Analysis of a Carbonate-Bicarbonate Mixture. BACKGROUND: Crude sodium carbonate (soda ash) is a common commercial neutralizing agent. Titrating with standard acid to the bromocresol green end point gives the total carbonate content. Results are usually expressed as the weight percent of sodium carbonate in the crude sample. As the samples are non-homogenous the method of aliquot portions is employed. During the second week of this experiment, you will determine the percent composition of sodium carbonate and sodium bicarbonate (baking soda) in the unknown sample. Analysis will involve two methods which will be compared. REACTIONS: 2HCl + Na2CO3 →CO2 + H2O H2CO3 ↔ H+ + HCO3- (pKa = 6.351) HCO3- ↔ H+ + CO32- (pKa = 10.329) PROCEDURE (WEEK 1): Part 1: Standardization of HCl 1. Prepare 1 L of ~0.1 M HCl from 37.2% wt. HCl (8.7 mL) in a capped polyethylene bottle. (Can you do the math to confirm that 8.7 mL of 37.2% HCl diluted into 1L equals ~0.1 M HCl?) 2. Your TA may have dried primary-standard-grade Na2CO3 for 1 hour at 105°C and cooled in a desiccator. 3. Calculate the amount (mass) of Na2CO3 it takes to react with ~25 mL of 0.1 M HCl. Weight out four samples and dissolved in ~25 mL of distilled water in 125 mL flasks. 4. Add 3 drops of bromocresol green indicator (or did you determine a better indicator from Expt 2?) and titrate with HCl to the approximate end point (blue to green). If you achieve a yellow color you have gone too far. Boil the solution to expel CO2. The solution should return to a blue color. Carefully add HCl from the buret until the solution turns green again. 5. Titrate one blank with three drops of your indicator in 50 mL of 0.05 NaCl. Subtract this amount from the volume of HCl used to titrate Na2CO3. Calculate the mean HCl molarity, standard deviation and %RSD. (%RSD < 0.25) You will turn in a Form Page at this point prior to receiving your unknown sample. Analysis of a Carbonate-Bicarbonate Mixture. Part 2: Method of aliquots in the determination of percent sodium carbonate in an unknown mixture 1. Weigh precisely ??? g (mass will be given by lab instructor) sample of dried unknown into a clean-dry 250 mL volumetric flask, remember to record your mass to the fourth decimal place. Dissolve this sample in ~ 125 mL of distilled water. 2. Once all of the solid is dissolved, add distilled water to the 250 mL mark. Mix contents of the volumetric flask by inversion (more than once). 3. Pipet 25 mL aliquot from volumetric flask into 125 mL Erlenmeyer flask and add 3-5 drops of bromocresol green. (Which glassware should you use? Transfer pipet, buret, graduated cylinder, or beaker. Which piece of glassware will give you the best data?) 4. Titrate with your standardized HCl from Part 1, once the indicator turns green boil the solution to expel the extra CO2. The solution might return to blue. Carefully add HCl until the solution turns green again. Repeat titration at least two more times. 5. Thoroughly clean the volumetric flask at the end of your titration, alkaline solutions should NEVER be left in volumetric glassware for long periods of time. Consider why. 6. Transfer your unknown mixture into a plastic bottle for Part 3 and Part 4 to be performed during week 2. (Why are you transferring your unknown solution to a plastic bottle?) Report the mass percentage of sodium carbonate (Na2CO3) in your unknown. Having a precision of 3 to 5 ppt is normal. PROCEDURE (WEEK 2): Part 3: Analysis of a mixture of carbonate and bicarbonate by manual pH titration. 1. Calibrate the pH meter using two standard pH buffers at pH 4.00 and pH 7.00. 2. Transfer 25.00 mL of the unknown solution into a 250 mL Erlenmeyer flask with a magnetic stirring bar and add 25 mL of distilled water. Place the beaker on a hot plate, immerse the pH electrode, and turn on the stirring function after you have clamped the pH electrode in place and make sure it will not be hit by the stir bar. (These electrodes will break if hit by the stir bar and they cost ~$100 per. If you break an electrode you will have to wait for another group to finish their experiment. If you break a second one, you are no longer allowed to do the lab and will receive a zero score.) 3. Titrate with standard HCl record both pH and mV readings every ~2.00 mL. 4. Plot the curve of pH vs. volume of HCl added and locate the approximate equivalence points (there will be two) on the graph. Exact equivalence points will be determined from the data collected in Step 5. Analysis of a Carbonate-Bicarbonate Mixture. 5. For your next titration take readings every ~2.00 mL to within ~3.00 mL of the first equivalence point. Take readings at every ~0.50 mL interval, quickly as the CO2 will alter the pH. Once past the first equivalence point, by ~3.00 mL, take readings every ~2.00 mL to within ~3.00 mL of the second equivalence point, when you will record values every ~0.50 mL till past the second equivalence point. Then continue to add HCl and record readings every ~2.00 mL till the pH stabilizes. Enter your data into a spreadsheet with columns for HCl and mV readings. (If you do not want to do two titrations, you could just record pH and mV readings every ~0.50 mL for the entire manual titration.) Part 4: Analysis of a mixture of carbonate and bicarbonate by automatic pH titration. 1. Pipet 5.0 mL of your unknown solution into a 125 mL Erlenmeyer flask and add 25 mL of distilled water into the titration beaker. (A 250 mL Erlenmeyer is too big.) 2. Get instructor assistance for titration assembly setup and preparing the program for your run. 3. Prime the pump with your standardized HCl. Measure the pump flow rate by delivering a known volume of HCl in a 10.0 mL measuring cylinder for a fixed time. 4. Start the computer pH program at the same time you turn the pump on. Allow the computer to record the pH until it drops to a stable acidic range. 5. The titration data of pH over time is recorded in Excel and the real time titration graph shows the end points, as well as, the end of the titration. 6. Convert flow time to volume of HCl added using the flow rate. pH vs. Volume 12.00 pH Data First derivative 10.00 8.00 pH 6.00 4.00 2.00 0.00 0.00 2.00 4.00 6.00 8.00 -2.00 Volume (ml) 10.00 12.00 14.00 Analysis of a Carbonate-Bicarbonate Mixture. Directions for processing data from Part 3 and Part 4: Formal report Expt 3b - Section 10-5 ‘Finding the End Point with a pH Electrode’ discusses how to calculate the first derivate of your data to determine the two equivalence points for bicarbonate and carbonate. Compare your total carbonate wt% from Part 2 with the values you get from Part 3 and Part 4. Then compare your bicarbonate weight percent values from Parts 3 and 4. Formal report Expt 3c – Within Section 10-5 ‘Using a Gran Plot to Find the End Point’ you will experimental calculate Ka1 and Ka2, and compare with literature values. Then compare your values from Parts 3 and 4. END OF REPORT QUESTIONS: 1. Explain why it is necessary to expel CO2 near the end of the titration. 2. The alkalinity of natural waters is usually controlled by OH-, CO32-, and HCO3-, which may be present alone or in combination. Titrating a 100.0 mL sample to a pH of 8.3 requires 18.70 mL of a 0.0281 M solution of HCl. A second 100.0 mL aliquot requires 48.20 mL of the same titrant to reach a pH of 4.5. Calculate the concentrations of CO32- and HCO3- in ppm. CHEM 321 Analysis of a Carbonate-Bicarbonate Mixture Data Sheet WEEK 1 Name: Lab Partner: Experiment Date: I. Data and Results Table 1. Standardization of Hydrochloric Acid Titrations Na2CO3 Na2CO3 (g) (mol) (±?) Blank 1 2 3 HCl (mol) Vinitial (mL) (±?) Vfinal (mL) (±?) Vtotal (mL) (±?) Molarity HCl (mol/L) Average = StdDev = %RSD = Table 2. Determination of Na2CO3 Weight Percent: Unknown _____ Sample Unknow n (mL) (± 0.?) Vinitial (mL) (±?) Vfinal (mL) (±?) Vtotal (mL) (±?) Conc. HCl (mol/L) HCl (mol) Na2CO3 (mol) Na2CO3 (g) Weight percent 1 2 3 Average = StdDev = %RSD = CI95% = Show calculations. ! 1! CHEM 321 Analysis of a Carbonate-Bicarbonate Mixture Data Sheet WEEK 2 Name: Lab Partner: Experiment Date: I. Data and Results Table 3: Determination of NaHCO3 and Na2CO3 Weight% for Unknown # Mass = ______ (±?) in Volume = ______ (±?) Titrations Unknown (mL) (± ?) Ve1 (mL) HCle1 (mol) Ve2 (mL) HCle2 (mol) Na2CO3 (mol) Na2CO3 (mol) Na2CO3 (g) NaHCO3 (mol) NaHCO3 (g) Na2CO3 (Wt%) NaHCO3 (Wt%) pH Manual pH Auto Titrations pH Manual pH Auto Table 7: Determination of Ka1 and Ka2 for Carbonic Acid. Literatures values for Ka1 = ______ and Ka2 = ______. Titration / Inflection point pH manual / Ve1 pH manual / Ve2 pH automatic / Ve1 pH automatic / Ve2 ! Ve1 or e2 (mL) Ve1 or e2 (mL) Slope Slope Error Intercept Intercept Ka1/Ka2 Ka1/Ka2 Error Error 1! DETERMINATION OF COMPOSITION OF A CARBONATE – BICARBONATE MIXTURE: METHOD pH TITRATION A typical auto-titration plot is shown in the following figure. pH vs. Volume 12.00 pH Data First derivative 10.00 8.00 pH 6.00 4.00 2.00 0.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 -2.00 Volume (ml) Gran Plot A Gran plot will be used to graphically determine the equivalence points from the titration data. Be sure to review the pages in your textbook (Ch 10 for the 8th ed.) before you plot your data according to the Gran function. 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 carbonate and bicarbonate ions can be used to derive the Gran function. Where, Va = volume of HCl added; Ka = acid dissociation constant for first dissociation of carbonic acid (H2CO3 ↔ H+ + HCO3-); = activity coefficients (Ch 7 for the 8th ed.); Ve = second equivalence volume; B and BH+ are the conjugate base-acid pairs, respectively. The above equation is given for the second end point region. The first equivalence point can be obtained similarly by using the data near the first inflection point. Which Ka value did you get from this region? Convince yourself by writing appropriate equilibrium expression. For this experiment you can assume the activity ratio as unity; therefore, they cancel out of the equation. A plot of the Gran plot of Va×10pH vs. Va for 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. Calculate Ka from the slope of the Gran plot, LINEST will also provide an error in the slope so review chapter 4 of your Harris textbook. A typical Gran plot is shown below. Gran Plot 1.00E+10 9.00E+09 8.00E+09 V. 10^pH 7.00E+09 6.00E+09 5.00E+09 4.00E+09 3.00E+09 2.00E+09 1.00E+09 0.00E+00 1.80 2.30 2.80 Volume HCl, mL 3.30 The Gran plot shown here was done with the above titration data in the region of first infection 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 to extrapolate volume on the x-axis as shown by the straight line. Alternatively, you can use ‘LINEST’ to calculate the volume only on the straight-line portions of the data. You can find the Ka2 of carbonic acid from the slope (m = -1/Ka2). Automated Titration The titration data- pH vs. time is recorded in xls format, Figure 1. Figure 1. Appearance of typical data acquired by Automated Titration. You must convert the time to volume of HCl added by the flow rate, for this example the flow rate was 1.85 mL per 60 seconds. Figure 2. Conversion of time to volume. Figure 3. XY Scatter plot of pH titration and 1st derivative [=ABS(SLOPE(Δy/Δx)]. Identify the two points of inflection. For this data: Ve2 = 3.24 mL and Ve1 = 9.71 mL Now you need to plot the data from 0.9Ve to Ve, so for Ve2 plot 2.92 mL to 3.24 mL and for Ve1 plot 8.74 mL to 9.71 mL. However, you need to first create a new column for your y-axis which is Va×10pH. Figure 4. Second inflection point to calculate Ka1. Figure 5. Deleted the last data point since it was not linear. The trendline has only one significant figure for the slope and no error, so LINEST was performed to calculate a truer value. If slope is equal to -1/Ka, then Ka = 1.20×10-7. From your textbook, Ka1 = 4.46×10-7. DATA AND RESULTS 1. pH titration: Obtain the pH titration XL file. Plot the pH-volume, the first derivative, and the Gran plots. Find the exact titration inflection points and the volume of HCl from the Gran plots. You must do two Gran plots: one for the first inflection region and the other for the second inflection region. 2. Also, obtain the Ka value from the Gran plot, with error so use LINEST. Compare the Ka1 and Ka2 with those of the literature, provide a percent error. 3. Calculate the percent composition (and errors) of the mixture by using the inflection volumes obtained from Gran plots, this is the x-intercept when y = 0. Example calculations are shown in the following pages. 4. Finally, compare and contrast the three methods as an analytical tool for this analysis. pH titration of CO32- and HCO3- mixture Use the final pH titration data for the following calculation Plot mV vs. Volume of HCl added Take first derivative of mV-mL data and find the volume of HCl at two inflection points: Ve1 and Ve2 Do Gran plot: Find precise Ve2, Ka1 and their errors from LINEST. Compare Ka1 with that of -7 + literature value (Ka1 = 4.46 x 10 for H2CO3 ↔ H + HCO3 ) 2Use Ve1 from derivative and Ve2 from Gran plot to calculate CO3 and HCO3 as follows: 2- moles of CO3 = Ve1 x MHCl moles of HCO3 = (Ve2 - 2Ve1) x MHCl 2- - Calculate the molarity of CO3 and HCO3 in the original solution: moles/volume of aliquot used. Also, calculate the alkalinity. Compare the results of the two methods. 2Calculate the wt% of CO3 and HCO3 in the original mixture. Compare the results with that of the indicator titration method. CHEM 321 Analysis of a Carbonate-Bicarbonate Mixture Full Report (Parts I and II) Name: Lab Partner: Experiment Date: Report Due Date: Abstract In one paragraph, summarize the results of your experiment. I. Data and Results Table 1. Standardization of Hydrochloric Acid Titrations Na2CO3 Na2CO3 (g) (mol) (±?) Blank 1 2 3 HCl (mol) Vinitial (mL) (±?) Vfinal (mL) (±?) Vtotal (mL) (±?) Molarity HCl (mol/L) Average = StdDev = %RSD = Discuss Table 1 in detail. ! 1! Table 2. Determination of Na2CO3 Weight Percent: Unknown _____ Sample Unknow n (mL) (± 0.?) Vinitial (mL) (±?) Vfinal (mL) (±?) Vtotal (mL) (±?) Conc. HCl (mol/L) HCl (mol) Na2CO3 (mol) Na2CO3 (g) Weight percent 1 2 3 Average = StdDev = %RSD = CI95% = Discuss Table 2 in detail. Figure 1: Manual Titration Curve and 1st Derivative for Unknown A or B. Figure 2: Automated Titration Curve and 1st Derivative for Unknown A or B. ! 2! Table 3: Determination of NaHCO3 and Na2CO3 Weight% for Unknown # Mass = ______ (±?) in Volume = ______ (±?) Titrations Unknown (mL) (± ?) Ve1 (mL) HCle1 (mol) Ve2 (mL) HCle2 (mol) Na2CO3 (mol) Na2CO3 (mol) Na2CO3 (g) NaHCO3 (mol) NaHCO3 (g) Na2CO3 (Wt%) NaHCO3 (Wt%) pH Manual pH Auto Titrations pH Manual pH Auto Discuss Table 3 in detail. Figures 3-6: Gran Plots for first inflection points and second inflection points. Tables 4-6: LINEST tables for all Figures 3-6. LINEST is mentioned in your textbook. The output you get from LINEST will give you not only slope and intercept but also the error in each value which you need to propagate along with your actual value to give you your final answer with error. ! 3! Table 7: Determination of Ka1 and Ka2 for Carbonic Acid. Literatures values for Ka1 = ______ and Ka2 = ______. Titration / Inflection point pH manual / Ve1 pH manual / Ve2 pH automatic / Ve1 pH automatic / Ve2 Ve1 or e2 (mL) Ve1 or e2 (mL) Slope Slope Error Intercept Intercept Ka1/Ka2 Ka1/Ka2 Error Error Discuss your Gran plots and results. You may do this right after each figure/table or after all four have been presented. Describe what the reader is seeing, how the plots were generated, what they show, why they’re important, etc. Make sure to address all Gran plot questions in the experimental in Part III below. II. Results and Conclusions Briefly summarize your results and describe your conclusions for the entire experiment. What are some important points for future students to know? How would you change the experiment to make it better? III. Questions Answer all questions found in the experimental. IV. Calculations You may hand-write or scan your notebook calculations. 1. Example calculation for one titration in Table 1. 2. Example calculation for one titration in Table 2. V. References Please use Journal of the American Chemical Society format. ! 4! Quantitative Chemical Analysis Chemistry 321 Analysis of a Carbonate-Bicarbonate Mixture Full Report: Part I and II 50 points Points 3 Report Abstract: All results reported, chemical reactions listed, RSDs and CI included 1 2 2 1 Data and Results Tables 1/2: Uncertainties, proper recording for temperature, burets, masses, etc. Tables 1/2: Calculations correct (must match instructor) Tables 1/2: RSD < 0.25% for standardization Tables 1/2: Discussions for each table complete 2 Figures 1/2: Figures complete, axes labeled 1 4 Table 3: Uncertainties, proper recording for temperature, volumes, masses, etc. Table 3: Calculations correct, must match instructor 10 7 5 0 Student Results vs. Known Sample Content Within 5% Within 10% Within 25% >25% 4 4 Figures 3-6: Gran plots for first and second inflection points Tables 4-6: Gran plots, LINEST tables, sig figs correct, complete 2 2 Table 7: Correct calculations, proper sig figs Ka values should be of the correct magnitude 4 1 Results and Conclusions Brief summary of results and well thought out conclusions. Recommendations for improving experiment. 4 Questions (2 points each) 1 Calculations 2 References in JACS format Table 1. Standarizaton of Hydrochloric Acid Titrations Na2CO3 (g) Blank 1 2 3 Na2CO3 (mol) HCL (mol) 1.331 1.397 1.388 Vinital (mL) Vfinal (mL) 1.48 1.20 0.91 1.20 1.58 25.95 27.01 27.17 Vtotal (mL) Molarity HCL (mol/l Table2. Determination of Na2CO3 Weight percent: Unknown Sample Unknown Vinital (mL) Vfinal (mL) 1 2 3 4.20 8.29 12.37 25 25 25 0.78 4.20 8.29 Vtotal (mL) Cone. HCl HCL (mol) (mol/L) Na2CO3 Na2CO3 Weight (mol) (g) percent Volume 0 0.51 1.01 1.51 2.01 2.51 3.01 3.51 4.01 4.69 5.09 5.71 6.17 6.71 7.08 7.69 8.11 8.55 9.1 9.58 10.05 10.58 11.03 11.6 12.11 12.52 13.11 13.52 14.01 14.54 15.09 15.6 16.01 16.56 17.09 17.55 18.02 18.59 19.07 19.6 20.04 20.62 PH 9.89 9.84 9.83 9.72 9.59 9.6 9.44 9.33 9.26 9.17 9.07 8.77 8.35 8.09 7.92 7.75 7.66 7.55 7.44 7.32 7.22 7.11 7.05 6.86 6.72 6.76 6.46 6.16 5.88 6 5.54 5.55 5.36 4.67 4.2 3.73 3.21 3.01 2.75 2.65 2.72 2.52 21.11 21.61 22.05 22.69 23.21 23.61 24.1 24.69 25.21 2.51 2.46 2.36 2.34 2.3 2.28 2.22 2.18 2.16 Vernier Format 2 sina.txt 2/29/2018 20:19:5 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 10.36 10.36 10.36 10.35 10.33 10.33 10.32 10.31 10.3 10.29 10.29 10.28 10.26 10.26 10.25 10.24 10.23 10.22 10.21 10.2 10.2 10.19 10.18 10.16 10.15 10.14 10.13 10.12 10.11 10.1 10.09 10.07 10.06 10.06 10.05 10.04 10.03 10.02 10.01 10 9.98 9.98 9.96 9.95 9.94 9.93 9.92 9.91 9.9 9.88 9.88 9.86 9.85 9.84 9.82 9.8 9.79 9.78 9.77 9.75 9.74 9.72 9.71 9.7 9.68 9.66 9.64 9.63 9.61 9.6 9.58 9.56 9.53 9.51 9.49 9.47 9.45 9.43 9.4 9.38 9.35 9.33 9.3 9.28 168 170 172 174 176 178 180 182 184 186 188 190 192 194 196 198 200 202 204 206 208 210 212 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 9.24 9.21 9.18 9.15 9.11 9.07 9.04 9 8.95 8.91 8.87 8.82 8.77 8.72 8.67 8.61 8.56 8.51 8.46 8.42 8.37 8.33 8.29 8.25 8.22 8.18 8.16 8.12 8.09 8.06 8.04 8.02 7.99 7.96 7.93 7.91 7.88 7.86 7.84 7.82 7.79 7.77 7.75 7.72 7.69 7.68 7.65 7.63 7.61 7.6 7.57 7.56 7.54 7.52 7.51 7.49 7.47 7.45 7.44 7.42 7.41 7.39 7.37 7.36 7.34 7.32 7.31 7.29 7.28 7.27 7.25 7.23 7.21 7.2 7.19 7.17 7.16 7.14 7.13 7.12 7.11 7.09 7.07 7.05 7.04 7.03 7.01 7 6.99 6.98 6.96 350 352 354 356 358 360 362 364 366 368 370 372 374 376 378 380 382 384 386 388 390 392 394 396 398 400 402 404 406 408 410 412 414 416 418 420 422 424 426 428 430 432 434 436 438 440 442 444 446 448 450 452 454 456 458 460 462 464 466 468 470 472 474 476 478 480 482 484 486 488 490 492 494 496 498 500 502 504 506 508 510 512 514 516 518 520 522 524 526 528 530 6.95 6.94 6.92 6.91 6.9 6.88 6.87 6.86 6.84 6.84 6.83 6.81 6.8 6.78 6.77 6.76 6.75 6.73 6.72 6.71 6.7 6.69 6.68 6.67 6.66 6.64 6.63 6.62 6.61 6.6 6.59 6.57 6.56 6.55 6.54 6.53 6.52 6.51 6.5 6.49 6.47 6.45 6.44 6.43 6.42 6.4 6.4 6.38 6.37 6.36 6.35 6.34 6.32 6.31 6.3 6.29 6.27 6.26 6.25 6.24 6.23 6.21 6.2 6.19 6.17 6.16 6.14 6.13 6.11 6.1 6.09 6.07 6.05 6.04 6.02 6.01 5.99 5.97 5.96 5.94 5.91 5.9 5.88 5.86 5.83 5.8 5.78 5.76 5.73 5.7 5.68 532 534 536 538 540 542 544 546 548 550 552 554 556 558 560 562 564 566 568 570 572 574 576 578 580 582 584 586 588 590 592 594 596 598 600 602 604 606 608 610 612 614 616 618 620 622 624 626 628 630 632 634 636 638 640 642 644 646 648 650 652 654 656 658 660 662 664 666 668 670 672 674 676 678 680 682 684 686 688 690 692 694 696 698 700 702 704 706 708 710 712 5.65 5.62 5.58 5.54 5.51 5.46 5.41 5.37 5.3 5.23 5.15 5.05 4.94 4.82 4.69 4.55 4.43 4.31 4.21 4.15 4.09 4.02 3.97 3.92 3.89 3.85 3.82 3.79 3.76 3.74 3.71 3.69 3.67 3.65 3.63 3.62 3.6 3.59 3.57 3.56 3.54 3.53 3.52 3.5 3.49 3.48 3.47 3.46 3.45 3.44 3.43 3.42 3.41 3.39 3.39 3.37 3.37 3.35 3.34 3.34 3.33 3.33 3.32 3.31 3.3 3.29 3.28 3.28 3.27 3.27 3.26 3.25 3.24 3.24 3.23 3.22 3.22 3.21 3.21 3.2 3.19 3.19 3.18 3.18 3.17 3.17 3.17 3.16 3.15 3.15 3.15 714 716 718 720 722 724 726 728 730 732 734 736 738 740 742 744 746 748 750 752 754 756 758 760 762 764 766 768 770 772 774 776 778 780 782 784 786 788 790 792 794 796 798 800 802 804 806 808 810 812 814 816 818 820 822 824 826 828 830 832 834 836 838 840 842 844 846 848 850 852 854 856 858 860 862 864 866 3.14 3.14 3.13 3.13 3.12 3.12 3.11 3.11 3.1 3.1 3.09 3.09 3.09 3.08 3.08 3.08 3.07 3.06 3.06 3.06 3.05 3.05 3.05 3.04 3.04 3.03 3.03 3.03 3.03 3.03 3.02 3.02 3.02 3.01 3.01 3.01 3.01 3 3 2.99 2.99 2.99 2.98 2.98 2.98 2.98 2.97 2.97 2.97 2.97 2.96 2.96 2.96 2.95 2.95 2.95 2.94 2.94 2.93 2.93 2.93 2.93 2.93 2.92 2.92 2.92 2.91 2.91 2.91 2.91 2.9 2.9 2.9 2.9 2.89 2.89 2.89
Purchase answer to see full attachment