CHE 226 ANALYTICAL CHEMISTRY EXAM II March 10, 2005 Name WRITE YOUR NAME ON EACH EXAM PAGE NOW. THERE ARE 10 QUESTIONS AND 109 POINTS TOTAL IN THIS EXAM. Show clearly all work on these pages. Use the proper number of significant figures and the correct units in all final answers. You must show your calculations and/or reasoning, including equations, on a question to obtain any credit; no credit for answers appearing out of the blue. Your work must be understandable at the time it is being graded to obtain any partial credit. Very little will be subtracted for routine arithmetic errors, but all numerical answers must be shown to the proper number of significant figures. Programmable calculators are not allowed, but may not be shared with anyone else. Tables of data and other information that may be useful are appended to the back of the exam. Use the backs of the pages as scrap paper. Anything written on the backs of pages is totally irrelevant to the grading process. Unless otherwise stated, assume all solutions are aqueous, density = 1.0000 g/ml; activity coefficients are unity (i.e., activity = concentration); temperature, T = 298 K; K w = 1.008 x 10-14. QUESTION 1 _ / 8 QUESTION 7 _ / 6 QUESTION 2 _ / 7 QUESTION 8 _ / 6 QUESTION 3 _ / 5 QUESTION 9 _ /10 QUESTION 4 _ /10 QUESTION 10 _ /10 QUESTION 5 _ /15 QUESTION 6 _ /32 TOTAL /109
1. (8 points) The determination of sulfur contamination in a coal sample yields the following results: 22.23, 22.09, 21.34, 22.10 ppm S. Can any of the measurements be rejected at the 95% confidence level? Show work to support your answer. 2. (7 points) Linear least-squares (LLS): a) (5 points) Name two reasons why LLS is useful. b) (2 points) In the LLS process, what exactly is being minimized? 3. (5 points) Name two of the four properties of an ideal precipitating reagent. CHE 226 Exam II 2
4. (10 points) Which type of precipitate will have the following properties? Use the labels COL for colloidal solid, CRY for crystalline solid, or B for both to select which type of precipitate best fits the description. Can undergo peptization during washing as electrolyte ions are removed. More prone to error in a gravimetric analysis due to surface adsorption. Prone to error due to mixed-crystal formation as contaminant ions exchange for analyte ions in the lattice. If supersaturation is minimized, you will get particles of a larger diameter, characteristic of this type of solid. Type of solid one typically has to deal with in a gravimetric analysis. 5. (15 points) For a solution that is 0.040 M Ca 3 (AsO 4 ) 2 and 0.025 M Mg(NO 3 ) 2 consider the following: a) (5 points) Calculate the ionic strength of the solution. b) (10 points) Calculate the activity coefficients (γ s) for the calcium and nitrate ions in the solution using the extended Debye-Hückel equation. CHE 226 Exam II 3
6. (32 points) For the following problems, consider a 10-2 M solution of acetic acid, CH 3 COOH, a weak acid (K a = 10-4.76 ). a) (8 points) Write all of the relevant equilibrium expressions with their associated K s (and their numerical values). b) (7 points) Write all relevant mass and charge balance expressions for the system. Include actual numeric values were possible. c) (6 points) What important assumption(s) can you make for this system to simplify the algebra? Show how any pertinent equations will be affected. d) (8 points) Based on the answers above, what is the ph of the system at equilibrium? e) (3 points) How much error was introduced by making your assumption(s)? CHE 226 Exam II 4
7. (6 points) Find the ph of 100.0 ml of 0.015 M HCl mixed with 100.0 ml of 10-2 M KCl. 8. (6 points) What is the ph of a 1.00 x 10-6 M NaOH solution? 9. (10 points) What is the simple solubility of PbCl 2? That is, ignore any complex equilibria that might arise from the dissolution of the solid and the autoprotolysis of water. K sp = 1.7 x 10-5 10. (10 points) What is the Ba +2 concentration in a solution prepared by mixing 50.0 ml of 0.0500 M Ba +2 with 50.0 ml of 0.0200 IO 3 -? For Ba(IO 3 ) 2, K sp = 1.57 x 10-9 and ignore the other complex equilibria and autoprotolysis of water that may arise. CHE 226 Exam II 5
SELECTED CONSTANTS, UNITS, AND CONVERSION FACTORS [The uncertainty in the last digit(s) is shown italicized in parentheses] Atomic mass constant: m u = 1.660 538 73 x 10-27 kg Avogadro s number: N = 6.022 141 99 (47) x 10 23 mol -1 Boltzmann constant: k = 1.380 6503 (24) x 10-23 J/K Elementary charge: e = 1.602 176 462 (63) x 10-19 C Faraday constant: F = 96 485.3415 (39) C/mol Molar gas constant: R = 8.314 472 (15) J/K-mol = 1.9872 cal/k-mol = 0.082 057 L-atm/K-mol = 0.022 414 m 3 /mol at STP Pi: π = 3.141 592 653 6 Planck s constant: h = 6.626 068 76 (52) x 10-34 J-s Speed of light (in a vacuum): c = 2.999 792 458 (exact) x 10 8 m/s Stefan-Boltzmann constant: σ = 5.670 400 (40) x 10-8 W/m 2 -K 4 Standard acceleration of gravity: g n = 9.806 65 (exact) m/s 2 Wein constant: k = 2.897 7686 (51) x 10-3 m-k Force: 1 N = 1 kg-m/s 2 Joule: 1 J = 1 N-m = 1 kg-m 2 /s 2 = 10 7 ergs = 1 V x 1 C = 1 V-C = (J/C)(C) Power: 1 W = 1 J/s = 1 V x 1 A = 1 V-A = (J/C)(C/s) Electron Volt: 1 ev = 1.602 176 462 (63) x 10-19 J = 3.827 x 10-20 cal Calorie (thermochemical): 1 cal = 4.184 J [Food calorie = 1 Cal = 1000 cal] Length: 1 km = 1000 m = 0.62137 mi 1 in = 2.54 cm (exactly) Mass: 1 kg = 1000 g 1 pound = 453.59237 g Pressure: 101 325 (exact) Pa = 1 atm = 760 mm Hg = 17.70 lb/in 2 133.322 Pa = 1 torr = 1 mm Hg 10 5 Pa = 1 bar 1 Pa = 1 N/m 2 Volume: 1 L = 10-3 m 3 = 1000 ml = 1000 cm 3 = 1.056710 quarts Nernst factor: (RT/nF) ln = (0.05916 V/n) log 10 at 25 o C nf/rt = 38.920 n V -1 RT/nF = 0.02569/n V G o = -nfe o = -RT(ln K eq ) G = -nfe = -RT(ln Q) µ = x + zσ/n 1/2 µ = x + ts/n 1/2 Ion Product for Water pk w = 14.3463 at 15 o C, 13.9965 at 25 o C, 13.5348 at 40 o C Some Less Common Multiplicative Prefixes: P = peta = 10 15 T = tera = 10 12 G = giga = 10 9 n = nano = 10-9 p = pico = 10-12 f = femto = 10-15 a = atto = 10-18 z = zepto = 10-21 y = yocto = 10-24 [See http://physics.nist.gov/cuu/index.html for additional information.] CHE 226 Exam II 6
Ion-size parameters in Angstroms (10-10 m) 11: Ce 4+, Sn 4+, Th 4+, Zr 4+ 9: Al 3+, Cr 3+, Eu 3+, Fe 3+, H +, In 3+, La 3+, Sc 3+, Y 3+, 8: Be 2+, Mg 2+ 6: Ca 2+, Co 2+, Cu 2+, Li +, Mn 2+, Ni 2+, Zn 2+ 5: Ba 2+, Cd 2+, Hg 2+, Ra 2+, Sr 2+, S 2-4.5: CH 3 COO, Pb 2+, CO 2 3, SO 2 3, MoO 2 4, S 2 O 2 2 3, HPO 4 4: Na +, IO 3, HSO 3, SO 2 3 4, PO 4 3.5: OH, F SCN, OCN, SH ; ClO 3, ClO 4, BrO 3 ; IO 4 3: CN, K +, Cl ; Br, I ; NO 2, NO 3 2.5: Ag +, Cs +, NH + 4, Rb +, Tl + Confidence Levels for Various Values of z Confidence Levels, z % 50.0 0.675 68.3 1.000 80.0 1.282 90.0 1.645 95.0 1.960 95.4 2.000 99.0 2.576 99.7 3.000 99.9 3.291 Critical Values for the Rejection Quotient, Q Number of Observations Q crit 90% Confidence 95% Confidence 3 0.941 0.970 0.994 4 0.765 0.829 0.926 5 0.642 0.710 0.821 6 0.560 0.625 0.740 7 0.507 0.568 0.680 8 0.468 0.526 0.634 9 0.437 0.493 0.598 10 0.412 0.466 0.568 99% Confidence CHE 226 Exam II 7