Proj.Total - Fall 2009 Chemistry 3000 Cornell University...

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Unformatted text preview: Fall 2009 Chemistry 3000 Cornell University Final Project: Meta-Analysis of Experiment 4 Data Last First Email: @cornell.edu [ ] Christina Cowman [ ] Yingchao (Alex) Yu [ ] Angela Bruneau [ ]Mon PM [ ]TuesAM [ ]Tues PM [ lWeds PM [ ]Thurs PM fl/W/U #7 _ aag Mam Vflfly Treat this project like a take—home exam: 1. You must work alone. You may not discuss this exam with any other student. even a stu— dent not taking Chemistry 3000. You may ask any course teaching assistant or the course § professor a question — in person during office hours is preferable to email. Office hours are ‘ posted on the course website. CU 2. In answering the Final Project questions, you may refer to your own notes, the class text, and any posted homework solutions. You may use the internet and other books as reference material, but you must document what resources you use other than those listed in the pre- vious sentence. Sites that you refer to other than sites widely regarded as being in the public domain, such as the online Microsoft Excel reference manual, must be attributed with a full ~t\\l . \; URL address in your report. § y/u Maxi/0 3. The exam is due at NOON on Wednesday 25 November. Turn in your exam to your teaching assistant’s mailbox in the Department of Chemistry and Chemical Biology’s Instructional Office. 4. Before beginning the project, you are responsible for reading and understanding the Cornell Code of Academic Integrity: /H\ http://cuinfo.cornell.edu/Academic/AiChtml Please sign the following acknowledgement. Exams turned in without a signed and dated academic integrity statement will be given a zero. I have read, and understand, the Final Project guidelines and the Cornell Code of Academic Integrity. Signature: The project questions begin on the next page. Date: g Attach calculations, written explanations, and spreadsheet printouts as needed to show your work. >jg Chem—3000—Lab—7—ver2.tex rev. 2009/11/20—0012 jam99 @ cornelledu VII-1 6’13 77th / Fall 2009 Chemistry 3000 Cornell University The goal of this project is to analyze the class’s data from Experiment 4, in which you deter- mined the iron content of a vitamin tablet. By examining the class’s aggregate data, we can draw additional conclusions about how to improve the experiment. Data. To complete this project, you will need to download the following Microsoft Excel spread- sheet of data which is posted on the class website: Chem3000_2009_Project_Data_distrib.xls The spreadsheet contains data from fifty five students in the class. Four columns of data are given: 1) the iron content of the vitamin tablet in mg/ g, 2) the mass of the vitamin tablet in g, 3) the slope of the calibration curve in a.u.lttM, and 4) the intercept of the calibration curve in a.u., where a.u. stands for absorbance units. Cumulative probability distribution. In lecture Lecture 3, on 09/10/09, I demonstrated how to plot the cumulative probability distribution function of data. A copy of the Lecture 3 slides can be found in the Course Documents section of the class website. The file is Chem 3000 —— Fall 2009 —— John Marohn —- Lecture 3 —— t-test post.pdf The cumulative distribution function 0]) expected for normally—distributed data .1? is 7,_ 1 I , _('y—#)2~, cp(a.)—W/_mexp( 202 )dg (l) where p, and a are the mean and standard deviation, respectively, of the normally distributed data. The function cp(;r) tells you the fraction of the data that lies below 1",. For example, chr) = 0.5; in words, half the data lies below the mean. The function (3])(17; n, a) is implemented in Microsoft Excel using NORMDIST (x, mean, std_dev, TRUE) where the option TRUE indicates that you wish to plot the cumulative probability. /f7973 1. From the data given you in the Excel file, fl _—.———. (a) Generate and plot the cumulative probability distribution of the iron content of the 9/03 3 vitamin tablet, the mass of the vitamin tablet. and the slope and intercept of the cali- »————-— bration curve. a 4/4 WW , . . . (b) We want to compare the cumulative probability distribution generated for each of these data sets to the distribution expected for normally distributed data. gm Use the data between the 25Lh and 75th percentile to estimate the mean of each data 5/,: set; this procedure will give a robust estimate of the mean ,u even if there are “outliers” 7‘j/M fl present in the data set. To get a similarly robust estimate each data set’s standard deviation 0, use the function NORMDIST to plot the normal cumulative probability ¢ //w W &F V distribution. Get an initial estimate of a by varying a by trial and error until the function goes through the observed cumulative probability distribution. Use trial and error to refine a by finding a a that minimizes the x2 deviation between the calculated and observed normal cumulative probability distribution. You can stop when you have determined a to at least two significant figures. Report p and (7 determined in this way for the iron content of the vitamin tablet, the mass of the Vitamin tablet, and the slope and intercept of the calibration curve. Report this data in a table and put a box around your answer. VII-2 Fall 2009 Chemistry 3000 Cornell University '3 923.. ff '- (c) Qualitatively, which of the four data sets follows a normal distribution most closely? 2. In the experiment, an iron solution was prepared from a vitamin tablet and the absorbance of this analyte solution was measured. mass of the Vitamin tablet as estimated above, compute the mean absorption (in a. u ) {£73 £0? (a) Using the class— —averaged iron content of the Vitamin tablet and the class averaged observed by the class A. Put a box around your answer. )In the experiment, four iron standard solutions were prepared with different concen- 3 50 73 trations C. The absorbance A of each of these solutions was measured, and the data fit 0? ggMJ'T to the function A = a + b C (2) 3 73' to obtain a calibration curve. The calibration curve was used to infer the iron concen— JC— 0},” tration 1n the analyte solutlon. w/ W The observed standard deviation in the iron concentration 00 has contributions from fl?do9. the standard deviation in the calibration intercept, 00, the standard deviation the cal- ibration slope, 0b, and the standard deviation in the measured absorbance, 0A. Use a k/ P 73- propagation-of—error calculation and 0C, 0“, and ab estimated in question lb to infer J; d (/6 My 0.4- Report 0A in a.u. and as a percentage of A. Put a box around your answer. / 0 3. Considering the various standard deviations found above, explain which of the following / steps in the experiment are likely introducing the largest error into your estimate of the . tablet’s iron concentration: N (a) Weighing the sample 8%? C ”0534 ' 0 . . . . W (b) Making solut1ons by filling volumetric flasks (4_ _€) (gym/g 7/3 fig?” (0) Transferring solutions with pipets ./ //' 2. CE: W Z ?/flQ/: (d) Reducing iron with hydroquinone £@// N/ (e) Complexing iron with phenanthroline ,z,a..-/r/ ”Ar/(r, /7zjjj (f) Dissolving the vitamin tablet with acid 6” Al‘ if /K' 75 ”/9 {j g) Adding buffer to control the pH £73641?/( g/é/ , 4. A second estimate of the error in absorbance can be obtained as follows. In class on 1 1/ 19/09 / 0 i I derived a formula for the variance in the slope of a best—fit line. Assuming uniform errors, show that this formula reduces to C/ (713 2 N. 2 1 N. 2 (3) pfl 21:11 —N(Zj=lxj) 05g; (/5/ where a is the error bar in each of the y data points. This formula agrees with Equation 5.16 in Harvey. Taking an and y to be the concentration and absorbance of the standard solutions, respec- Q p73 tively, use this formula and the error bar 0;, in the best—fit slope determined in question lb to estimate the standard deviation of the absorbance data. y 5 (I ' Report your answer for 0A in a.u. Put a box around your answer. VII-3 Km P/fgfilgfifl 1 flaw” a? ”770% : ‘2 J/flmfll é? /% 6&1/8. My 7 1 «(9,31% 5,2. WIS g a : ”1/722?ngth 4. a, w 0. M29 1 4061?? :: Flo/05.; a,¢¢.//a/M 0. 0//00":é awwy $755 44773639435 ybéozr (DW : 5a 77,- 67: 4/46) /. W 1&7“ fl/fidéé: #OJ‘VJWO 7'3 mfg/592,.) ____[7/W73 i Oé’iUDg/Z m?” 529-??? A? Z a 6322’- ‘1’?“2/ flafl fl/W'f’kéé , a,” 047129 72 (>5? 7- ”4/ $722. a; V .2. J72). (249 53x2}; «(529:7 [2 )7"? .44, ($29 ’62,? 779/25 ma filmy/a , MW/m/ 2w} 1/2 = 3 (£P0§~ (pa/n-64r37/2 r 77/5 W419” a; wwww War; (9/7457; x4? 3/075 77/5 #542,177»; «7/5729‘6W7 J 777:? 4W, 55“ . 77/0649}; 97 59(3. A/fliz #:0674522 //1/ Pfigyf‘w. #1? 700569.05? X3 731.? We [ywfi’pur J76 W77? ”7M! WW? ail-‘7” 994 , mean [mm CD CD calc reSidAz Fe content of vitamin ch] sq 0.05256 mean 47.158 m 1.00 std. dev 34.982031 Q 3 15.4% 27:: 0.75 3 17.624 0.018 0.000 0.000 E 29.889 0.036 0.047 0.000 g 0-50 31.252 0.055 0.073 0.000 a; 32.800 0.073 0.114 0.002 E 025 32.843 0.091 0.115 0.001 = 33.000 0.109 0.120 0.000 U 33.300 0.127 0.130 0.000 0-00 33.620 0.145 0.142 0.000 35.030 0.164 0.199 0.001 Fe content [mg/9] 35.211 0.182 0.207 0.001 35.740 0.200 0.232 0.001 36.170 0.218 0.254 0.001 36.700 0.236 0.282 0.002 36.750 0.255 0.285 0.001 36.790 0.273 0.287 0.000 36.800 0.291 0.288 0.000 36.830 0.309 0.289 0.000 37.190 0.327 0.309 0.000 37.790 0.345 0.344 0.000 38.150 0.364 0.366 0.000 38.600 0.382 0.394 0.000 38.900 0.400 0.412 0.000 39.200 0.418 0.431 0.000 39.317 0.436 0.439 0.000 40.100 0.455 0.489 0.001 40.100 0.473 0.489 0.000 40.230 0.491 0.497 0.000 40.300 0.509 0.502 0.000 40.500 0.527 0.515 0.000 41.150 0.545 0.556 0.000 41.500 0.564 0.578 0.000 41.700 0.582 0.591 0.000 41.811 0.600 0.598 0.000 42.030 0.618 0.612 0.000 42.300 0.636 0.628 0.000 42.450 0.655 0.637 0.000 42.900 0.673 0.664 0.000 43.320 0.691 0.688 0.000 43.500 0.709 0.699 0.000 43.560 0.727 0.702 0.001 43.900 0.745 0.721 0.001 44.280 0.764 0.741 0.001 45.100 45.160 48.010 48.250 48.900 50.720 51.000 51.790 54.650 54.700 58.500 200.100 241.700 0.782 0.800 0.818 0.836 0.855 0.873 0.891 0.909 0.927 0.945 0.964 0.982 1.000 0.782 0.785 0.894 0.901 0.918 0.954 0.958 0.968 0.990 0.990 0.998 1.000 1.000 0.000 0.000 0.006 0.004 0.004 0.007 0.005 0.004 0.004 0.002 0.001 0.000 0.000 mean 1mm cra cp ca'c r951“ Wig/7— chi sq 0.06264 mean 0.362 0.3600 1.00 «1...... __.. w... W. , std. dev 0.0135762 0.0039 1.10/0 1'? E 0.75 — 0.3441 0.018 0.000 0.000 g 0.3539 0.036 0.059 0.001 E 0 50 7 0.3540 0.055 0.063 0.000 “2’ ' 0.3544 0.073 0.076 0.000 5 0.3549 0.091 0.096 0.000 g 0.25 _ 0.3556 0.109 0.131 0.000 5 0.3557 0.127 0.136 0.000 ‘ , 0.3559 0.145 0.148 0.000 0.00 4 / . 0.3560 0.164 0.154 0.000 0.340 0.360 0.380 0.3567 0.182 0.200 0.000 tablet mass [9] 0.3568 0.200 0.207 0.000 0.3569 0.218 0.215 0.000 0.3574 0.236 0.254 0.000 0.3580 0.255 0.306 0.003 0.3581 0.273 0.315 0.002 0.3585 0.291 0.352 0.004 0.3587 0.309 0.371 0.004 0.3588 0.327 0.381 0.003 0.3588 0.345 0.381 0.001 0.3589 0.364 0.391 0.001 0.3590 0.382 0.401 0.000 0.3591 0.400 0.411 0.000 0.3591 0.418 0.411 0.000 0.3594 0.436 0.441 0.000 0.3595 0.455 0.451 0.000 0.3595 0.473 0.451 0.000 0.3595 0.491 0.451 0.002 0.3596 0.509 0.461 0.002 0.3598 0.527 0.481 0.002 0.3599 0.545 0.492 0.003 0.3601 0.564 0.512 0.003 0.3601 0.582 0.512 0.005 0.3603 0.600 0.532 0.005 0.3605 0.618 0.553 0.004 0.3610 0.636 0.603 0.001 0.3617 0.655 0.670 0.000 0.3619 0.673 0.689 0.000 0.3622 0.691 0.715 0.001 0.3624 0.709 0.732 0.001 0.3625 0.727 0.741 0.000 0.3626 0.745 0.749 0.000 0.3629 0.764 0.773 0.000 0.3635 0.3636 0.3637 0.3640 0.3649 0.3657 0.3658 0.3660 0.3669 0.3692 0.3707 0.3724 0.4550 0.782 0.800 0.818 0.836 0.855 0.873 0.891 0.909 0.927 0.945 0.964 0.982 1.000 0.816 0.823 0.830 0.849 0.896 0.929 0.932 0.939 0.962 0.991 0.997 0.999 1.000 0.001 0.001 0.000 0.000 0.002 0.003 0.002 0.001 0.001 0.002 0.001 0.000 0.000 mean [au/mM cg cp calc resid"2 chi sq 0.21159 mean 0.011 9.47% std. dev 0.0008707 M 3.1% 0.00800 0.018 0.000 0.000 0.00825 0.036 0.000 0.001 0.00841 0.055 0.000 0.003 0.00972 0.073 0.000 0.005 0.01025 0.091 0.007 0.007 0.01030 0.109 0.011 0.010 0.01040 0.127 0.023 0.011 0.01040 0.145 0.023 0.015 0.01050 0.164 0.044 0.014 0.01057 0.182 0.066 0.013 0.01065 0.200 0.102 0.010 0.01070 0.218 0.131 0.008 0.01080 0.236 0.204 0.001 0.01080 0.255 0.204 0.003 0.01090 0.273 0.297 0.001 0.01090 0.291 0.297 0.000 0.01090 0.309 0.297 0.000 0.01100 0.327 0.406 0.006 0.01100 0.345 0.406 0.004 0.01100 0.364 0.406 0.002 0.01100 0.382 0.406 0.001 0.01100 0.400 0.406 0.000 0.01102 0.418 0.429 0.000 0.01110 0.436 0.522 0.007 0.01110 0.455 0.522 0.005 0.01110 0.473 0.522 0.002 0.01110 0.491 0.522 0.001 0.01110 0.509 0.522 0.000 0.01110 0.527 0.522 0.000 0.01110 0.545 0.522 0.001 0.01110 0.564 0.522 0.002 0.01114 0.582 0.569 0.000 0.01118 0.600 0.615 0.000 0.01119 0.618 0.626 0.000 0.01120 0.636 0.637 0.000 0.01120 0.655 0.637 0.000 0.01120 0.673 0.637 0.001 0.01120 0.691 0.637 0.003 0.01120 0.709 0.637 0.005 0.01122 0.727 0.654 0.005 0.01122 0.745 0.659 0.008 0.01124 0.764 0.677 0.007 Cumulative Probability 1.00 0.75 0.50 0.25 0.00 Calibration slope 0.009 0.010 0.011 0.012 slope [au/uM] 0.013 0.01127 0.01127 0.01130 0.01130 0.01130 0.01156 0.01160 0.01161 0.01166 0.01180 0.01200 0.01200 0.01392 0.782 0.800 0.818 0.836 0.855 0.873 0.891 0.909 0.927 0.945 0.964 0.982 1.000 0.713 0.715 0.740 0.740 0.740 0.921 0.937 0.941 0.956 0.983 0.997 0.997 1.000 0.005 0.007 0.006 0.009 0.013 0.002 0.002 0.001 0.001 0.001 0.001 0.000 0.000 mean [auZmN cg cp calc residAZ Calibration intercept chi sq 0.14642 mean -0.002 -0.00287 std. dev 0.0201772 0.00940 ,2 E B O -5.76E-02 0.018 0.000 0.000 E -4.68E-02 0.036 0.000 0.001 g -3.89E-02 0.055 0.000 0.003 53 -3.13E-02 0.073 0.001 0.005 E -3.07E-02 0.091 0.002 0.008 5 -2.725-02 0.109 0.005 0.011 » _ -2.61E-02 0.127 0.007 0.015 -035 0.00 005 -1.47E-02 0.145 0.104 0.002 intercept [an] -1.26E-02 0.164 0.150 0.000 -l.16E-02 0.182 0.176 0.000 -1.11E-02 0.200 0.189 0.000 -1.03E-02 0.218 0.213 0.000 -9.00E-O3 0.236 0.257 0.000 -8.9OE-O3 0.255 0.260 0.000 -8.31E-03 0.273 0.281 0.000 -7.50E-O3 0.291 0.311 0.000 -7.20E—03 0.309 0.322 0.000 -5.31E-O3 0.327 0.397 0.005 -5.28E-03 0.345 0.399 0.003 5205-03 0.364 0.402 0.001 -4.20E-03 0.382 0.444 0.004 -4.1OE-03 0.400 0.448 0.002 -3.61E-03 0.418 0.468 0.003 -3.57E-03 0.436 0.470 0.001 3505-03 0.455 0.473 0.000 3005-03 0.473 0.494 0.000 -3.00E-03 0.491 0.494 0.000 -2.96E-03 0.509 0.496 0.000 2305-03 0.527 0.524 0.000 -2.00E-03 0.545 0.537 0.000 -2.00E-03 0.564 0.537 0.001 -1.83E-O3 0.582 0.544 0.001 1105-03 0.600 0.574 0.001 -9.49E-04 0.618 0.581 0.001 -7.97E-O4 0.636 0.587 0.002 -6.35E-04 0.655 0.594 0.004 —1.72E-O4 0.673 0.613 0.004 4.60E-04 0.691 0.638 0.003 1.62E-O3 0.709 0.683 0.001 2.205-03 0.727 0.705 0.000 2.905-03 0.745 0.730 0.000 3.225-03 0.764 0.741 0.000 3.27E-03 5.80E-03 6.00E-03 1.14E-02 1.32E-02 1.71E-02 1.89E-02 2.16E-02 2.80E—02 3.05E-02 4.10E-02 5.02E-02 5.56E-02 0.782 0.800 0.818 0.836 0.855 0.873 0.891 0.909 0.927 0.945 0.964 0.982 1.000 0.743 0.822 0.827 0.935 0.957 0.983 0.990 0.995 0.999 1.000 1.000 1.000 1.000 0.002 0.000 0.000 0.010 0.010 0.012 0.010 0.007 0.005 0.003 0.001 0.000 0.000 {5179: V/Eagéé’m c2 (q) mg Méflw 6mm. as Z/m/ MJ 4/; 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