Unit 1. Equilibrium in Aqueous Solutions
Matthew Ryen Lockett
Department of Chemistry
Lineberger Comprehensive Cancer Center
UNC Chapel Hill
What hypotheses could we test based on this data?
antibody
Experimental Setup
•
•
We dissolved 1.0x10–8 moles of antibody
(anti-hCG) and 1.0x10–8 moles of antigen
(hCG) in 1.0 mL of buffered solutions with
different pH values.
We measured the percentage of the
antibody-antigen complex that formed in
each solution.
antigen
antibody-antigen
complex
Data
pH =
5.0
5.5
6.0
6.5
7.0
7.5
8.0
40 %
44 %
55 %
78 %
99 %
96 %
55 %
complex formed
2
All biological fluids have water as the solvent
3
All biological fluids have water as the solvent
pH paper (colorimetric)
pH meter (electrochemical)
4
How do we lower the pH of a solution?
A strong inorganic acid
HNO3 (aq) + H2O (l) → NO3– (aq) + H3O+ (aq)
A weak inorganic acid has an associated Ka-statement
HClO (aq) + H2O (l) ⇄ ClO– (aq) + H3O+ (aq)
5
How do we raise the pH of a solution?
A strong inorganic base
NaOH (s) → Na+ (aq) + OH– (aq)
A weak inorganic base has an associated Kb statement
NH3 (l) + H2O (l) ⇄ NH4+ (aq) + OH– (aq)
AgOH (s) ⇄ Ag+ (aq) + OH– (aq)
Reaction affecting a solution’s pH
NaOH
6
Organic functional groups
Carboxylic acids are weak organic acids in water
formic acid
pKa = 3.75
benzoic acid
pKa = 4.20
acetic acid
pKa = 4.75
chloroacetic acid
pKa = 2.87
4-nitrobenzoic acid
pKa = 3.41
propanoic acid
pKa = 4.88
2-naphthoic acid
pKa = 4.16
butanoic acid
pKa = 4.82
1-naphthoic acid
pKa = 3.67
7
Organic functional groups
What is the balanced chemical equation and equilibrium expression for
solid benzoic acid dissolved in water?
8
Organic functional groups
What is the balanced chemical equation and equilibrium expression for solid
sodium benzoate dissolved in water?
9
Organic functional groups
Alcohols are weak organic acids in water
methanol
pKa = 15.54
ethanol
pKa = 16.00
phenol
pKa = 9.997
4-methylphenol
pKa = 10.27
trifluoroethanol
pKa = 12.40
4-nitrophenol
pKa = 7.15
propanol
pKa = 16.10
1-naphthol
pKa = 9.42
isopropanol
pKa = 17.10
2-naphthol
pKa = 9.57
10
Organic functional groups
What is the balanced chemical equation and equilibrium expression for
solid phenol dissolved in water?
11
Organic functional groups
What is the balanced chemical equation and equilibrium expression for
solid sodium phenolate dissolved in water?
12
Organic functional groups
Amines are weak organic bases in water
NH3 (aq) + H2O (l) ⇄ NH4+ (aq) + OH- (aq)
Ammonia
Primary amine
Secondary amine
Tertiary amine
13
Organic functional groups
Amines are weak organic bases in water
methylamine
pKa = 10.63
cyclohexylamine
pKa = 10.57
ethylamine
pKa = 10.67
diethylamine
pKa = 11.00
aniline
pKa = 4.60
4-methoxyaniline
pKa = 5.36
triethylamine
pKa = 10.72
pyridine
pKa = 9.35
aziridine
pKa = 8.04
benzylamine
pKa = 9.35
14
Organic functional groups
What is the balanced chemical equation and equilibrium expression for
solid trimethyl amine dissolved in water?
15
Organic functional groups
What is the balanced chemical equation and equilibrium expression for
solid trimethyl amine dissolved in water?
16
Organic functional groups
pH < pKa
pH > pKa
When pH = pKa,
there is no
predominant
species in solution.
17
Organic functional groups
If you prepared (separately) 1.0 mM solutions of the following in 1.0 L
H2O, what is the overall charge of the solution?
pKa = 3.7
pKa = 5.23
18
Does pKa value matter when thinking
about acid-base properties?
19
Organic functional groups
Would you expect these three 1.0x10-4 M solutions to have the same pH?
Formic acid
pKa = 3.744
Acetic acid
pKa = 4.756
Butanoic acid
pKa = 4.818
Note, pH is concentration-dependent but volume-independent.
20
Organic functional groups
Would you expect these three 1.0x10-4 M solutions to have the same pH?
Formic acid
pKa = 3.744
When you dissolve a protonated (or deprotonated) molecule in water, we think about ICE tables and concentration.
21
Organic functional groups
Would you expect these three 1.0x10-4 M solutions to have the same pH?
Formic acid
Acetic acid
Butanoic acid
cF (F)
1.00x10-4 F
1.00x10-4 F
1.00x10-4 F
pKa
3.744
4.756
4.818
cH3O+eqm (M)
4.15x10–5
3.40x10–5
3.21x10–5
pH
4.15
4.47
4.49
22
All organic functional groups
formic acid
pKa = 3.744
acetic acid
pKa = 4.756
butanoic acid
pKa = 4.818
decreasing (toward 0)pKa.
Weak acid strength increases with __________________
increasing (toward 1) Ka.
Weak acid strength increases with __________________
aniline
pKa = 4.60
pyridine
pKa = 9.35
ethylamine
pKa = 10.67
23
All organic functional groups
formic acid
pKa = 3.744
acetic acid
pKa = 4.756
butanoic acid
pKa = 4.818
increasing (toward 14)pKa.
Weak base strength increases with __________________
decreasing (smaller than 1) Ka.
Weak base strength increases with ______________________
aniline
pKa = 4.60
pyridine
pKa = 9.35
ethylamine
pKa = 10.67
24
All organic functional groups
formic acid
pKa = 3.744
acetic acid
pKa = 4.756
butanoic acid
pKa = 4.818
decreasing (toward 0) pKb.
Weak base strength increases with ___________________
increasing (toward 1)Kb.
Weak base strength increases with ________________
aniline
pKa = 4.60
pyridine
pKa = 9.35
ethylamine
pKa = 10.67
25
Does concentration matter when
considering a weak acid (or weak
base) dissociation in water?
26
Organic functional groups
Would you expect three different concentrations of an acetic acid
solution to have the same pH?
Acetic acid
pKa = 4.756
Add 10.0 mL of 1.00x10-3 F acetic acid
Add 1.0 mL of _________ F acetic acid
Fill to the 100.0 mL mark with DI water
Fill to the 100.0 mL mark with DI water
c = 1.00x10-3 F
c = ________ F
c = ________ F
27
Organic functional groups
Would you expect three different concentrations of an acetic acid
solution to have the same pH?
Acetic acid
pKa = 4.756
c = 1.00x10-3 F
28
Organic functional groups
Would you expect three different concentrations of an acetic acid
solution to have the same pH?
Acetic acid
pKa = 4.756
cF
cF
1.00x10-3 F
1.00x10-4 F
1.00x10-6 F
cH3O+eqm (M)
1.24x10-4 F
3.40x10-5 F
9.49x10-7 F
pH
3.91
4.47
6.02
% HAdissociated
12.4%
34%
94.9%
29
Visualizing and calculating the
concentration-dependent dissociation
of a weak acid (or weak base)
30
Organic functional groups
We can calculate the fraction of dissociation for any weak acid solution. This
value helps to quantify how many of the molecules have ionized.
To calculate this
value we need the
equilibrium conc.
Note this axis is
decreasing in cF
10-1 = 0.1 F
10-3 = 0.001F
31
Organic functional groups
We can calculate the fraction of dissociation for any protonated species in
solution (a weak acid or the conj. of a weak base).
Note. Protonated forms of our organic functional group will act as weak acids.
32
Organic functional groups
We can calculate the fraction of association for any deprotonated species in
solution (a weak base or the conj. of a weak acid).
Note. Deprotonated forms of our organic functional group will act as weak bases.
33
Organic functional groups
Why does the % dissociation increase when the concentration of protonated
species decreases?
Would you expect the same concentration-dependence for deprotonated
species?
34
Organic functional groups
Which species will dissociate in water more (result in a lower pH)?
0.001 mol/L HCl
or
0.001 mol/L HNO2
0.005 mol/L NH3
or
0.001 mol/L NH4Cl
0.001 mol/L HA
or
0.004 mol/L HB
Ka = 4.5x10–5
Ka = 4.5x10–3
35
36
Is there a way to prevent the pH of a
solution from changing when the
volume changes?
37
What is the value of a buffered solution?
antibody
Experimental Setup
•
•
We dissolved 1.0x10–8 moles of antibody
(anti-hCG) and 1.0x10–8 moles of antigen
(hCG) in 1.0 mL of buffered solutions with
different pH values.
We measured the percentage of the
antibody-antigen complex that formed in
each solution.
antigen
antibody-antigen
complex
Data
pH =
5.0
5.5
6.0
6.5
7.0
7.5
8.0
40 %
44 %
55 %
78 %
99 %
96 %
55 %
complex formed
38
What is the value of a buffered solution?
Buffers are solutions that contain a weak acid-weak base conjugate pair before the
equilibrium process occurs, allowing the solution to resist changes in pH when…
1. small amounts of strong or weak acids are added
2. small amounts of strong or weak bases are added
3. the solution is diluted
CO2 (g) + 2H2O (l) ⇄ HCO3- (aq) + H3O+ (aq)
39
What is the value of a buffered solution?
https://doi.org/10.1113/JP283579
1 ATP
3 NADH-H+
1 FADH2
40
What is the value of a buffered solution?
Nitrophenol
acetic acid
Catalytic efficiency of carbonic anhydrase
Nitrophenyl acetate
41
What is the value of a buffered solution?
How do we identify a buffer?
• 0.001 moles of HCN (weak) dissolved in 100 mL of H2O?
• 0.001 moles of NaCN (weak) dissolved in 100 mL of H2O?
?
• 0.01 moles of NaCN and 0.01 moles of HCN (weak) dissolved in
100 mL of H2O?
• 0.001 moles of NaCN (weak) dissolved in 100 mL of H2O,
followed by the addition of 0.0005 moles of HCl?
• 0.001 moles of NaCN (weak) dissolved in 100 mL of H2O,
followed by the addition of 0.0005 moles of NaOH?
• 0.001 moles of HCN (weak) dissolved in 100 mL of H2O, followed
by the addition of 0.0005 moles of NaOH?
42
The Henderson-Hasselbalch equation is an exact solution for calculating the pH
of a solution containing a conjugate pair before equilibrium occurs (i.e., a buffer).
H3O+ × deprot
=
1.
prot
2. log
= log
(
H3O+ × deprot
prot
3. −log H3O+ = − log
+ log
= log H3O+ ×
)
(
(
= log( H3O+) + log
(
prot )
deprot
prot )
deprot
prot )
deprot
( prot )
The solved answers from the HH equation are not always accurate, as there is
an assumption we must make (and a limitation when at extremes).
𝑐
𝑐
𝑐
𝑐
𝑐
𝑐
𝑐
𝑐
𝑐
𝑎
𝑐
𝑐
𝐾
𝑎
𝑝
𝑐
𝐾
𝑐
𝑎
𝐾
𝑎
𝑐
𝑐
deprot
+ log
𝑐
4. pH =
𝑐
𝐾
What is the value of a buffered solution?
43
What is the value of a buffered solution?
How do we make effective buffers in the lab? Method 1.
1. Determine the amount of acetic acid and sodium acetate
needed for a 100 mM solution at pH = 5.00.
2. Mass out the appropriate amount of each species, place it in a
beaker, and dissolve it in 75.00 mL of deionized water.
3. Measure pH, and add concentrated (e.g., 1.00 M) HCl(aq) or
NaOH(aq) until you achieve the correct pH.
4. Transfer the solution to a 100.0 mL volumetric flask and fill to the
mark with deionized water.
5. Mix thoroughly, and voila!
• Use HH to get the masses of each chemical needed
44
What is the value of a buffered solution?
How do we make effective buffers in the lab? Method 1.
1. Determine the amount of acetic acid and sodium acetate
needed for a 100 mM solution at pH = 5.00.
2. Mass out the appropriate amount of each species, place it in a
beaker, and dissolve it in 75.00 mL of deionized water.
3. Measure pH, and add concentrated (e.g., 1.00 M) HCl(aq) or
NaOH(aq) until you achieve the correct pH.
4. Transfer the solution to a 100.0 mL volumetric flask and fill to the
mark with deionized water.
5. Mix thoroughly, and voila!
the HH
pH to
is off,
couldn’t
account
for something
• • IfUse
getthe
theHH
masses
of each
chemical
needed
in the system
45
What is the value of a buffered solution?
How do we make effective buffers in the lab? Method 1.
1. Determine the amount of acetic acid and sodium acetate
needed for a 100 mM solution at pH = 5.00.
2. Mass out the appropriate amount of each species, place it in a
beaker, and dissolve it in 75.00 mL of deionized water.
3. Measure pH, and add concentrated (e.g., 1.00 M) HCl(aq) or
NaOH(aq) until you achieve the correct pH.
4. Transfer the solution to a 100.0 mL volumetric flask and fill to
the mark with deionized water.
5. Mix thoroughly, and voila!
46
What is the value of a buffered solution?
How do we make effective buffers in the lab? Method 2.
1. Mass out 0.100 millimole of sodium acetate, and place in a beaker.
2. Add approximately 75.0 mL of deionized water and ensure the
solid is thoroughly dissolved.
3. Measure the pH of the solution and add a concentrated HCl(aq)
(e.g., 1.00 M) until you achieve the correct pH.
4. Transfer the solution to a 100.0 mL volumetric flask and fill to the
mark with deionized water.
5. Mix thoroughly, and voila!
47
What is the value of a buffered solution?
How do we make effective buffers in the lab? Method 2.
1. Mass out 0.100 millimole of sodium acetate, and place in a beaker.
2. Add approximately 75.0 mL of deionized water and ensure the
solid is thoroughly dissolved.
3. Measure the pH of the solution and add a concentrated HCl(aq)
(e.g., 1.00 M) until you achieve the correct pH.
4. Transfer the solution to a 100.0 mL volumetric flask and fill to the
mark with deionized water.
5. Mix thoroughly, and voila!
48
What is the value of a buffered solution?
How do we make effective buffers in the lab? Method 2.
1. Mass out 0.100 millimole of sodium acetate, and place in a
beaker.
2. Add approximately 75.0 mL of deionized water and ensure
the solid is thoroughly dissolved.
3. Measure the pH of the solution and add a concentrated
HCl(aq) (e.g., 1.00 M) until you achieve the correct pH.
4. Transfer the solution to a 100.0 mL volumetric flask and fill
to the mark with deionized water.
5. Mix thoroughly, and voila!
49
What is the value of a buffered solution?
Buffers are solutions that contain a weak acid-weak base conjugate pair before
equilibrium process occurs, allowing the solution to resist changes in pH when…
!
s
’
e
t
Le par
m
o
c
100.0 mL of
1.00x10-2 M
acetic acid
100.0 mL of
1.00x10-2 M
acetic acid and
1.00x10-2 M
sodium acetate
+
5.00x10-4
moles NaOH
= ???
+
5.00x10-4
moles NaOH
= ???
50
What is the value of a buffered solution?
pH before
NaOH
100.0 mL of
1.00x10-2 M
acetic acid
100.0 mL of
1.00x10-2 M
acetic acid and
1.00x10-2 M
sodium acetate
3.38
pH after
NaOH
4.75
(1.37 change)
⍺d before
NaOH
⍺d after
NaOH
4.13%
50%
0.18%
25%
5.23
4.75
(0.48 change)
51
What is the value of a buffered solution?
We wish to generate synthetic urine by preparing a mixture of salts, small organic
molecules representing common metabolites, and a buffering system maintaining the
pH of physiological urine. What buffered systems would be appropriate?
52
What is the value of a buffered solution?
A urine pH between 6.5 – 7.0 is
ideal for healthy individuals
A urine pH of 8.0 represents
someone with a UTI from ureaproducing bacteria
53
What is the best pH
range for my buffer?
54
Effectiveness of the buffer to
withstand acid or base
What is the value of a buffered solution?
55
What is the value of a buffered solution?
Why do we express buffers regarding formal concentration (but weak acid
solutions in molarity)?
56
Can water act as a buffer?
H2O (l) + H2O (l) ⇄ OH– (aq) + H3O+ (aq)
57
What is the value of a buffered solution?
Can water act as a buffer? Ca(OH)2 as our example
cF (M)
Calculated pH
Measured pH
0.50 x 10-2
12.00
12.00
0.50 x 10-5
9.00
9.00
0.50 x 10-7
7.00
7.20
0.50 x 10-9
5.00 ?!
7.00
58
What is the value of a buffered solution?
Can water act as a buffer?
We will need to use an ICE
table
or HH equation…
59
Can we use HH to determine the
predominant species in solution when
the pH is adjusted to a certain value?
60
What is the value of a buffered solution?
We can also use the pH and pKa to determine the fractional composition in
solution. Note that we are imposing the pH on the solution here.
61
What is the value of a buffered solution?
We can also use the pH and pKa to determine the fractional composition in
solution. Note that we are imposing the pH on the solution here.
62
63
Diprotic species
monoprotic species
have one pKa value
diprotic species
have two pKa values
triprotic species
have three pKa values
nitrous acid
oxalic acid
acetic acid
trimethyl amine
phenol
p-hydroxy
benzoic acid
sulfurous acid
ethylene diamine
phosphoric acid
1,3,5-benzenetri
carboxylic acid
64
Diprotic species
Just like monoprotic species, we can also use the pH and pKa to determine the
fractional composition in solution of diprotic species in solution
65
Diprotic species
H2A (aq) + H2O (l) ⇄ HA- (aq) + H3O+ (aq)
HA- (aq) + H2O (l) ⇄ A-2 (aq) + H3O+ (aq)
66
Diprotic species
67
Diprotic species
fully protonated
fully deprotonated
intermediate
68
Do we have to consider the exchange
of both protons with water (or only
one) for diprotic species?
69
Diprotic species
What is the pH of a 0.001 M sulfurous acid solution?
pKa1 = 1.857 and pKa2 = 7.172.
1. We label pKa values from most acidic proton to least acidic proton
2. Proton loss is sequential
H2SO3 (aq) + H2O (l) ⇄ HSO3- (aq) + H3O+ (aq)
pKa1 = 1.857
HSO3- (aq) + H2O (l) ⇄ SO3-2 (aq) + H3O+ (aq)
pKa2 = 7.172
70
Fully protonated. Loss of the first proton
H2SO3 (aq)
+
H2O (l)
⇄
HSO3- (aq)
+
H3O+ (aq)
I
0.001 M
0M
0M
C
–x
+x
+x
E
0.001 – x
x
x
−1.857
10
=
2
0.001 −
𝑥
= 9.3685 × 10−4
𝑥
𝑥
Diprotic species
This is not a buffered solution.
71
Fully protonated. Loss of the second proton
HSO3- (aq)
+
H2O (l)
⇄
SO3-2 (aq)
+
H3O+ (aq)
I 9.3685x10–4 M
0M
9.3685x10–4 M
C
–x
+x
+x
E 9.3685x10–4 – x
x
9.3685x10–4 + x
2
+ 9.3685 × 10−4
=
9.3685 × 10−4 −
−7.172
10
𝑥
𝑥
= 6.7288 × 10−8
𝑥
𝑥
Diprotic species
This is not a buffered solution.
72
Fully protonated. Comparing the pH
1. Loss of the first proton (pKa = 1.857)
= − log(9.3685 × 10−4) = .
2. Loss of the second proton (pKa = 7.172)
𝟑
𝟎
𝟑
𝟑
𝟎
𝟑
𝐻
= − log(9.3685 × 10−4 + 6.7288 × 10−8) = .
𝐻
𝑝
𝑝
Diprotic species
73
Diprotic species
Fully deprotonated species example.
What is the pH of a 1.0 L solution containing 0.001 moles of
sodium sulfite (pKa1 = 1.857, pKa2 = 7.172 )?
74
Diprotic species
Partially protonated species example.
What is the pH of a 1.0 L solution containing 0.001 moles of
sodium hydrogen sulfite (pKa1 = 1.857, pKa2 = 7.172 )?
75
Diprotic species
Partially protonated species example.
We can approximate the pH of a solution containing an intermediate
species, using the equation below:
If Ka2F is much greater than Kw, we can disregard Ka1Kw.
If Ka1 is much smaller than F, we can further simplify the denominator.
76
pKa1 = 5.40
pKa2 = 7.20
O
HO
C
C
OH
O
How do we approach problems in
which strong acids (or bases) are
added to the solution?
77
What is the pH of 50.0 mL of a 1.00 mM malic acid
solution, before we begin the titration?
50.00 mL
1.00 mM
H2 A
pKa1 = 5.40
pKa2 = 7.20
O
HO
C
C
OH
O
78
What is the pH of 50.0 mL of a 1.00 mM malic acid
solution if we added 1.00 mL of 10.0 mM NaOH?
50.00 mL
1.00 mM
H2 A
1.00 mL
10.00mM NaOH
51.00 mL
??
pKa1 = 5.40
pKa2 = 7.20
O
HO
C
C
OH
O
79
What is the pH of 50.0 mL of a 1.00 mM malic acid
solution if we added 5.00 mL of 10.0 mM NaOH?
50.00 mL
1.00 mM
H2 A
5.00 mL
10.00mM NaOH
55.00 mL
??
pKa1 = 5.40
pKa2 = 7.20
O
HO
C
C
OH
O
80
What is the pH of 50.0 mL of a 1.00 mM malic acid
solution if we added 7.50 mL of 10.0 mM NaOH?
50.00 mL
1.00 mM
H2 A
7.50 mL
10.00mM NaOH
57.50 mL
??
pKa1 = 5.40
pKa2 = 7.20
O
HO
C
C
OH
O
81
What is the pH of 50.0 mL of a 1.00 mM malic acid
solution if we added 10.00 mL of 10.0 mM NaOH?
50.00 mL
1.00 mM
H2 A
10.00 mL
10.00mM NaOH
60.00 mL
??
pKa1 = 5.40
pKa2 = 7.20
O
HO
C
C
OH
O
82
What is the pH of 50.0 mL of a 1.00 mM malic acid
solution if we added 11.00 mL of 10.0 mM NaOH?
50.00 mL
1.00 mM
H2 A
11.00 mL
10.00mM NaOH
61.00 mL
??
pKa1 = 5.40
pKa2 = 7.20
O
HO
C
C
OH
O
83
84
85
Biological molecules… mono, di, tri… polyprotic
decreasing order and complexity
Proteins are polyprotic species composed of 20(ish) building blocks.
86
Biological molecules… mono, di, tri… polyprotic
Proteins are polyprotic species composed of 20(ish) building blocks.
Glu
Phe
Gly
Asn
We can hydrolyze the primary structure into individual components
87
Biological molecules… mono, di, tri… polyprotic
Proteins are polyprotic species composed of 20(ish) building blocks.
Proteins are polyprotic species composed of 20(ish) building blocks.
amin
o
acid
pKa >> 7.00
pKa << 7.00
The side chain is labeled with an “R”
because it could be one of 20 different
structures, some ionizable in water.
88
Biological molecules… mono, di, tri… polyprotic
89
Biological molecules… mono, di, tri… polyprotic
90
Biological molecules… mono, di, tri… polyprotic
pKa = 10.07
pKa = 8.18
pKa = 4.25
pKa = 12.48
pKa = 3.65
pKa = 10.53
pKa = 4.25
91
Biological molecules… mono, di, tri… polyprotic
Upon dissolution, the solid amino acids maintain an overall neutral charge but
form a zwitterion. A zwitterion contains negatively and positively charged
functional groups simultaneously.
pKa1 = 2.350
pKa2 = 9.778
(s)
(aq)
92
How do we approach problems in
which amino acids are dissolved in
water?
93
Biological molecules… mono, di, tri… polyprotic
What is the pH of a solution prepared by dissolving 0.010
moles of solid glycine hydrochloride in 1.0 L of water?
pKa2 = 9.778
pKa1 = 2.350
94
Biological molecules… mono, di, tri… polyprotic
What is the pH of a solution prepared by dissolving 0.010
moles of solid glycine sodium salt in 1.0 L of water?
pKa2 = 9.778
pKa1 = 2.350
95
Biological molecules… mono, di, tri… polyprotic
What is the pH of a solution prepared by dissolving 0.010
moles of solid glycine in 1.0 L of water?
pKa2 = 9.778
pKa1 = 2.350
96
Biological molecules… mono, di, tri… polyprotic
The pH of a solution after a zwitterion dissolves is called its isoionic
point. This pH is concentration-dependent and is determined with an ICE
table or our forgotten friend, the equation below.
(s)
⇄
⇄
(aq)
97
Biological molecules… mono, di, tri… polyprotic
What is the isoionic point for a 0.001 M solution of valine (pKa1 =2.32 and
pKa2 = 9.62)?
What is the isoionic point for a 0.001 M solution of glutamic acid (pKa1 =2.19,
pKa2 = 4.25, pKa3 = 9.67)?
98
How do we approach problems where
amino acids are dissolved in a buffered
solution (or water where the pH is
adjusted with a strong acid or base?
99
Biological molecules… mono, di, tri… polyprotic
If we were to start at pH = 1.00 and slowly raise the
pH to 12.00, what different predominate species
would arise?
pKa3 = 10.02
pKa1 = 1.99
pKa2 = 8.95
pH = 4.00
pH = 1.00
⇄
pH = 9.50
⇄
pH = 12.00
⇄
100
Biological molecules… mono, di, tri… polyprotic
When we impose the pH on the amino acids, we can determine their
isoelectric point (the pH where all the zwitterions have a net charge 0). The
isoelectric point is concentration-independent.
We use a technique called isoelectric focusing to determine the pI of a
zwitterionic species (e.g., amino acids, proteins, polymers). There are lots of
configurations for IEF, we will focus on gel pre-prepared strips.
Video of an example of IEF gel setup and visualization: https://www.youtube.com/watch?v=C8g0VKz_Sc4
101
Step 1. Load an unknown mixture of zwitterionic species (amino acids, proteins,
polymers) onto the gel strip.
•
In the absence of voltage, the ions can diffuse throughout the gel
Step 2. Apply a voltage (potential) gradient across
102
Biological molecules… mono, di, tri… polyprotic
pH = 3.00
(+)
pH = 5.00
pH = 7.00
Where would each of these species focus in the IEF gel?
pH = 4.00
pH = 6.00
pH = 8.00
pKa = 9.0
pKa = 3.0
pKa = 9.0
(-)
pKa = 10.5
pKa = 3.2
pKa = 11.0
pKa = 5.0
103
Biological molecules… mono, di, tri… polyprotic
What is the difference between an IEF separation where the species are
0.01 M and 0.0001 M?
104
Biological molecules… mono, di, tri… polyprotic
pH = 3.00
(+)
pH = 5.00
Where would each of these species focus in the IEF gel?
pH = 4.00
pKa = 2.34
pH = 6.00
pKa =9.67
(-)
pH = 8.00
pKa = 1.82
pKa = 2.19
pKa =4.25
pKa = 9.69
pH = 7.00
pKa =6.00
pKa =9.17
105
Biological molecules… mono, di, tri… polyprotic
What does the pI tell us about the amino
acid sequence (generally) of hCG?
Human chorionic gonadotropin (hCG)
• produced by the placenta when the
fertilized egg implants
• 36.7 kDa (1 Da = 1 g/mole)
• pI of purified protein = 3.6
If we inoculated a goat with hCG and it made
anti-hCG antibodies, which of these antibodies
would be acceptable for a pregnancy test?
a. pI = 3.2
b. pI = 7.8
c. pI = 10.0
106
107
Noncovalent affinity interactions
Antibodies as analytical reagents
108
Noncovalent affinity interactions
Antibodies as analytical reagents
109
Noncovalent affinity interactions
Antibodies as analytical reagents
Fab region
Fc region
110
Noncovalent affinity interactions
Antibodies as analytical reagents
111
Noncovalent affinity interactions
Antibodies as analytical reagents
antibody
antigen
antibody-antigen
complex
112
Noncovalent affinity interactions
Antibodies as analytical reagents
antibody-antigen
complex
antigen
antibody
113
Noncovalent affinity interactions
The ghost of Christmas past…
Experimental Setup
•
•
We dissolved 1.0x10–8 moles of antibody
(anti-hCG) and 1.0x10–8 moles of antigen
(hCG) in 1.0 mL of buffered solutions with
different pH values.
We measured the percentage of the
antibody-antigen complex that formed in
each solution.
Data
pH =
5.0
5.5
6.0
6.5
7.0
7.5
8.0
40 %
44 %
55 %
78 %
99 %
96 %
55 %
complex formed
Based on what we have covered, reformulate your earlier hypothesis for this dataset
focused on molecular interactions.
114
Noncovalent affinity interactions
Antibodies as analytical reagents
115
Noncovalent affinity interactions
Antibodies as analytical reagents
rabbit-anti-urea
chicken-anti-E. coli
mouse-anti-hCG
goat-anti-HIV1 p24
116
Noncovalent affinity interactions
Polyclonal antibodies = mixture of antibodies for the same target antigen,
each B cell makes a single type of antibody (monoclonal)
All of the antibodies are
collected and purified from the
serum (or eggs if from a
chicken).
This collection of antibodies
recognize the same antigen but
come from multiple different
cells… we say that these are
polyclonal antibodies.
It is not possible to separate
them into antibodies from a
unique cells.
117
Noncovalent affinity interactions
Polyclonal antibodies = mixture of antibodies for the same target antigen,
each B cell makes a single type of antibody (monoclonal)
epitope 1
epitope 2
epitope 3
Polyclonal antibodies recognize different regions
(epitopes) of the same antigen. The binding affinity
of each antigen-antibody interaction is unique.
118
Noncovalent affinity interactions
Polyclonal antibodies = mixture of antibodies for the same target antigen,
each B cell makes a single type of antibody (monoclonal)
119
Noncovalent affinity interactions
monoclonal antibodies = antibodies that recognize a single epitope only
The source of the antibodies
must be sacrificed, to obtain
each cell (clone).
The cells are separated and
immortalized. Each cell
produces one antibody that
binds only one epitope…we say
that these are monoclonal
antibodies.
120
Noncovalent affinity interactions
1. If we wanted to detect a particular variant of the SARS-CoV-2 virus, would we
want to use a monoclonal or a polyclonal?
2. If you were in a clinical laboratory, evaluating samples for total and virulent
strains of E. coli, what kinds of antibodies would you want?
3. HIV is a retrovirus with a mutation rate of 10–4 to 10–6 mutations per base pair
per replication cycle. Its genome is ~9.6 kilobases. What is the fear or using a
monoclonal antibody in an HIV rapid test?
4. If we wanted to recover as much insulin from a large batch reactor (where CHO
cells are engineered to make tons of it), would a monoclonal or polyclonal
antibody be better?
121
Noncovalent affinity interactions
An agglutination assay uses antibody-antigen complex formation to
detect a particular antigen. The assay relies on the formation of large
aggregates that are visualized.
antigen complex
(agglutination)
In a blood typing experiment, antibodies recognize particular proteins on the surface of red
blood cells to give distinct agglutination that corresponds to blood type.
122
Noncovalent affinity interactions
An agglutination assay uses antibody-antigen complex formation to
detect a particular antigen. The assay relies on the formation of large
aggregates that are visualized.
1. If we used monoclonal antibodies for the blood agglutination assay on the
previous slide, what would have to be true of our analyte (red blood cells)?
2. Sometimes latex beads are used in agglutination assays when the analytes are
too small to form easily visualized clumps (think proteins that can’t be seen by
eye). If you wanted to prepare a pregnancy test that was agglutination-based,
how would you do it?
123
Noncovalent affinity interactions
Antibody sandwich assays like the one used in the pregnancy test are
more selective than assays that use a single antibody. Why?
124
Noncovalent affinity interactions
Would you use monoclonal or polyclonal antibodies for these sandwich
assays? Why?
125