britain and pIon (http://www.pion-inc.com/ ) in the
USA. Sirius has developed a system that will determine the partition constant between organic and
aqueous solvents while determining the pKa with the same experimental procedure. Also, there has been
significant computational research on the calculation of pKa based on the chemical structure of the
compounds. An example of a company that has a product in this area is ACD in Toronto.
(http://www.acdlabs.com/) They also have freeware for structure drawing and IUPAC naming that might
be useful for you to download.
The Method:
The method determining pKa at 1/2Ve is really just a special case of the Henderson Hasselbalch equation
where the log term with [HA] and [A-] goes to zero. Once you know your equivalence point you can
determine what faction of the acid has reacted and you can plug this into that term and determine the pKa at
any point along the buffer region of the titration curve.
Recall that the Henderson-Hasselbalch equation is just the pKa equilibrium expression in log form and is:
pH  pK a  log
[ A ]
[ HA]
This can be rearranged to solve for pKa.
[ A ]
pK a  pH  log
[ HA]
or
pK a  pH  log
[ HA ]
[ A ]
The values of [A-], [HA] are determined for several points along the titration and the pKa is determined at
each of these points. The mean value of these points is determined and reported with the associated
standard deviation. If the standard deviation is greater than 0.1 or there is a trend in the values then data is
further examined. Usually these determinations are carried out on pure solids of know purity so V e is
known at the outset of the experiment.
In addition, when [H+] is large relative to [HA] and [A-] then we must correct for this in the above equation.
From the amount of weak acid present and the amount neutralized in the course of the titration we can
calculate the concentration HA and A- . The amount of acid correction can also be determined (see below)
and this correction applied to give us a more accurate value.
Method of Albert and Serjeant
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To see what correction should be applied we start with the charge balance for this titration.
[A-] + [OH-] = [Na+] + [H+]
Since the amount of Na+ is this solution is from the NaOH that we have added we can use the formal
concentration, which is CNaOH
This gives us the expression for [A-] as
[A-] = CNaOH + [H+] - [OH-]
To find the value appropriate for [HA] we then need the mass balance
CHA = [HA] + [A-]
Which when rearranging and plugging into the expression for [A-] gives us
[HA] = CHA - CNaOH - [H+] + [OH-]
Since we are in the acid range the [OH-] can be ignored as compared to the other terms.
Activity correction can also be applied.
In this lab you will be looking at potassium hydrogen phthalate. The treatment would be the same since
you are titrating the second proton. You must take ionic charges into account if you carry out the activity
correction.
KHA  NaOH 
 A2   H 2O  Na
Method of Albert and Serjeant
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The Calculation
The data is best presented in table form and Excel is well suited for this task.
The Table would be formatted as follows:
Table for Calculation of
pKa
Volbase
Moles
Vtot
Base
pH
[H+]
Moles HA Moles A-
Ratio
H+
Adjusted
Ratio
Log HH pKa
Term
Starting Entries
Starting Volume
Moles HA Start
Conc
Base
Calculations used for columns
Vtot = Starting Volume + Vol Base
Moles base = Vol Base*Conc Base
[H+] = 10^(-1*pH)
Moles HA = Moles HA Start - Moles Base
Moles A- = Moles Base
Ratio = Moles HA / Moles AH+ adjusted ratio = (moles HA/Vtot - [H+])/(moles A-/Vtot + [H+])
pKa = pH + log Col HH term
Method of Albert and Serjeant
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Once your data is entered then you calculate pKa from 0.1 Ve to 0.9 Ve. Example data is provided below.
Table for Calculation of
pKa
Volbase
Moles
Vtot
Base
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.005
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0.0004
0.00045
0.0005
0.05
0.0505
0.051
0.0515
0.052
0.0525
0.053
0.0535
0.054
0.0545
0.055
Starting Entries
Starting Volume
Moles HA Start
Conc
Base
[H+]
pH
3.07
3.35
3.59
3.79
3.96
4.14
4.32
4.5
4.71
5.06
6.45
Moles HA Moles A-
9E-04
4E-04
3E-04
2E-04
1E-04
7E-05
5E-05
3E-05
2E-05
9E-06
4E-07
0.0005
0.00045
0.0004
0.00035
0.0003
0.00025
0.0002
0.00015
0.0001
0.00005
0
Ratio
H+ Adjusted
Ratio
Log HH pKa
Term
0 #DIV/0! 10.7489755
0.00005
9 5.89108435
0.0001
4
3.420514
0.00015 2.3333 2.15751606
0.0002
1.5 1.43070443
0.00025
1 0.97002963
0.0003 0.6667 0.65269184
0.00035 0.4286 0.42169927
0.0004
0.25 0.24671828
0.00045 0.1111 0.10994031
0.0005
0 -3.9028E-05
1.0314
0.7702
0.5341
0.334
0.1555
-0.0132
-0.1853
-0.375
-0.6078
-0.9588
Ave
StdDev
0.05
0.0005
0.1
Calculations used for columns
Vtot = Starting Volume + Vol Base
Moles base = Vol Base*Conc Base
[H+] = 10^(-1*pH)
Moles HA = Moles HA Start - Moles Base
Moles A- = Moles Base
Ratio = Moles HA / Moles AH+ adjusted ratio = (moles HA/Vtot - [H+])/(moles A-/Vtot + [H+])
pKa = pH + log Col HH term
This is for a sample of Benzoic Acid where 0.0611 g dissolved in 50.0 mL of water and is then titrated
with 0.1000 N NaOH.
Experimental.
For this titration we will reexamine the KHP pKa. The difference will be that you use an "Ionic Strength
Buffer". For this you will add NaCl to the KHP solution and this excess of ions will keep the ionic strength
relatively constant through the titration. Weigh out about 0.5 grams (known exactly) of KHP and
accurately add 50.00 mL of 0.10 M NaCl. You will titrate with ~0.1 M NaOH and monitor the progress of
you titration with a calibrated pH meter.
Take pH readings at 0*Ve, 0.1*Ve, 0.2*Ve etc. until you are near your equivalence point. Then you will
want to take values at much tighter intervals. (15 pH determinations should be sufficient for this lab) . This
is done should you need to use an experimentally determined V e. Often solids are not pure and this allows
you to correct for this. (excess water or solvents are often present)
Method of Albert and Serjeant
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4.1202
4.1241
4.124
4.1155
4.1268
4.1347
4.125
4.1022
4.1012
4.1193
0.0112
Your Calculations.
Calculate the pKa without making activity corrections.
Next modify (save the old first) you spreadsheet to make activity corrections. Which values will need to be
modified in your table?
To determine the activity coefficients you should use Equation 8-6 in your text. Use  = 0.1.
How do the values compare to the Gran plot method and the value given in the back of the text. You will
be determining the value for pKa2 . The derivation above were for a weak monoprotic acid but is are valid
for this determination also.
Reference:
A. Albert and E. P. Serjeant, Ionization Constants of Acids and Bases, (New York, Wiley, 1962).
Method of Albert and Serjeant
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