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Biological Sciences 102
Answer Key
Fall, 2009
K. Hilt
Homework #1
Learn the structures and one-letter codes of the twenty amino acids.
Assigned problems in
Biochemical Calculations
(Segel), concerning weak acid/base concepts:
Example 1
13 on page 18
#17, 24, 25 (a
d), 29, 31, 32, 34, 36, 38 (a, d, j), 40, and 41 on pages 92 and 93.
See appendix IV of
Biochemical Calculations
for pK
a
values needed in some of the above questions.
Comments:
1.
Example 1-13 reminds us that if you add an extremely small amount of H
+
or OH
to a container of water,
the pH is determined mainly by the H
+
coming from water.
2.
In #17 c, we are reminded that strong bases always win when added to weak acids.
3.
In #24, “amine” means that the weak acid/base is fully unprotonated. The solution is at the top of the
titration curve. Use
K
b
= x
2
/ y-x
to solve.
4.
In #25 b and c, these are intermediate ions. Use pH = (pK
a1
+ pK
a2
)/ 2 to solve. The K
+
ions have no effect
on the pH.
5.
In #29, do not forget that addition of 0.06 moles of H
+
generates 0.06 moles of NH
4
+
. We also have 0.02
moles of NH
3
remaining. Use the Henderson-Hasselbalch equation to solve.
6.
In #40, addition of H
+
causes a decrease in the pH. You will need two Henderson-Hasselbalch equations to
solve this. The first equation yields the [b] and [a] at time zero. The second equation essentially works
backwards: the new H-H equation is pH = 7.21 + log {[b] – [x]}/{[a] + [x]}. We know [b] and [a] from the
first equation and x = 0.004 M.
For the questions below, use the following pK
a
values for the amino acids:
-COOH (2.1),
-NH
3
+
(9.6); side chains---see the class handout on amino acid structures
For oligopeptides, pK
a
values are: N-terminus (7.4), C-terminus (3.6)
1.
Which amino acid has a net charge of “+ 0.09” at pH 7? Show all calculations. Draw the structure of the
amino acid that would predominate at this pH.
Histidine.
To calculate the net charge of histidine at pH 7, we can deal with two of the groups, the
α
-carboxyl
group and
α
-amino group, by inspection. Their charges are “-1” and “+1”, respectively. This is because their
pKa’s are more than two units away from pH 7. After having worked with the Henderson-Hasselbalch equation
enough, we will realize that whenever the pH and pKa differ by two or more units, the inverse log will be at
least 100/1 in favor of either “a” or “b”. For the side chain imidazole group, whose pKa is 6.0, we need to use
the Henderson-Hasselbalch equation and calculate the percentage of the population in the “a” form (why?).
In drawing the structure of histidine at pH 7, the