Chemistry ( writing a lab report)

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Tenpr032

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I need help to write a lab report. Attached the experiment procedure and grading rubric and other important documents.

For the gran plot, if you did it in Excel please send a copy of the work because I want explanation how to use it. I arlday know how to do gran plot but with our date I did not know how can i use them. For example how to convert time to volume and dealing with huge data.

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pH titration of TRIS, tris- (hydroxymethyl) aminomethane, with HCl and the measurement of end point pH range, equivalence point and pKa of TRIS PROCEDURE Automated titration Accurately deliver 10.0 mL of TRIS solution into a 50 mL beaker. Add 20.0 mL water to it. Put a small stir bar and place it on a magnetic stirrer. Place a pH electrode, start the stirrer and ensure that the pH sensor tip is dipped in the solution and not hitting the spinning stir-bar. Prime the pump with the standard HCl. Measure pump flow rate by delivering 10.0 mL of HCl into a measuring cylinder for a fixed time. Assemble the titration setup and ready for the program run. Ask your instructor to help you in this step. The pump and the Vernier (or computer) controlled pH measurement system must be started simultaneously. Record the pH until it drops to a stable acidic range (about 2). The real time titration graph shows the inflection point and the titration plateau. Save the titration datapH vs. time as a text file (export function in Vernier). You must convert the time to volume of HCl added by the flow rate. A typical auto-titration plot is shown in the following figure: 449 data points in 449 s 10 25 8 20 6 10 2 5 5.000 10.000 15.000 0 0.000 mL HCl added Ve = 8.568 mL, pH range = 4-6 Ve/2 = 4.28 mL, pH = pKa = 8.13 First derivative 15 4 0 0.000 449 data points in 449 s TRIS with HCl 30 pH pH TRIS with HCl 12 5.000 10.000 15.000 mL HCl added Ve from first derivative max = 8.568 mL Gran Plot A Gran plot will be used to graphically determine the equivalence point from the titration data. This will be discussed in class. Other descriptions of plotting potentiometric end points are provided in the textbook. Be sure to review these pages before you plot your data according to the Gran function. Gran function is only valid near the equivalence point. Therefore, use the titration data at preceding and up to the equivalence point (i.e., 0.9Ve to Ve) for the Gran plot. The acid dissociation equilibrium equation for the protonation of TRIS (conjugate acid) can be used to derive the Gran  1 γ A-  pH ( V e - V H ) x V H x 10 =   K a γ HA  function (read Harris). Where, VH = volume of HCl added; Ka = acid dissociation constant for protonated TRIS; γ = activity coefficients for respective conjugate pairs; Ve = equivalence volume; HA and A are the conjugate acid base pairs, respectively. For this experiment you can assume that the activity coefficient ratio as unity. A plot of VH x 10pH vs. VH is known as the Gran plot. The titration volumes near and up to the equivalence point provides a straight line, which is extrapolated to the x-axis to find Ve. You should only consider the straight line portion to find the slope and the intercept from a linear regression equation. A typical Gran plot is shown below. Gran Plot 9.00E+07 8.00E+07 VH x 10^pH 7.00E+07 6.00E+07 5.00E+07 4.00E+07 3.00E+07 2.00E+07 1.00E+07 0.00E+00 7.500 7.700 7.900 8.100 8.300 8.500 8.700 Volume HCl, mL Slope =-1.2 x 108 , intercept = 9.98 x 108 r2= 0.9899. Ve = VH intercept = 9.98/1.2 = 8.91 mL Ka = 1/slope = 8.079 The Gran plot shown here was done with the above titration data in the region of equivalence point. This region should be selected such that it covers data points from the foot to the peak of the second derivative (as your guide). Then chose the linear portion and use the linear regression analysis (not Trendline- Why?) to find the equation of the straight line. The VH intercept is equal to Ve. How this Ve compares with that of the first derivative value? Find Ka from the slope which is = -1/Ka. How this compares with the pH at Ve/2 and that of the literature value: 8.072? Compare these methods and the sources of error. DATA AND RESULTS 1. Show all three plots. Determine the Ve from the Gran plot and calculate the molarity of HCl. 2. Determine the pKa of TRIS by two methods shown above. Which is more accurate? 3. Determine the pH range for the inflection point. Compare this range with the pH range of the indicators from the Harris text. How does it compare with your results? What is the best indicator? 4. Assuming the pH titration gives the true equivalence point what is the percent error in the molarity of HCl for each visual titration? Vernier Format 2 aa-sn-ag.txt 2/8/2018 22:11:29 Run 1 Time pH T p s 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 160 162 164 166 10.43 10.41 10.29 10.31 10.13 10.03 9.95 9.92 9.84 9.79 9.72 9.66 9.61 9.59 9.53 9.50 9.47 9.45 9.42 9.41 9.37 9.36 9.34 9.32 9.31 9.29 9.26 9.24 9.24 9.23 9.22 9.20 9.18 9.17 9.16 9.15 9.14 9.11 9.11 9.10 9.10 9.09 9.08 9.07 9.05 9.05 9.04 9.03 9.02 9.02 9.01 9.00 9.00 8.99 8.98 8.97 8.97 8.96 8.96 8.94 8.93 8.93 8.92 8.92 8.91 8.90 8.89 8.88 8.88 8.88 8.88 8.87 8.86 8.85 8.85 8.84 8.83 8.83 8.82 8.82 8.81 8.80 8.80 8.80 168 170 172 174 176 178 180 182 184 186 188 190 192 194 196 198 200 202 204 206 208 210 212 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 8.79 8.79 8.78 8.78 8.77 8.76 8.76 8.76 8.75 8.75 8.74 8.74 8.73 8.73 8.72 8.72 8.71 8.70 8.70 8.70 8.70 8.69 8.68 8.68 8.67 8.67 8.66 8.66 8.65 8.64 8.64 8.64 8.63 8.63 8.62 8.62 8.61 8.61 8.60 8.60 8.60 8.60 8.59 8.58 8.58 8.57 8.57 8.57 8.56 8.56 8.56 8.55 8.55 8.54 8.54 8.53 8.53 8.53 8.52 8.52 8.51 8.51 8.51 8.50 8.50 8.49 8.49 8.48 8.48 8.48 8.47 8.47 8.46 8.46 8.46 8.45 8.44 8.44 8.44 8.43 8.43 8.42 8.42 8.41 8.41 8.40 8.40 8.39 8.39 8.39 8.38 350 352 354 356 358 360 362 364 366 368 370 372 374 376 378 380 382 384 386 388 390 392 394 396 398 400 402 404 406 408 410 412 414 416 418 420 422 424 426 428 430 432 434 436 438 440 442 444 446 448 450 452 454 456 458 460 462 464 466 468 470 472 474 476 478 480 482 484 486 488 490 492 494 496 498 500 502 504 506 508 510 512 514 516 518 520 522 524 526 528 530 8.38 8.38 8.37 8.37 8.37 8.36 8.35 8.35 8.35 8.34 8.34 8.34 8.34 8.33 8.33 8.32 8.32 8.31 8.31 8.31 8.30 8.30 8.29 8.29 8.29 8.28 8.28 8.28 8.27 8.27 8.27 8.26 8.26 8.26 8.25 8.25 8.24 8.24 8.23 8.23 8.23 8.22 8.22 8.22 8.21 8.20 8.20 8.20 8.19 8.19 8.18 8.18 8.17 8.17 8.16 8.16 8.15 8.15 8.15 8.15 8.14 8.14 8.13 8.13 8.13 8.12 8.12 8.11 8.11 8.11 8.10 8.10 8.09 8.09 8.09 8.08 8.08 8.07 8.07 8.07 8.06 8.06 8.05 8.05 8.04 8.04 8.03 8.03 8.03 8.02 8.02 532 534 536 538 540 542 544 546 548 550 552 554 556 558 560 562 564 566 568 570 572 574 576 578 580 582 584 586 588 590 592 594 596 598 600 602 604 606 608 610 612 614 616 618 620 622 624 626 628 630 632 634 636 638 640 642 644 646 648 650 652 654 656 658 660 662 664 666 668 670 672 674 676 678 680 682 684 686 688 690 692 694 696 698 700 702 704 706 708 710 712 8.02 8.01 8.01 8.00 8.00 8.00 7.99 7.99 7.98 7.98 7.97 7.97 7.96 7.96 7.95 7.95 7.95 7.94 7.93 7.93 7.93 7.92 7.92 7.91 7.91 7.90 7.90 7.90 7.89 7.89 7.89 7.88 7.88 7.87 7.87 7.87 7.86 7.85 7.86 7.84 7.84 7.83 7.83 7.82 7.82 7.81 7.81 7.79 7.78 7.78 7.77 7.77 7.76 7.76 7.75 7.75 7.74 7.73 7.72 7.71 7.70 7.69 7.69 7.68 7.67 7.67 7.66 7.66 7.65 7.64 7.64 7.63 7.63 7.62 7.61 7.61 7.61 7.60 7.59 7.58 7.57 7.56 7.55 7.54 7.54 7.53 7.53 7.51 7.51 7.50 7.49 714 716 718 720 722 724 726 728 730 732 734 736 738 740 742 744 746 748 750 752 754 756 758 760 762 764 766 768 770 772 774 776 778 780 782 784 786 788 790 792 794 796 798 800 802 804 806 808 810 812 814 816 818 820 822 824 826 828 830 832 834 836 838 840 842 844 846 848 850 852 854 856 858 860 862 864 866 868 870 872 874 876 878 880 882 884 886 888 890 892 894 7.49 7.48 7.47 7.47 7.46 7.45 7.44 7.43 7.43 7.42 7.41 7.40 7.39 7.39 7.37 7.36 7.36 7.35 7.34 7.33 7.32 7.31 7.30 7.30 7.29 7.28 7.27 7.25 7.24 7.22 7.20 7.20 7.18 7.18 7.16 7.14 7.12 7.10 7.10 7.08 7.06 7.05 7.04 7.02 7.01 6.98 6.97 6.96 6.93 6.92 6.87 6.83 6.82 6.80 6.78 6.75 6.72 6.69 6.65 6.59 6.54 6.49 6.41 6.37 6.26 6.23 6.11 5.97 5.79 5.57 5.44 5.00 4.72 4.48 4.24 4.07 3.86 3.66 3.46 3.33 3.14 2.98 2.88 2.77 2.66 2.60 2.54 2.50 2.43 2.41 2.37 896 898 900 902 904 906 908 910 912 914 916 918 920 922 924 926 928 930 932 934 936 938 940 942 944 946 948 950 952 954 956 958 960 962 964 966 968 970 972 974 976 978 980 982 984 986 988 990 992 994 996 998 1000 1002 1004 1006 1008 1010 1012 1014 1016 1018 1020 1022 1024 1026 1028 1030 1032 1034 1036 1038 1040 1042 1044 1046 1048 1050 1052 1054 1056 1058 1060 1062 1064 1066 1068 1070 1072 1074 1076 2.35 2.33 2.32 2.29 2.28 2.27 2.25 2.24 2.23 2.21 2.19 2.18 2.17 2.16 2.16 2.14 2.13 2.13 2.11 2.12 2.11 2.10 2.09 2.09 2.08 2.08 2.07 2.06 2.05 2.05 2.05 2.03 2.02 2.03 2.02 2.01 2.00 2.00 1.99 1.99 1.99 1.98 1.97 1.96 1.96 1.96 1.96 1.95 1.94 1.95 1.94 1.93 1.93 1.93 1.92 1.92 1.92 1.91 1.91 1.91 1.91 1.89 1.90 1.89 1.89 1.88 1.88 1.87 1.88 1.87 1.87 1.87 1.86 1.85 1.85 1.85 1.85 1.85 1.85 1.84 1.83 1.83 1.83 1.82 1.82 1.82 1.82 1.81 1.81 1.80 1.81 1078 1080 1082 1084 1086 1088 1090 1092 1094 1096 1098 1100 1102 1104 1106 1108 1110 1112 1114 1116 1118 1120 1122 1124 1126 1128 1130 1132 1134 1136 1138 1140 1142 1144 1146 1148 1150 1152 1154 1156 1158 1160 1162 1164 1166 1168 1170 1172 1174 1176 1178 1180 1182 1184 1186 1188 1190 1192 1194 1196 1198 1200 1202 1204 1206 1208 1210 1212 1214 1216 1218 1220 1222 1224 1226 1228 1230 1232 1234 1236 1238 1240 1242 1244 1246 1248 1250 1252 1254 1256 1258 1.80 1.80 1.80 1.79 1.79 1.79 1.79 1.78 1.78 1.78 1.77 1.77 1.77 1.77 1.76 1.76 1.77 1.76 1.76 1.76 1.76 1.76 1.75 1.74 1.75 1.74 1.74 1.74 1.74 1.73 1.73 1.73 1.72 1.73 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.71 1.71 1.71 1.71 1.70 1.70 1.69 1.70 1.70 1.69 1.69 1.69 1.69 1.69 1.69 1.68 1.68 1.68 1.68 1.67 1.68 1.67 1.67 1.67 1.67 1.66 1.66 1.66 1.66 1.66 1.66 1.66 1.65 1.65 1.65 1.65 1.65 1.65 1.64 1.64 1.64 1.64 1.64 1.64 1.64 1.63 1.63 1.63 1.63 1.63 1260 1262 1264 1266 1268 1270 1272 1274 1276 1278 1280 1282 1284 1286 1288 1290 1292 1294 1296 1298 1300 1302 1304 1306 1308 1310 1312 1314 1316 1318 1320 1322 1324 1326 1328 1330 1332 1334 1336 1338 1340 1342 1344 1346 1348 1350 1352 1354 1356 1358 1360 1362 1364 1366 1368 1370 1372 1374 1376 1378 1380 1382 1384 1386 1388 1390 1392 1394 1396 1398 1400 1402 1404 1406 1.63 1.63 1.63 1.62 1.62 1.62 1.62 1.61 1.61 1.61 1.61 1.61 1.61 1.61 1.61 1.61 1.60 1.61 1.60 1.60 1.60 1.60 1.59 1.59 1.59 1.59 1.59 1.59 1.59 1.59 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.57 1.58 1.57 1.57 1.57 1.57 1.57 1.56 1.56 1.57 1.56 1.56 1.56 1.56 1.56 1.55 1.56 1.56 1.56 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.54 1.54 1.54 1.54 1.54 1.54 1.54 1.54 Table 1: Titration of Tris and HCl using Bromothymol Blue (BB) Titrations Scout 1 Tris (g) 0.4893 0.4828 Vintial (mL) 0.80 1.60 Vfinal (mL) 41.85 42.00 Vtotal (mL) Color change HCl (M) NA Color change Light pink Light pink HCl (M) NA Table 2: Titrations of Tris and HCl using Methyl Red (MR) Titrations Scout 1 Tris (g) 0.4893 0.4840 Vintial (mL) 0.70 0.51 Vfinal (mL) 41.80 41.41 Vtotal (mL) Table 3: Titrations of Tris and HCl using Bromocresol green (BG) Titrations Scout 1 Tris (g) 0.4866 0.4861 Vintial (mL) 0.11 0.22 Vfinal (mL) 41.29 41.51 Vtotal (mL) Color change green green HCl (M) NA Color change red red HCl (M) NA Table 4: Titrations of Tris and HCl using Methyl Orange (MO) Titrations Scout 1 Tris (g) 0.4766 0.4744 Vintial (mL) 0.85 0.31 Vfinal (mL) 42.51 40.60 Vtotal (mL) Evaluation of Acid-Base Indicators1 You will compare the accuracy of different indicators in locating the end point in the titration of the base Tris(hydroxymethyl)aminomethane (tris) with hydrochloric acid: Tris Base Tris.HCl (HOCH2)3CNH2 + H+ → (HOCH2)3CNH3+ Tris(hydroxymethyl)aminomethane - "tris" REAGENTS ~0.1 M HCl: Each student needs ~500 mL of unstandardized solution, all from a single batch that will be analyzed by the whole class. Tris: Solid, primary standard powder should be available (~4 g/student). Indicators: Bromothymol blue (BB), methyl red (MR), bromocresol green (BG), methyl orange (MO), and should be available in dropper bottles. Color changes for the titration of tris with HCl are: BB: blue (pH 7.6) → yellow (pH 6.0) (end point is disappearance of green) MR: yellow (pH 6.0) → red (pH 4.8) (end point is disappearance of orange) BG: blue (pH 5.4) → yellow (pH 3.8) (end point is green) MO: yellow (pH 4.4) → red (pH 3.1) (end point is first appearance of orange) PROCEDURE Each student should carry out the following procedure with all four indicators. 1. Calculate the mass of tris base required to react with 40 mL of 0.10 M HCl. Weigh this much tris into a 125-mL Erlenmeyer flask, dissolve in 20 mL of DI H2O and add 2-4 drops of indicator. 2. It is good practice to rinse a buret with a new solution to wash away traces of previous reagents. Wash your 50-mL buret with three 10-mL portions of 0.1 M HCl and discard the washings. Tilt and rotate the buret so that the liquid washes the walls, and drain the liquid through the stopcock. Then fill the buret with 0.1 M HCl to near the 0-mL mark, allow a minute for the liquid to settle, and record the reading to the nearest 0.01 mL. 3. The first scout titration will be rapid, to allow you to find the approximate end point of the titration. Add ~20 mL of HCl from the buret to the flask and swirl to dissolve. Titrate with ~1-mL aliquots of HCl to determine the end point, observe the color change and record the reading to the nearest 0.01 mL. 4. From the first scout titration (step 3), weigh the same amount of tris into a clean 125-mL Erlenmeyer flask, dissolve with ~20 mL DI H2O. Refill your buret to near 0 mL and record the reading to the nearest 0.01 mL. Repeat the titration in Step 3, but use 1 drop at a time near the end point. When you are very near the end point, use less than a drop at a time. To do this, carefully suspend a fraction of a drop from the buret tip and touch it to the inside wall of the flask. Carefully tilt the flask so that the bulk solution overtakes the droplet and then swirl the flask to mix the solution. Record the total volume of HCl required to reach the end point to the nearest 0.01 mL. Calculate the molarity of HCl. 5. Repeat the titration to obtain at least one accurate quantitative measurements of the HCl molarity, for each indicator. (You should be performing a minimum of 8 titrations, 2 titrations per indicator (one scout and one quantitative). REFERENCES 1. D.T. Harvey, J. Chem. Ed. 1991, 68, 329. Evaluation of Acid-Base Indicators CHEM321: Statistical Evaluation of A-B Indicator Name: _________________________ Experiment date: _______________ Lab Partner: ____________________ Table&1:&Titration&of&Tris&and&HCl&using&Bromothymol&Blue&(BB)& & & Tris&(g)& Vinitial&(mL)& Vfinal&(mL)& Vtotal&(mL)& Scout& (±&0.0002)& & (±0.05)& & (±0.05)& & (±0.07)& & 1& & & & & & & & & & & & & & Titrations& Color&Change& & & HCl&(M)& & & Table&2:&Titration&of&Tris&and&HCl&using&Methyl&Red&(MR)& NA& & & Tris&(g)& Vinitial&(mL)& Vfinal&(mL)& Vtotal&(mL)& Scout& (±&0.0002)& & (±0.05)& & (±0.05)& & (±0.07)& & 1& & & & & & & & & & & & & & Titrations& Color&Change& & Tris&(g)& & & Table&3:&Titration&of&Tris&and&HCl&using&Bromocresol&green&(BG)& Titrations& & HCl&(M)& NA& & Vinitial&(mL)& Vfinal&(mL)& Vtotal&(mL)& & Color&Change& HCl&(M)& Scout& (±&0.0002)& && (±0.05)& && (±0.05)& && (±0.07)& && && && 1& && && && && && & & && && && && && & Table&4:&Titration&of&Tris&and&HCl&using&Methyl&Orange&(MO)& Titrations& Tris&(g)& & NA& & Vinitial&(mL)& Vfinal&(mL)& Vtotal&(mL)& & & Color&Change& HCl&(M)& Scout& (±&0.0002)& && (±0.05)& && (±0.05)& && (±0.07)& && && && 1& && && && && && & & && && && && && & & & NA& CHEM 321 Evaluation of Acid-Base Indicators: Manual and Auto-pH titration of TRIS with HCl Report Name: Lab Partner: Experiment Date: Report Due Date: *When typing your report, please 1.5 or 2.0 space your text. Remember to submit your report to Safe Assign and turn in a hard copy to your instructor. The hard copy may be printed on both sides of the paper. *When you write a report, please remove all questions/text that we have included to guide your responses. You may leave the questions at the end in the report. You may need to reformat your tables to fit your data. Do not treat this as a “fill in” worksheet – it should appear like a formal lab report when printed out. Abstract 6 pts (- 5 pts for names + title + date) In one paragraph, summarize the goal(s), results, and conclusions of your experiment. Include all pertinent information as described in earlier reports. I. Results and Discussion 26 pts (4 pts per table + discussion, 2 pts per figure, 4 pts for discussion of Gran) Table 1. Titration of Tris and HCl using Bromothymol Blue (BB) Discuss the data in Table 1.   1   Table 2. Titration of Tris and HCl using Methyl Red (MR) Discuss the data in Table 2. Table 3. Titration of Tris and HCl using Bromothymol Blue (BB) Discuss the data in Table 3. Table 4. Titration of Tris and HCl using Methyl Red (MR) Discuss the data in Table 4.   2   Figure 1. Plot of pH vs. Volume for … describe the figure with a descriptive/detailed caption. Figure 2. Plot of first derivative of … describe the figure with a descriptive/detailed caption. Figure 3. Gran plot for … describe the figure with a descriptive/detailed caption. Discuss the plots and interpret your results. Explain how to use the Gran plot and report the Ka value from the Gran plot. Obtain error by using LINEST and report LINEST results. Compare with literature and report a percent error. Discuss the calculation of weight percent (using Ve) from the Gran plot. Compare the results from the Gran plot analysis with results from the titration using acid-base indicators . II. Conclusions (8 pts) Briefly summarize your results and conclusions. Include specific results for each part of the experiment. This section should include everything that appears in your abstract as well as a thoughtful analysis of the experiment. 1. Which indicator is best for standardizing HCl? Explain. 2. Write out the reaction taking place and draw chemical structures. 3. Do your experimental results agree with what you predicted before the lab? 4. Explain why you should never use more than a few drops of indicator and why the number of drops you use should be consistent over the course of your experiment. Summarize the utility of the Gran plot as compared to the indicator titration method. Compare and contrast the methods. III. Questions (8 pts = 2+2+4 pts) 1. Based on the results of this experiment, what indicator would you use for an experiment using Tris and nitric acid? 2. Consider a titration curve for a weak base and a strong acid. Suppose both phenolphthalein and bromocresol green are present in the solution. What color changes would occur at pH 10, pH 7, and pH 3? 3. Students measured the concentration of HCl in a solution by various titrations in which different indicators were used to find the end point.   3   Is the difference between indicators significant at the 95% confidence level? a. Compare indicators 1 and 2. b. Compare indicators 2 and 3. c. Compare indicators 1 and 3. d. Relate these results back to your experimental findings. IV. Calculations (- 5 pts if not there and complete) You may hand-write or scan your notebook calculations. Please include calculations even if you submitted them on your data sheet. V. References (2 pts) Please use Journal of the American Chemical Society format.   4  
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Vernier Format 2
aa-sn-ag.txt 2/8/2018 22:11:29
Run 1
Time
volume (ml)=flow rate*time pH
T
V
p
s
ml
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66

0
0.0995
0.199
0.2985
0.398
0.4975
0.597
0.6965
0.796
0.8955
0.995
1.0945
1.194
1.2935
1.393
1.4925
1.592
1.6915
1.791
1.8905
1.99
2.0895
2.189
2.2885
2.388
2.4875
2.587
2.6865
2.786
2.8855
2.985
3.0845
3.184
3.2835

averange volume
10.43
10.41
10.29
10.31
10.13
10.03
9.95
9.92
9.84
9.79
9.72
9.66
9.61
9.59
9.53
9.5
9.47
9.45
9.42
9.41
9.37
9.36
9.34
9.32
9.31
9.29
9.26
9.24
9.24
9.23
9.22
9.2
9.18
9.17

0.04975
0.14925
0.24875
0.34825
0.44775
0.54725
0.64675
0.74625
0.84575
0.94525
1.04475
1.14425
1.24375
1.34325
1.44275
1.54225
1.64175
1.74125
1.84075
1.94025
2.03975
2.13925
2.23875
2.33825
2.43775
2.53725
2.63675
2.73625
2.83575
2.93525
3.03475
3.13425
3.23375

68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148

3.383
3.4825
3.582
3.6815
3.781
3.8805
3.98
4.0795
4.179
4.2785
4.378
4.4775
4.577
4.6765
4.776
4.8755
4.975
5.0745
5.174
5.2735
5.373
5.4725
5.572
5.6715
5.771
5.8705
5.97
6.0695
6.169
6.2685
6.368
6.4675
6.567
6.6665
6.766
6.8655
6.965
7.0645
7.164
7.2635
7.363

9.16
9.15
9.14
9.11
9.11
9.1
9.1
9.09
9.08
9.07
9.05
9.05
9.04
9.03
9.02
9.02
9.01
9
9
8.99
8.98
8.97
8.97
8.96
8.96
8.94
8.93
8.93
8.92
8.92
8.91
8.9
8.89
8.88
8.88
8.88
8.88
8.87
8.86
8.85
8.85

3.33325
3.43275
3.53225
3.63175
3.73125
3.83075
3.93025
4.02975
4.12925
4.22875
4.32825
4.42775
4.52725
4.62675
4.72625
4.82575
4.92525
5.02475
5.12425
5.22375
5.32325
5.42275
5.52225
5.62175
5.72125
5.82075
5.92025
6.01975
6.11925
6.21875
6.31825
6.41775
6.51725
6.61675
6.71625
6.81575
6.91525
7.01475
7.11425
7.21375
7.31325

150
152
154
156
158
160
162
164
166
168
170
172
174
176
178
180
182
184
186
188
190
192
194
196
198
200
202
204
206
208
210
212
214
216
218
220
222
224
226
228
230

7.4625
7.562
7.6615
7.761
7.8605
7.96
8.0595
8.159
8.2585
8.358
8.4575
8.557
8.6565
8.756
8.8555
8.955
9.0545
9.154
9.2535
9.353
9.4525
9.552
9.6515
9.751
9.8505
9.95
10.0495
10.149
10.2485
10.348
10.4475
10.547
10.6465
10.746
10.8455
10.945
11.0445
11.144
11.2435
11.343
11.4425

8.84
8.83
8.83
8.82
8.82
8.81
8.8
8.8
8.8
8.79
8.79
8.78
8.78
8.77
8.76
8.76
8.76
8.75
8.75
8.74
8.74
8.73
8.73
8.72
8.72
8.71
8.7
8.7
8.7
8.7
8.69
8.68
8.68
8.67
8.67
8.66
8.66
8.65
8.64
8.64
8.64

7.41275
7.51225
7.61175
7.71125
7.81075
7.91025
8.00975
8.10925
8.20875
8.30825
8.40775
8.50725
8.60675
8.70625
8.80575
8.90525
9.00475
9.10425
9.20375
9.30325
9.40275
9.50225
9.60175
9.70125
9.80075
9.90025
9.99975
10.09925
10.19875
10.29825
10.39775
10.49725
10.59675
10.69625
10.79575
10.89525
10.99475
11.09425
11.19375
11.29325
11.39275

232
234
236
238
240
242
244
246
248
250
252
254
256
258
260
262
264
266
268
270
272
274
276
278
280
282
284
286
288
290
292
294
296
298
300
302
304
306
308
310
312

11.542
11.6415
11.741
11.8405
11.94
12.0395
12.139
12.2385
12.338
12.4375
12.537
12.6365
12.736
12.8355
12.935
13.0345
13.134
13.2335
13.333
13.4325
13.532
13.6315
13.731
13.8305
13.93
14.0295
14.129
14.2285
14.328
14.4275
14.527
14.6265
14.726
14.8255
14.925
15.0245
15.124
15.2235
15.323
15.4225
15.522

8.63
8.63
8.62
8.62
8.61
8.61
8.6
8.6
8.6
8.6
8.59
8.58
8.58
8.57
8.57
8.57
8.56
8.56
8.56
8.55
8.55
8.54
8.54
8.53
8.53
8.53
8.52
8.52
8.51
8.51
8.51
8.5
8.5
8.49
8.49
8.48
8.48
8.48
8.47
8.47
8.46

11.49225
11.59175
11.69125
11.79075
11.89025
11.98975
12.08925
12.18875
12.28825
12.38775
12.48725
12.58675
12.68625
12.78575
12.88525
12.98475
13.08425
13.18375
13.28325
13.38275
13.48225
13.58175
13.68125
13.78075
13.88025
13.97975
14.07925
14.17875
14.27825
14.37775
14.47725
14.57675
14.67625
14.77575
14.87525
14.97475
15.07425
15.17375
15.27325
15.37275
15.47225

314
316
318
320
322
324
326
328
330
332
334
336
338
340
342
344
346
348
350
352
354
356
358
360
362
364
366
368
370
372
374
376
378
380
382
384
386
388
390
392
394

15.6215
15.721
15.8205
15.92
16.0195
16.119
16.2185
16.318
16.4175
16.517
16.6165
16.716
16.8155
16.915
17.0145
17.114
17.2135
17.313
17.4125
17.512
17.6115
17.711
17.8105
17.91
18.0095
18.109
18.2085
18.308
18.4075
18.507
18.6065
18.706
18.8055
18.905
19.0045
19.104
19.2035
19.303
19.4025
19.502
19.6015

8.46
8.46
8.45
8.44
8.44
8.44
8.43
8.43
8.42
8.42
8.41
8.41
8.4
8.4
8.39
8.39
8.39
8.38
8.38
8.38
8.37
8.37
8.37
8.36
8.35
8.35
8.35
8.34
8.34
8.34
8.34
8.33
8.33
8.32
8.32
8.31
8.31
8.31
8.3
8.3
8.29

15.57175
15.67125
15.77075
15.87025
15.96975
16.06925
16.16875
16.26825
16.36775
16.46725
16.56675
16.66625
16.76575
16.86525
16.96475
17.06425
17.16375
17.26325
17.36275
17.46225
17.56175
17.66125
17.76075
17.86025
17.95975
18.05925
18.15875
18.25825
18.35775
18.45725
18.55675
18.65625
18.75575
18.85525
18.95475
19.05425
19.15375
19.25325
19.35275
19.45225
19.55175

396
398
400
402
404
406
408
410
412
414
416
418
420
422
424
426
428
430
432
434
436
438
440
442
444
446
448
450
452
454
456
458
460
462
464
466
468
470
472
474
476

19.701
19.8005
19.9
19.9995
20.099
20.1985
20.298
20.3975
20.497
20.5965
20.696
20.7955
20.895
20.9945
21.094
21.1935
21.293
21.3925
21.492
21.5915
21.691
21.7905
21.89
21.9895
22.089
22.1885
22.288
22.3875
22.487
22.5865
22.686
22.7855
22.885
22.9845
23.084
23.1835
23.283
23.3825
23.482
23.5815
23.681

8.29
8.29
8.28
8.28
8.28
8.27
8.27
8.27
8.26
8.26
8.26
8.25
8.25
8.24
8.24
8.23
8.23
8.23
8.22
8.22
8.22
8.21
8.2
8.2
8.2
8.19
8.19
8.18
8.18
8.17
8.17
8.16
8.16
8.15
8.15
8.15
8.15
8.14
8.14
8.13
8.13

19.65125
19.75075
19.85025
19.94975
20.04925
20.14875
20.24825
20.34775
20.44725
20.54675
20.64625
20.74575
20.84525
20.94475
21.04425
21.14375
21.24325
21.34275
21.44225
21.54175
21.64125
21.74075
21.84025
21.93975
22.03925
22.13875
22.23825
22.33775
22.43725
22.53675
22.63625
22.73575
22.83525
22.93475
23.03425
23.13375
23.23325
23.33275
23.43225
23.53175
23.63125

478
480
482
484
486
488
490
492
494
496
498
500
502
504
506
508
510
512
514
516
518
520
522
524
526
528
530
532
534
536
538
540
542
544
546
548
550
552
554
556
558

23.7805
23.88
23.9795
24.079
24.1785
24.278
24.3775
24.477
24.5765
24.676
24.7755
24.875
24.9745
25.074
25.1735
25.273
25.3725
25.472
25.5715
25.671
25.7705
25.87
25.9695
26.069
26.1685
26.268
26.3675
26.467
26.5665
26.666
26.7655
26.865
26.9645
27.064
27.1635
27.263
27.3625
27.462
27.5615
27.661
27.7605

8.13
8.12
8.12
8.11
8.11
8.11
8.1
8.1
8.09
8.09
8.09
8.08
8.08
8.07
8.07
8.07
8.06
8.06
8.05
8.05
8.04
8.04
8.03
8.03
8.03
8.02
8.02
8.02
8.01
8.01
8
8
8
7.99
7.99
7.98
7.98
7.97
7.97
7.96
7.96

23.73075
23.83025
23.92975
24.02925
24.12875
24.22825
24.32775
24.42725
24.52675
24.62625
24.72575
24.82525
24.92475
25.02425
25.12375
25.22325
25.32275
25.42225
25.52175
25.62125
25.72075
25.82025
25.91975
26.01925
26.11875
26.21825
26.31775
26.41725
26.51675
26.61625
26.71575
26.81525
26.91475
27.01425
27.11375
27.21325
27.31275
27.41225
27.51175
27.61125
27.71075

560
562
564
566
568
570
572
574
576
578
580
582
584
586
588
590
592
594
596
598
600
602
604
606
60...


Anonymous
Excellent resource! Really helped me get the gist of things.

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