NAME:__________solutions_______________ Chem 51, fall, 2002, Exam 1

A periodic table of the elements is included as an insert. You may use the back for scratch work but enter all work to be graded in the space provided with each question. Show your work in all questions involving computation in order to receive any credit. Unless otherwise noted, all reactions are conducted in water at 25.00°C.

1) (36 points) A chemist is studying the enzyme carboxypeptidase and wishes to measure its activity at pH 3.20. The following acids and the sodium salts of their conjugate bases are available:

acid: pyruvic chloroacetic lactic formic acetic

pK_a: 2.39 2.85 3.08 3.75 4.76

a) Select the acid/conjugate base pair best suited for the preparation of a pH 3.20 buffer. Briefly provide the rationale for your choice.

The pK_a of the ideal acid should be as close as possible to the target pH, 3.20. The optimal choice is lactic acid.

b) For your choice of acid /conjugate base, determine the composition of the buffer, i.e. concentrations that can be provided to a technician. Two constraints apply on your calculation. To maximize buffering capacity, the concentration of the solutes should be as large as possible. In order to minimize the deviations from ideal-solution behavior, the concentration of the conjugate base should not exceed 0.100 M.

The constraints on concentrations set the concentration of the lactate anion, L^-,to be 0.1 M. The chemical equation for the relevant reaction is HL(aq) = H+(aq) + L-(aq) for which

K_a = 10^-3.08 = 0.00083 = [H+][L-]/[HL] = (10-3.20)(0.100 M)/[HL}.

Solving for [HL}, one obtains [HL] = 0.076 M.

2) (45 points) Write a balanced, net ionic equation for the reaction that occurs when the following sets of aqueous solutions or slurries are mixed:

a) strontium carbonate plus hydrobromic acid.

Strontium carbonate is insoluble but the carbonate ion generated when a small amount dissolves reacts with two moles of hydronium ions.

SrCO₃(s) + 2 H⁺(aq) = Sr⁺²(aq) + H₂O(l) + CO₂(g)

b) iron(II) hydroxide plus potassium cyanide

Iron(II) hydroxide is insoluble but the iron cation formed when a small amount dissolves forms a complex with the strong ligand cyanide.

Fe(OH)₂(s) + 6 CN^-(aq) = Fe(CN)₆^-4(aq) + 2 OH^-(aq)

c) hot 6 M nitric acid plus copper metal

The hydronium ion is a very weak oxidizing agent and only accept electrons from a strong reducing agent. Copper, a coinage metal in the same family as gold and silver, is not sufficiently reactive to react with a strong acid. Nitric acid is a potent oxidizing agent and it will act as such in this case as the solution is hot and concentrated. Use the method of half reactions to balance the equation.

reduction: 3 e^-1 + 4 H⁺ + NO₃^- = NO + 2 H₂O

oxidation: Cu = Cu⁺² + 2 e-

net: 3 Cu(s) + 8 H⁺(aq) + 2 NO₃^-(aq) = 3 Cu⁺²⁽aq) + 2 NO(g) + 2H₂O(l).

3) (20 points) The beta activity of a uranium sample was measured using a Geiger-Mueller counter and a counting period of 0.100 min. The average and standard deviation obtained from 10 measurements were 427.5 counts and 21.7 counts, respectively.

Student’s t: 1 2 3 4 5 6 7 8 9 10

degrees of freedom: 12.7 4.30 3.18 2.78 2.57 2.45 2.37 2.31 2.26 2.23

a) Present the average to the correct number of significant digits.

Use the standard deviation of the mean, 21.7/(10)^0.5 = 6.9 counts, to determine the number of significant digits. The statistic shows that the units place is the least significant digit. Hence round out to 428 counts.

b) What quantitative improvement, if any, would be observed in the relative uncertainty of a single measurement if the counting period were increased from 0.100 min to 0.900 minutes?

Increasing the counting time will reduce the random noise by averaging. The standard deviation of the mean equals the standard deviation divided by the square root of the number of measurements, N. Since N is proportional to the measurement period, the random error will be reduced by a factor of [(0.9 min)/(0.1 min)]^0.5 or 3.

c) An eleventh measurement of the radioactivity yielded a value of 451 counts. Is the result an outlier or is the value consistent with the other 10 measurements? Briefly explain.

Use the standard deviation of a single measurement here. Its 95% confidence interval = ts = (2.26)(21.7) = 49 counts. The difference between the mean and the suspected outlier is 450 – 427.5 = 22.5. This is less than the 95% confidence interval. Hence a random error this large is possible. Do not reject the datum.

4) (30 points) Sodium propionate (CH₃CH₂CO₂Na; MW, 96.1 g/mol) which is the sodium salt of propionic acid (CH₃CH₂CO₂H) is used as a preservative in food preparations. A new brand of soup contains 2.0 g of sodium propionate per 500.0 ml. Calculate the pH of the soup. Assume that the sodium propionate is the only species contributing to the pH. The pK_a of propionic acid is 4.86.

This problem falls into the category of a weak base, B-. The relevant net ionic equation is B^-(aq) + H₂O(l ) = HB(aq) + OH^-(aq) for which

K_b = K_w/K_a = (1.00 x 10^-14)/(10^-4.86) = 7.24 x 10^-10 = [OH^-][HB]/[B^-].

The base is weak but not very weak and we can make the usual simplifying approximations:

[OH^-] = [HB] and [HB} = [HB]₀ = (2.0 g/96.1 g/mol)/(0.5 l) = 0.042 M.

Hence, 7.24 x 10^-10 = [OH^-]²/0.042. Solving for the unknown, one obtains [OH-] = 5.5 x 10^-6 M and pOH = 5.26 and pH = 14 – pOH = 8.73.

5) (19 points) Joe DeSimone, Professor of Chemistry at Carolina, studies supercritical solvents, i.e. solvents under conditions of temperature and pressure where differences between the liquid and gaseous states vanish. In a recent article on “Green Chemistry”, Professor DeSimone wrote:

“Supercritical water behaves as a non-polar solvent primarily because hydrogen bonding is lost under these extreme conditions. The dielectric constant of water decreases from 80 at ambient conditions to <5 above the critical point.”

Make predictions on the solubility of substances--polar, ionic, and non-polar--in supercritical water. Discuss how your predictions follow from molecular structure and the properties of supercritical water.

Note that Professor DeSimone states the supercritical water is behaving as if it were non-polar. He is not claiming that a single water molecule is non-polar.

One can predict that non-polar compounds will be soluble in supercritical water and ionic compounds will not. The loss of hydrogen bonding is the key feature for the case of non-polar solutes. Separating the water molecules no longer involves breaking hydrogen bonds and the energetic costs will be low. Entropy always favors dissolving which entails scrambling things. Consequently, non-polar compounds will dissolve easily.

The case of ionic compounds involves a bit more thought. Single water molecules will still be polar and can still hydrate ions. This mechanism for the lowering of the energy is not lost. Decreasing the dielectric constant, however, will increase the forces between the solvated ions and will make it more difficult to pry the crystal apart. Solubility will be greatly reduced and when some of the salt does dissolve, one will not end up with freely mobile hydrated cations and anions. The anions and cations will be found close to one another.

The case of polar compounds is problematic. If the polar solute exhibits hydrogen bonding that is retained under the experimental conditions, there will be a large energy cost for separating them from one another. If the water molecules will be unable to form hydrogen bonds with the solute, then one retains the energy cost and loses the compensation. The material will exhibit reduced solubility. If the compound is only somewhat polar, it will probably be more soluble in supercritical water than it was in normal water. The energy cost of breaking the water’s hydrogen bonds no longer has to be paid and the cost of separating the solute molecules remains but is small.

ex51_1_02.htm, WES, 1 October 2002