Quantitative Chemical Analysis 7e

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Chapter 09 Polyprotic Acid-Base Equilibria
Proteins perform biological functions such as
structural support, catalysis of chemical
reactions, immune response to foreign substances,
transport of molecules across membranes, and
control of genetic expression. The
three-dimensional structure and function of a
protein is determined by the sequence of amino
acids from which the protein is made. The diagram
below shows how amino acids are connected to make
a polypeptide.
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Polyprotic systems-acids or bases can donate or
accept more than one proton. Diprotic systems
(with two acidic or basic sites).
9-1 Diprotic Acids and Bases
The amino acid building blocks of proteins have
the general structure
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Therefore, the nonionized form rearranges
spontaneously to the zwitterion
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Diprotic acid H2L HL H
Ka1 K1 (10-1)
HL L-
H Ka2 K2
(10-2) Diprotic base L- H2O HL
OH- Kb1
(10-3) HL H2O
H2L OH- Kb2
(10-4)
That is, we would use the same procedure to find
the pH of the diprotic H2A, Where A is anything,
or H2L, where HL is leucine.
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The Acidic Form, H2L
In summary, a solution of a diprotic acid behaves
like a solution of a monoprotic acid, with Ka
Ka1.
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The Basic Form, L-
L- H2O HL OH- Kb1 KW/Ka2
5.55 X 10-5 HL H2O H2L OH-
Kb2 KW/Ka1 2.13 X 10-12
Kb1 tells us that L- will not hydrolyze (react
with water) very much to give HL.
In summary, if there is any reasonable separation
between Ka1 and Ka2 (and, therefore, between
Kb1and Kb2), the fully basic form of a diprotic
acid can be treated as monobasic, with Kb Kb1.
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BOX 9-1 Carbon Dioxide in the Air and Ocean
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The Intermediate Form, HL
HL H L- Ka Ka2
1.80 X 10-10 (10-8) HL H2O H2L
OH- Kb Kb2 2.13 X 10-12 (10-9)
A molecule that can both donate and accept a
proton is said to be amphiprotic. However, the
results apply to the intermediate form of any
diprotic acid, regardless of its charge.
H H2L L- OH- or H2L L-
H OH- 0
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Simplified Calculation for the Intermediate Form
Equation 10-12 says that the pH of the
intermediate form of a diprotic acid is close to
midway between pK1 and pK2, regardless of the
formal concentration.
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Advice When faced with the intermediate form of
a diprotic acid, use Equation 10-11 to calculate
the pH. The answer should be close to 1/2(pK1
pK2).
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Box 9-1 Carbon Dioxide in the Air and Ocean
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Box 9-2 Successive Approximations
The method of successive approximations is a good
way to deal with difficult equations that do not
have simple solutions.
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HM-2 F H2M1 M2-1 0.001
00 0.000 129 0.000 175 0.000 696 M
? H2M2 8.53 X 10-5 M M2-2 1.28 X
10-4 M
HM-3 F H2M2 M2-2 0.000 786 M
H3 4.37 X
10-5 H4
4.35 X 10-5
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Summary of Diprotic Acid Calculations
Solution of H2A
1. Treat H2A as a monoprotic acid with Ka K1 to
find H, HA-, and H2A.
2. Use the K2 equilibrium to solve for A2-.
Solution of HA-
1. Use the approximation HA- F and find the
pH with Equation 10-11.
The pH should be close to 1/2(pK1 pK2).
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2. With H from step 1 and HA- F, solve for
H2A and A2-, using the K1 and K2 equilibria.
Solution of A2-
1. Treat A2- as monobasic, with Kb Kb1 KW/Ka2
to find A2-, HA-, and H.
2. Use the K1 equilibrium to solve for H2A.
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9-2 Diprotic Buffers
For the acid H2A, we can Write two
Henderson-Hasselebalch equations, both of which
are always true.
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9-3 Polyprotic Acids and Bases
H3A H2A- H- Ka1
K1 H2A- HA2- H
Ka2 K2 HA2- A3- H
Ka3 K3 A3- H2O HA2- OH-
Kb1 KW/Ka3 HA2- H2O H2A- OH-
Kb2 KW/Ka2 H2A- H2O H3A OH-
Kb3 KW/Ka1
1. H3A is treated as a monoprotic weak acid, with
Ka K1. 2. H2A- is treated as the intermediate
form of a diprotic acid.
3. HA2- is also treated as the intermediate form
of a diprotic acid. However, HA2- is surrounded
by H2A- and A3-, so the equilibrium constants to
use are K2 and K3, instead of K1 and K2.
4. A3- is treated as monobasic, with Kb Kb1
KW/Ka3.
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When you encounter an acid or base, decide
whether you are dealing with an acidic, basic, or
intermediate form.
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9-4 Which Is the Principal Species?
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Speciation describes the distribution of analyte
among possible species.
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9-5 Fractional Composition Equations
Monoprotic Systems
The Fraction of molecules in the form HA is
called aHA.
In a similar manner, the fraction in the form A-,
designated aA-, can be obtained
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Diprotic Systems
For a diprotic system, we designate the fraction
in the form H2A as aH2A, the fraction in the form
HA- as aHA-, and the fraction in the form A2- as
aA2-.
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9-6 Isoelectric and Isoionic pH
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The isoionic point (or isoionic pH) is the pH
obtained when the pure, neutral polyprotic acid
HA (the neutral zwitterions) is dissolved in
water. The only ions are H2A, A-, H, and OH-.
Most alanine is in the form HA, and the
concentrations of H2A and A- are not equal to
each other. The isoelectric point (or
isoelectric pH) is the pH at which the average
charge of the polyprotic acid is 0. Most of the
molecules are in the uncharged form HA, and the
concentrations of H2A and A- are equal to each
other.
When alanine is dissolved in water, the pH of the
solution, by definition, is the isoionic pH.
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From H, K1, and K2, you could calculate H2A
1.68 X 10-5 M and A- 1.76 X 10-5 M for pure
alanine in water ( the isoionic solution). The
isoelectric point is the pH at which H2A
A-, and, therefore, the average charge of
alanine is 0. To go from the isoionic solution (
pure HA in water) to the isoelectric solution, we
could add just enough strong acid to decrease
A- and increase H2A until they are equal.
Isoelectric point pH 1/2(pK1 pK2)
(10-23)
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BOX 9-2 Isoelectric Focusing
At its isoelectric point, the average charge of
all forms of a protein is 0. This effect is the
basis of a sensitive technique of protein
separation called isoelectric focusing. A
mixture of seven proteins( and some impurities)
was applied to a polyacrylamide gel containing a
mixture of polyprotic compounds called ampholytes.
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The instrument that measures absorbance as a
function of position along the gel is called a
densitometer.
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For a protein, the isoionic pH is the pH of a
solution of pure protein with no other ions
except H and OH-.
When the protein is subjected to intensive
dialysis (Demonstration 27-1) against pure water,
the ph in the protein compartment approaches the
isoionic point if the counterions are free to
pass through the semipermeable dialysis membrane
that retains the protein. The isoelectric point
is the pH at which the protein has no net charge.
The pH of zero charge is the pH at which SiOH2
SiO- and, therefore, the surface has no net
charge. Colloidal particles (those with diameters
in the range 1-100 nm) tend to remain dispersed
when they are charged, but they flocculate (come
together and precipitate) near the pH of zero
charge.