CHE 226 ANALYTICAL CHEMISTRY Fall 2004

Transcription

1 CHE 226 ANALYTICAL CHEMISTRY FINAL EXAM December 14, 2004 Name WRITE YOUR NAME ON EACH EXAM PAGE NOW. THERE ARE 11 QUESTIONS AND 145 POINTS TOTAL IN THIS EXAM. FINAL % SCORE = # POINTS/135. 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. You do not have to do the final arithmetic on a question unless you need to have a numerical value for the next part of a question or for a statistical test, as long as the answer is expressed in its final form and all algebraic manipulations have been made. 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 must have all memory erased. A calculator may be used, but not 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 will be ignored unless you add an explanatory note on the front of the page. Unless otherwise stated, assume all solutions are aqueous, density = g/ml; activity coefficients are unity (i.e., activity = concentration); temperature, T = 298 K; K w = x QUESTION 1 /20 QUESTION 7 /5 QUESTION 2 /10 QUESTION 8 /10 QUESTION 3 /10 QUESTION 9 /15 QUESTION 4 /10 QUESTION 10 /10 QUESTION 5 /30 QUESTION 11 /10 QUESTION 6 /15 TOTAL /145

2 1. (20 Points) Tripolyphosphoric acid, H 5 P 3 O 10 was a common ingredient in high-phosphate detergents as its penta-sodium salt. It was relatively cheap, would make the washing solution quite basic, and was also a good complexing agent for sequestering ions in the tap water used and those extracted from the soiled clothes. It has largely been replaced in modern detergents because of concerns about excessive phosphate pollution of natural waters. For simplicity, designate the fully protonated acid as H 5 TPP. The acid s five pk a s are listed as ~1, ~2, 2.79, 6.47, and 9.24, respectively. (a) (10 Points) What would be the predominant chemical form of H 5 TPP in natural waters, assuming the ph = 7.00? What fraction of the total TPP-containing forms present would this form constitute? [Remember, you do not need to do the final arithmetic.] (b) (10 Points) It was stated that the penta-sodium salt of TPP makes a clothes-washing solution quite basic. Assume that you have a 0.50 M solution of Na 5 TPP. Calculate the ph of that solution. CHE 226 Final Exam 2

3 2. (10 Points) Write the mass-balance equations for a solution that is saturated in calcium phosphate Ca 3 (PO 4 ) 2 and also contains M CaCl 2. Let the molar solubility be represented by S. Assume no complexation of the calcium ion takes place. 3. (10 Points) Write the charge-balance equation for a solution that is 0.05 M in lead dibromide, PbBr 2. The lead ion can complex up to two bromide ions to form soluble complexes. 4. (10 Points) Auric chloride, AuCl 3, is relatively insoluble, K sp = 3.2 x Calculate the theoretical solubility, S, of auric chloride. Assume that no hydrolysis or complexation reactions occur. CHE 226 Final Exam 3

4 5. (30 Points) Manufacturers of blood-glucose meters routinely test large lots of the test strips used in their meters with standard glucose solutions for quality-control purposes. The analysis report included in one lot of the test strips for an Accu-Chek Compact TM glucometer is shown in the small table below. Answer the questions posed. [I believe that the actual unit involved is the clinically common, but weird, unit of mg/dl.] Control Range Mean Low High (a) (5 Points) Assume that the Range indicated for the Low and High glucose Control standards represent ± 3σ for a rather large number of replicate measurements on this lot of test strips. What fraction (or %) of all measurements should fall within the assumed Range of ± 3σ around the Mean. (b) (15 Points) Let the general term error in this problem mean plus or minus one standard deviation, ± s or ± σ. Calculate both the relative (± e rel ) and the absolute (± e abs ) errors for both the Low and the High standard solutions. [Hint: Construct a 2 x 2 table showing your calculations and the resultant values.] (c) (10 Points) Consider your results from (b). If someone asked you, what is the single, best estimate of the error in a blood-glucose measurement over the entire measurement range of , what would you say? Why? You ve got to give them one simple value: It s about plus and minus... CHE 226 Final Exam 4

5 6. (15 Points) Ferric ion can be complexed by up to three chloride ions to form soluble complexes. The values of the stepwise formational constants, K f s, are equal to 30, 135 and 98, respectively. (a) (5 Points) Calculate the value of the overall formational constant, which would be denoted as β 3, for the reaction Fe Cl - FeCl 3 (aq) (b) (10 Points) You wish to do a quick-and-dirty, back-of-the-envelope calculation on the possible absorption of ferric ion in the stomach. Stomach acid is about 0.1 M HCl. If you add a small amount of ferric ion (say about 10-4 M) to 0.1 M HCl, what fraction of the iron added remains in the form of free, uncomplexed Fe 3+? To simplify the situation for a very crude estimate, ignore the first two stepwise formational constants and do the calculation using only the β 3. [Note: Two additional simplifying assumptions will greatly simplify the arithmetic.] 7. (5 Points) The maximum upper limit for the pesticide chlordane (C 10 H 6 Cl 8 ) in drinking water is 3 ng/l. If the molar mass of chlordane is , what is this upper limit in molar units? CHE 226 Final Exam 5

6 8. (10 Points) If you use a calcium ion-selective electrode to measure Ca 2+ concentrations, the electrode actually responds directly to the activity of Ca 2+ in the solution, not to its concentration. This therefore requires that you take activity coefficients into account in some way or another. Calculate the activity coefficient for Ca 2+, γ Ca2+, in a solution that is 0.10 M in ionic strength. [Relevant information is provided at the back of the exam.] 9. (15 Points) Draw a plot of ph vs. the volume of hydrochloric acid added for the titration of a weak monoprotic base B. Clearly indicate the important specific points and regions on the curve. For each of these points and regions also include a balanced equation for the equilibrium chemical reaction that essentially controls the ph of the solution. CHE 226 Final Exam 6

7 10. (10 Points) A chemist analyzed a standard sample of Bovine Liver obtained from the National Institute of Standards and Technology (NIST) for trace lead. The average and standard deviation for 4 replicate analyses were ± µg/g. If the NIST certified ( true ) value is µg/g, is the analyzed value significantly different (at the 95% confidence level)? 11. (10 Points) Write a few comments critiquing the inclusion of Excel assignments in CHE 226 for the first time this semester. There s little point in continuing something if it s not particularly valuable? Some possible points to touch on might be: Was it an overall worthwhile experience for you? Were there too many or too few assignments? Did you first learn how to use Excel, greatly improve your previous skills in using Excel, or were so familiar with Excel it helped little? Is 4% of the course an appropriate amount of credit for the dozen assigned problems? Should the Excel assignments be retained in or dropped from the course? If retained, any changes in the system? CHE 226 Final Exam 7

8 SELECTED CONSTANTS, UNITS, AND CONVERSION FACTORS [The uncertainty in the last digit(s) is shown italicized in parentheses] Atomic mass constant: m u = x kg Avogadro s number: N = (47) x mol -1 Boltzmann constant: k = (24) x J/K Elementary charge: e = (63) x C Faraday constant: F = (39) C/mol Molar gas constant: R = (15) J/K-mol = cal/k-mol = L-atm/K-mol = m 3 /mol at STP Pi: π = Planck s constant: h = (52) x J-s Speed of light (in a vacuum): c = (exactly) x 10 8 m/s Stefan-Boltzmann constant: σ = (40) x 10-8 W/m 2 -K 4 Standard acceleration of gravity: g n = (exact) m/s 2 Wein constant: k = (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 = (63) x J = x cal Calorie (thermochemical): 1 cal = J [A food calorie = 1 Cal = 1000 cal] Length: 1 km = 1000 m = mi 1 in = 2.54 cm (exactly) Mass: 1 kg = 1000 g 1 pound = g Pressure: (exact) Pa = 1 atm = 760 mm Hg = lb/in 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 = quarts Nernst factor: (RT/nF) ln = ( V/n) log 10 at 25 o C nf/rt = n V -1 RT/nF = /n V G o = -nfe o = - RT(ln K eq ) G = - nfe = - RT(ln Q) µ = x + zσ/n 1/2 = x + zσ m µ = x + ts/n 1/2 = x + ts m Some Less Common Multiplicative Prefixes: P = peta = T = tera = G = giga = 10 9 n = nano = 10-9 p = pico = f = femto = a = atto = z = zepto = y = yocto = [See for additional information.] CHE 226 Final Exam 8

9 Ion Product for Water: pk w = at 15 o C, at 25 o C, at 40 o C Debye-Huckel Theory Debye-Huckel Limiting Law (DHLL): - log γ i = A z 2 i µ ½ = 0.5 z 2 i µ ½ Debye-Huckel Equation (DHE): - log γ i = (A z 2 i µ ½ )/(1 + B a o µ ½ ) = (0.51 z 2 i µ ½ )/( a o µ ½ ) A = , B = on a volume (molar) basis at 298 K A = , B = on a mass (molal) basis at 298 K Ion-size parameters, a o, in Angstroms 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 + Amphiprotic Salts (e.g., for NaHA): [H + ] = [(K a2 C NaHA + K w ) / (1 + C NaHA /K a1 )] ½ CHE 226 Final Exam 9

10 Confidence Levels for Various Values of z Confidence Level, % z [ z = (x µ)/σ ] Values of t for Various Levels of Probability Two-Tailed Test (±) Degrees of Factors for the Confidence Interval Freedom, ν 80% 90% 95% 99% 99.9%_ Number of Q crit (Reject if Q calc > Q crit ) Observations, n 90% C.L. 95% C.L. 99% C.L CHE 226 Final Exam 10