Biochemistry PROBLEM SET

For problems 1-3, assume an activity coefficient of 1 for all substances and no effect of ionic strength. Eliminate terms in quadratic solutions for [H⁺] only if the weak acid is dissociated < 5%. Reported pKa values can vary depending on the conditions under which they were measured; therefore, in solving the following problems use the pKa values given with the problems.

Q1. (a) What is the pH of a 10 mM solution of hydrochloric acid (HCl)? Hydrochloric acid Ka > 1.

(b) What is the pH of a 10 mM solution of nitrous acid (HNO2)? Nitrous acid Ka = 4.00 x 10^-4 M.

(c) What is the pH of a 10 mM solution of acetic acid (CH3COOH)? Acetic acid Ka = 1.76 x 10^-5 M.

(d) Describe and explain the trend observed for the 10 mM acid solutions as Ka is decreased in parts (a) through (c).

Use the following information for questions 2 and 3.

Phosphoric acid (H₃PO₄) is a triprotic acid.

H₃PO₄ H⁺ + H₂PO₄^-                       pK_{a_1} = 2.12

H₂PO₄^- H⁺ + HPO₄^2-                     pK_{a_2} = 7.21

HPO₄^2- H⁺ + PO₄^3-                       pK_{a_3} = 12.32

Q2. (a) At what pH is [HPO₄^2-] double that of [PO₄^3-]?

(b) At what pH is [HPO₄^2-] equal to [PO₄^3-]?

(c) At what pH is [HPO₄^2-] half that of [PO₄^3-]?

(d) Guided by your answers in parts (a) through (c), explain the relationship between [acid], [conjugate base] and pKa.

Q3. (a) If 6 volumes of 12 mM KOH are mixed with 1 volume of 45 mM H₃PO₄, what will be the pH of the final mixture?

(b) If 30 µmoles of lactic acid is generated in a 4.0 ml enzymatic reaction buffered by 50 mM Naphosphate (pH 7.0), what will be the final pH of the reaction mixture? Lactic acid pKa = 3.86.

Q4. In the first step of glucose breakdown in our bodies, hexokinase catalyzes the following reaction;

glucose + Pi glucose-6-phosphate

ΔG^o' at 25^oC for this reaction is 13.8 KJ/mol.

(a) Does the ΔG^o' indicate that formation of glucose-6-phosphate is favored at 25^oC ? Explain your answer; no calculations required.

(b) In certain conditions, the formation of glucose-6-phosphate can be coupled to ATP hydrolysis. What is Keq' for the coupled reaction?

ATP ADP + P_i

ΔG^o' at 25^oC for this reaction is -30.5 kJ/mol.

(c) If ATP and ADP are present at 0.8 mM and 0.2 mM, what is the equilibrium ratio of glucose-6-phosphate to glucose?

(d) If glucose-6-phosphate is removed such that the ratio decreases 10-fold, what will be the resulting change in ΔG'?

Q5. The following Keq values were measured for the enzymatic breakdown of A into B and C.

Temperature (^oC)                  Keq (M)

6.85                                       0.38

16.85                                     0.86

26.85                                     2.00

36.85                                     4.44

46.85                                     9.12

(a) Is the breakdown of A into B and C more favored at high temperatures or low temperatures? Explain your answer.

(b) Using Excel, or a similar program, make a van't Hoff plot. Include a table showing any results from calculations, a trendline and an equation of best fit.

(c) What are the corresponding ΔH^o' and ΔS^o' for the breakdown of A into B and C?

(d) At 98^oC, is the breakdown of A into B and C favorable? If so, is it driven by entropy, enthalpy, or both? Assume that ΔH^o' and ΔS^o' are constant with respect to temperature.

6. The following peptide is from a protein that is both methylated and acetylated at lysine residues in the cell.

ala-lys-thr-lys-gln-thr-ala-ala-lys-ser-thr

(a) Write the single letter sequence of the peptide and indicate above the sequence the charges the residues will carry at pH 7.0. Use approximate pKas discussed in class.

(b) What will be the charge of the peptide at pH 7.0 if it is;

(i) acetylated at two lysine residues?

(ii) acetylated at all lysine residues?

(iii) methylated at all lysine residues?

(c) Describe how each of these modified peptides would behave on an ion exchange column with an 'S' (SO₃^-) resin at pH 7.0. Which peptides would bind the column and, of those bound, which would elute first in a [NaCl] gradient?