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
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