CHE 226 ANALYTICAL CHEMISTRY Fall 2004 EXAM I – September 23, 2004 Name ______________________________ WRITE YOUR NAME ON EACH EXAM PAGE NOW. THERE ARE 8 QUESTIONS AND 106 PERCENT 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. 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, 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 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; Kw = 1.008 x 10-14. QUESTION 1 ___________ / 9 Question 7 ___________ /9 QUESTION 2 ___________ /12 Question 8 ___________ /8 QUESTION 3 ___________ / 8 Question 9 ___________ / QUESTION 4 ___________ /19 Question 10 ___________ / QUESTION 5 ___________ /35 Question 11 ___________ / QUESTION 6 ___________ /6 TOTAL ___________ /106Name __________________________________ 1. (9 Points) Express the results of the following calculations, as obtained from the readout of a hand calculator, to the proper number of significant figures. That is, “round off” the numerical answers indicated according to the simple rules for rounding. (a) 16.54 - 0.05152 + 1.527 = 18.01548000 = (b) 15.27 x 0.041 = 0.45765351 = 1.368 (c) log10 (10.3) = 1.01283723 = 2. (12 points) A sample of soil was dried, ground, and sieved to prepare a laboratory sample. It was then analyzed and found to contain 3.51% (by mass) of aluminum (Al), which occurs in soil largely in the form of aluminosilicates in clays. When soil scientists report such analyses, it is quite common to state results as the % by mass of the stable oxide form, in this case as aluminum oxide – Al2O3. [Al = 26.982 g/mol. O = 15.9994 g/mol.] This has advantages for doing mass balances of elements. Calculate – (a) (8 Points) The % by mass of aluminum oxide in the sample. (b) (4 Points) The ppm (mg/kg) of aluminum oxide in the sample. CHE 226 Exam I Fall 2004 2Name __________________________________ 3. (8 points) List two of the important characteristics of determinate or systematic error. 4. (19 Points) Currently, the element whose atomic mass is least well known is palladium, which is reported as 106.4 g/mol. This is because the relative abundances of the six stable, naturally occurring isotopes of Pd vary substantially from one source of Pd to another. The most well known atomic mass is that of fluorine, at 18.998403 g/mol, because F has only one stable isotope. Assuming that the values stated in this manner imply the conventional uncertainty or “error” of ± 1 in the least significant digit (and corresponds to a standard deviation), calculate: (a) (4 Points) The absolute uncertainty in the atomic mass for Pd. (b) (6 Points) The relative uncertainty in the atomic mass for F. (c) (9 Points) The relative uncertainty of the molar mass for PdF3. CHE 226 Exam I Fall 2004 3Name __________________________________ 5. (35 Points) Consider the following set of replicate measurements (in µg/g) and then calculate: 2.3, 2.6, 2.2, 2.9, 2.5 (a) (4 Points) The median. (b) (16 Points) The standard deviation (or “standard error”) of the mean, sm. (c) (8 Points) The 95% confidence limit of the set of data. (d) (7 Points) Can any of the values from the set of data be statistically rejected (by the Q-test) with 90% confidence? That is, are there any “outliers”? CHE 226 Exam I Fall 2004 4Name __________________________________ 6. (6 points) Very briefly explain exactly what is a “pooled standard deviation,” sp, and what is its primary purpose, point, or use. In other words, why did measurement scientists and statisticians go to the trouble of specially defining it? 7. (9 Points) A titrimetric method for the determination of calcium in limestone was tested by analyzing a NIST (National Institute of Standards and Technology) standard sample of limestone that had a certified value of 24.45% (by mass) CaO. Five replicate analyses gave: x ± s = 24.66% ± 0.085% (by mass) CaO. Do these data by themselves indicate the presence of a systematic error at the 95% confidence level? 8. (8 points) In a Gaussian distribution, what percentage of all the data would be expected to fall in the range from µ + σ to µ + 2σ? [Strong hint: Draw a picture.] CHE 226 Exam I Fall 2004 5Name __________________________________ Confidence Levels for Various Values of z Confidence Level, % z [ z = (x – µ)/σ ] 50 0.675 68.3 1.000 80.0 1.282 90 1.645 95 1.960 95.4 2.000 99 2.576 99.7 3.000 99.9 3.291 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%_ 1 3.08 6.31 12.7 63.7 637 2 1.89 2.92 4.30 9.92 31.6 3 1.64 2.35 3.18 5.84 12.9 4 1.53 2.13 2.78 4.60 8.60 5 1.48 2.02 2.57 4.03 6.86 6 1.44 1.94 2.45 3.71 5.96 7 1.42 1.90 2.36 3.50 5.40 8 1.40 1.86 2.31 3.36 5.04 9 1.38 1.83 2.26 3.25 4.78 10 1.37 1.81 2.23 3.17 4.59 11 1.36 1.80 2.20 3.11 4.44 12 1.36 1.78 2.18 3.06 4.32 13 1.35 1.77 2.16 3.01 4.22 14 1.34 1.76 2.14 2.98