Biochemistry I
Lecture 4
January 21, 2013
Lecture 4: Environmental pKa shifts, Titration curves, & Buffers.
Assigned reading - Horton: 2.9, 2.10. Nelson: 2.2, 2.3.
Key Terms:
 Environmental effects on pKa
 Titration curve
 Equivalents


Buffer capacity
Buffer construction
4A. Environmental effects on acid strength:
The environment of an ionizable group can change the pKa of that group, by affecting the energy of either the
protonated or depronated states- remember, it is the relative energy difference that matters.
HO
i) Why does the pKa increase for subsequent deprotonations for
phosphate (pKa1~3, pKa2~7, pKa3~12)
HO
HO
O
HO
P
O
P
pKa1
OH
HO
O P O
pKa2
O
O
O
pKa3
O
ii) How will a positively charged environment affect the pKa of
histidine (normally 6.0)
H
H
N
+
N
H
N
N
+
N
N
+
H
+
N
H
+
N
+
H
H
H
Titration
4B. Measuring the pKa: Titration Curves
14
13
Ka values, or acidity constants, must be measured by direct
12
experiment, usually with a pH titration. Known amounts of
11
a strong base (NaOH) are added to a solution of weak acid
10
and the pH is measured as the amount of NaOH is added.
9
As the base is added it removes the proton from the acid, as
8
7
well as increasing the pH by removing free protons from
6
water.
5
Key features of titration curves:
4
3
Equivalents: the x-axis scale for titrations is given in
2
moles of base/moles of acid. Therefore, it varies from
1
0 to 1 for an acid that releases one proton
0
(monoprotic), from 0 to 2 for a diprotic acid, 0 to 3 for
0
0.1
a triprotic acid, etc.
Equivalence Point: Complete deprotonation of the weak
acid occurs when the amount of added base is equal to,
or equivalent, to the total number of ionizable protons
that were originally on the weak acid. This point in the
titration is referred to as the equivalence point. The
equivalence point can be used to determine the
concentration of the acid
Inflection Point (pH = pKa): You can prove from the HendersonHasselbalch equation that the smallest change in pH occurs when
the pH = pKa.
0.2
0.3
0.4
0.5
0.6
0.7
0.8
eq NaOH
pKa1 O
HO
O pK
a2
OH
pKa2
pH
pKa1
Equivalents
1
0.9
1
P
O
O
Biochemistry I
Lecture 4
January 21, 2013
4C. Buffers: A pH buffer is an acid that resists changes in the solution pH by absorbing or releasing protons.
Buffers play an important role in cellular processes because they maintain the pH at an optimal level for
biological processes. They are also widely used to control pH in laboratory processes.
Titration
14
13
13
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
pH
14
0
0.2
0.4
0.6
0.8
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
eq NaOH
Fraction Protonated
Buffering range:
Buffering capacity:
4D. Steps in Making a Buffer of concentration [AT]:
[ A ]
Goal:
pH  pK A  log
Method:
[ HA]
1. Select a weak acid whose pKa is within one pH unit of the desired pH.
2. Determine the fraction protonated and deprotonated at the desired pH, fHA & fA3. Obtain this ratio of [HA] to [A-] by one of the following three methods: 1
i) Mix the indicated concentration of the weak acid and its conjugate base (e.g. sodium salt) to give the
desired pH:
[HA]= fHA  [AT]
[AT]=[HA]+[A-]
[A-]= fA-  [AT]
ii) Use [AT] amount of the acid form of the weak acid and add sufficient strong base (e.g. NaOH) to make
the required concentration of [A-] to attain the desired pH. The added base converts HA to A-. The
amount of strong base to add is fA- equivalents, or a total of fA-  [AT]. You are titrating starting from
the left side.
iii) Use [AT] amount of the conjugate base form of the weak acid and add sufficient strong acid (e.g. HCl)
to make the required concentration of [HA] to attain the desired pH. The added acid converts A- to HA.
The amount of strong acid to add is fHA equivalents, or a total of fHA  [AT].
1
In practice, the number of moles of NaOH or HCl is not directly measured, rather a pH electrode is used to monitor the pH
of the solution, and sufficient NaOH or HCl is added until the desired pH is reached.
2
1
Biochemistry I
Example:
Buffer
Histidine
Pyruvic Acid
Lecture 4
January 21, 2013
Make 1L of 1 M buffer solution at pH 5.0 using one of the following two buffers.
1. Which buffer would you use and why?
pKa
Approx. MW
6.0 (sidechain)
2.50
155 g/mol
110 g/mol
2. Determine fraction protonated and deprotonated at the desired pH
R  10 ( pH  pKa )
1
f HA 
1 R
pH titration
f A 
R
1 R
9
8
7
pH
6
5
4
3
3. Obtain the desired ration of [HA] and [A-]
i) Mixing the appropriate amount of the acid and base form of
the buffering acid.
2
1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Equivalents
pH titration
9
8
7
6
pH
ii) Starting with the pure weak acid., HA, add fA- equivalents of a
strong base, or fA- [AT] moles of the strong base.
5
4
3
2
1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Equivalents
pH titration
iii) Starting with the pure sodium salt, NaA, add fHA equivalents of
a strong acid, or fAH [AT] moles of the strong acid.
9
8
7
pH
6
5
4
3
2
1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Equivalents
3
1
Biochemistry I
Lecture 4
January 21, 2013
Polyprotic Buffers:
1. Select weak acid based on any of its pKa values.
2. Use pKa closest to desired pH to calculate fHA and fA-.
3.
i) Use chemical forms of “(HA)” and “(A-)” that represent the species present at the pKa you choose, e.g.
NaH2PO4/Na2HPO4 if the middle ionization was used.
ii) Starting from completely protonated form (e.g. H3PO4). Add sufficient whole equivalents (n) to reach the
buffer region you are using, add (n + fA-) equivalents of strong base, or (n + fA-) [AT] moles of strong base.
iii) Starting from completely ionized form (e.g. Na3PO4). Add sufficient whole equivalents (n) to reach the
buffer region you are using, add (n + fAH) equivalents of acid, or (n + fAH) [AT] moles of strong acid.
Practice:
1. Assume that the histidine containing protein also contains a group that ionizes with a pKa
of 4, draw the curve of fraction protonated versus pH for that group on the same graph.
The curve for the histidine is already plotted for you.
N
+
N
H
2. Which region of the plot corresponds to both groups being fully deprotonated.
Fraction Protonated
H
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
pH
4
O
OH