1: Experiment Buret Preparation and Calibration Abstract: A buret was prepared and calibrated for use in future experiments. The first part involved determining the value of drops/mL of water and the second part involved finding the correction for a range of volumes. The drops/mL was calculated to be 18.40 0.88 drops/mL In buret calibration, the average correction value was 0.09 mL and the created is shown in Table 13. Both parts of the experiment seemed to provide poor results. Introduction In doing quantitative measurements, instruments such as pipets, pH meters, and volumetric flasks are used. But, one important instrument in doing quantitative measurements is a buret which dispenses known volumes of liquid. Although the buret can deliver known volumes, it can never be exact due to the presence of indeterminate error which is error that will always be present in an experiment due to limitations in the procedures and the equipment used (so for example, one can never deliver the "exact" amount of liquid with a buret due to the thickness of the marks on the buret and the human eye's inability to detect when the "exact" volume has been delivered). But as said, this is unavoidable and thus must be accepted. One type of error that must be avoided when using a buret however is determinate (systematic) error which is bias in measurements which leads to measured values being systematically too high or systematically too low. The bias can come from the environment, methods of observation, and the equipment used. So in the instance of a buret, when it is produced from the manufacturer the marks may not be accurate thus the reading of the volume may be different from what was actually obtained. Because of this, determinate errors must be eliminated or minimized. In the case of the buret, it can be calibrated so that the reading of the volume can be properly adjusted to present its true value. The first part of this experiment (Part A) involves preparing the buret for use and using it to determine the volume of per drop of water. From this its reciprocal, drops per 1 mL of water (drops/volume), will be determined The second part of this experiment (Part B) involves the calibration of the buret. The procedure involves delivering a certain amount of water and comparing the volume reading to its actual volume which will be determined from the mass of the water and the density of it. It's important to note however that the density of water changes with temperature. So the temperature of the water will be noted and the density at that temperature will come from a table of values (Table 14) which are corrected for buoyancy. By comparing the reading to the actual value over a range of volumes, adjustments can be made and can thus be used for further experiments which involve the usage of the buret. Experimental In Part A, 400-mL of deionized water (will be used for entire experiment) was allowed to equilibrate to room temperature in a beaker covered with a watch glass. The buret was prepared before its first use by filling it with deionized water and then forcing out any air bubbles through draining. The buret was checked for leakage by observing the buret tip for thirty seconds (if it did leak the o-ring would be replaced). The buret was then drained to the 50-mL mark and it was checked to see if there were any drops on the wall (If there were drops on the inside wall, it would be washed with soap and water until it was fixed and then it would be rinsed three times with deionized water). With the buret now ready for use, it was refilled with deionized water and drained to near (but below) the 0.00 mark. The volume level was then recorded (bottom of the meniscus). Forty drops were then delivered from the buret. A wait time of thirty seconds was allowed for any drops on the inside wall to drain before the final reading of the volume level was taken. From this, the total volume delivered was calculated using the equation:
Volume delivered, mL (Final volume reading, mL) - (Initial volume reading, mL)
This procedure of delivering forty drops was then repeated until ten trials were taken. If the ten values of "volume delivered" showed any outlier, a Q-test would be applied to justify removing it and then replacing it with any trial. With the data, the volume per drop of water was calculated using the equation:
Volume per drop, mL/drop
Volume delivered, mL number of drops
From this, the reciprocal was taken to give the number of drops per 1 mL of water (drops/mL). The value of all the trials will be compared to the trials of the rest of the class. In Figure 1: Part B, a dry 60-mL plastic bottle with a cap was massed. The buret was filled and drained to approximately the 0.00-mL mark. Then about 10-mL of water was delivered to the bottle which was then Picture of a capped immediately to avoid evaporation. The bottle with the cap and water was then massed. The final buret1 volume was then recorded (after allowing thirty seconds for drainage). About 10-mL of water was delivered to the same bottle with the water from the previous transfer still in it. The bottle was once again massed and the final reading on the buret was recorded as well. The procedure was repeated with the same bottle until the buret reached close to the 50.00-mL mark. The temperature of the water in the bottle was then taken. (Throughout the whole experiment, the bottle and cap were only handled with a paper towel to avoid adding mass). The volumes delivered from the readings were compared with the actual volumes which were calculated from the mass of water and the density of water at the temperature recorded (with the correction factor from Table 14) using the equation:
Actual volume, mL (Mass of water, g) (Correctio factor (T )) n
The volume reading (volume delivered) was then finally compared to the actual volume by doing a correction:
Correction mL (Volume delivered, mL) - (Actual volume, mL) ,
Results and Discussion Part A: Calculation of Drops/Volume and Volume/Drop
Table 1: Part A Data (individual) Trial Number Vused 1 2 3 4 5 6 7 8 9 10 (mL) 2.00 2.08 2.16 2.23 2.30 2.30 2.10 2.12 2.20 2.28
V/drop (mL/drop) 0.0500 0.0520 0.0540 0.0558 0.0575 0.0575 0.0525 0.0530 0.0550 0.0570
Drop/V (drop/mL) 20.0 19.2 18.5 17.9 17.4 17.4 19.0 18.9 18.2 17.5
Table 2: Statistics of individual data from Table 1 Calculation V/drop Drop/V (mL/drop) (drop/mL) Range (mL)= 0.0075 2.6 Mean (mL)= 0.0544 18.4 Sd (mL)= 0.0026 0.88 Absolute 0.0026 0.88 uncertainty() (mL)= Relative uncertainty= 0.0470 0.05 % relative uncertainty 4.70 4.77 (%)= 90%CI= 0.0559 18.9 0.0529 17.9 99%CI= 0.0571 19.3 0.0518 17.5 Table 3: Results for each value calculated from Table 1 Type of Data Mean with uncertainty
Volume/Drop (mL/drop) Drop/Volume (drop/mL)
0.0544 0.0026 18.40 0.88
Mean with uncertainty (reported as percent relative standard deviation) 0.0544 4.70% 18.40 4.77%
Table 4: Plot of individual Drops/Volume values for each trial
Drops/V vs. Trial Number
20.5 20.0
Drops/Volume (drops/mL)
19.5 19.0 18.5 18.0 17.5 17.0 16.5 16.0 1 2 3 4 5 6 7 8 9 10 Trial Number
.Table 5: Statistics of volume/drop values of all trials from Class Data n= 1610 Max (drops/mL) 42.55 = min (drops/mL)= 12.70 mean 19.28 (drops/mL)= median 19.14 (drops/mL)= mode 20 (drops/mL)= sd (drops/mL)= 1.80 90%CL = 19.35 19.20 99%CL = 19.39 19.16 Table 6: Statistics of mean volume/drop values of each student from Class Data n= 161 Max (drops/mL) 25.62 = min (drops/mL)= 16.36 mean 19.28 (drops/mL)= median 19.17 (drops/mL)= mode #N/A (drops/mL)= sd (drops/mL)= 1.28 90%CL = 19.44 19.11 99%CL = 19.54 19.02
Table 7: Results of Class Data with uncertainty Type of Data Mean with uncertainty (drops/mL) All data from Class Data (mL) Means of each student from Class Data 19.28 1.80 19.28 1.28
Mean with uncertainty (reported as percent relative standard deviation) (drops/mL) 19.28 9.35 19.28 6.65
Table 8: Histogram based on all Drops/Volume values from Class Data
Histogram of All Drop/V
700 600 500
Frequency
400 300 200 100 0 15 16 17 18 19 20 21 22 23 24 Bin (mL)
Table 9: Histogram based on mean Drops/Volume values calculated from Class Data
Histogram of Mean Drop/V
70 60 50
Frequency
40 30 20 10 0 15 16 17 18 19 20 21 22 23 24 Bin (mL)
Table 10: Plot of mean Drops/Volume values from Class Data vs Trial number
Means of Drops/V vs. Trials (First 100 Data Points)
35.00 33.00
means, Drops/V (drops/mL)
31.00 29.00 27.00 25.00 23.00 21.00 19.00 17.00 15.00 0 20 40 60 Trials 80 100 120
The volumes of water delivered each trial for Table 1 did not seem to be very consistent with one another as seen in Table 3, especially trials 5 and 6. But a q-test on those trials was not able to remove them and was thus kept. This would lead to a large range in drop/V of 17.4-20.0 drops/mL (Table 2). As seen in the class data of Table 8, the most common drops/volume values were from 19.00-21.00 drops/mL. Looking at the Table 1 values, 3 one trials fell in this range. When comparing the mean drop/v, which was calculated from data in Table 1 and shown in Table 3, with the means of the class data, further evidence of inconsistency in the data points was shown. The mean calculated from the individual data was 18.40 0.88 but looking at Table 9, the most frequent values were from 19.00-21.00 drops/mL. The individual mean did however fall in the range of uncertainty of both the mean of all trials from class data and the mean of all means of each student from the class data (Table 7). Even so, the large magnitude of frequency at which values of 19.00-21.00 drops/mL occur in Table 8 and Table 9 are better in determining whether a value is valid than seeing if it falls within the range of uncertainty. There are also outliers in the class data as shown in Table 10 which can increase the standard deviation of the mean of means and thus wider the range of uncertainty making it easier for values to comply with the "true" values. The class data provided showed a good representation of what the mean value should be. This can clearly be seen by the Gaussian curves of both Table 8 and Table 9 indicating the obvious distribution of data. And the high frequency of 19.00 and 20.00 drops/mL Table 8, Table 9, and Table 10 provide a reliable range to test the results. Possible sources of error which lead to these inconsistent values are the inability to read the bottom of the meniscus properly, not waiting long enough for the drops on the inside walls of the buret to drain down, improper washing of the buret to make sure that drops were not sticking to the sides, and not removing the last drop at the tip of the buret before performing a trial and thus counting that drop as one of the forty drops. There was of course indeterminate error present which was in difficulty in interpolating between the marks of the buret but this would not matter when comparing values with class data because everyone had the same error so it would just offset each other. To improve upon this part of the experiment, the key is not to do more trials but to increase the precision of each trial. And to increase precision, the trials should be done more carefully (i.e. don't let drops drain from the buret too fast).
Part B: Buret Calibration Calibration of the buret involves transferring specific volumes of water and then massing the volumes. The mass is then multiplied by the density of the water (based on the temperature measured) to obtain the actual volume. By comparing the volume delivered with the actual volume, the correction is obtained as shown in Table 11. From the various volumes and the respective correction, a calibration can be created so that when any volume is delivered with the buret, it can be adjusted with the correction value (Table 14) Table 11: Part B Data Calibration 10 Buret Volume (mL) 0 - 10 Final Volume delivered (mL) 10.02 Mass of water (g) 9.9281 Temperature (C) 21.2 Actual Volume (mL) 9.9579 Correction (mL) 0.06 Percent Error (%) 0.62
20 ~10 - ~20 20.00 19.8739 21.2 19.9335 0.07 0.33
30 20 - 30 30.02 29.7953 21.2 29.8847 0.14 0.45
40 30 - 40 40.00 39.7509 21.2 39.8702 0.13 0.33
50 40 50 49.94 49.7273 21.2 49.8765 0.06 0.13
Table 12: Average Correction calculated from Correction values in Table 11 Average correction (mL) 0.09 Table 13: Calibration Curve of Correction vs. Volume Delivered
Calibration Curve of Correction vs. Volume Delivered
0.16 0.14
Correction (mL)
0.12 0.10 0.08 0.06 0.04 0.00
10.00
20.00
30.00
40.00
50.00
60.00
Volume Delivered (mL)
Looking at Table 12, something seems wrong with the calibration curve. The first three points behave they way it should by increasing because with increased volume comes increased tolerance. But at the forth and fifth data points, the correction starts decreasing which seems irregular especially at the fifth point where the maximum tolerance should be due to the large volume. The average correction value of 0.09 mL as shown in Table 12 seems to be somewhat large since 0.09 is close to a 0.10 marking on a buret. The fact that all the corrections are positive however, is not irregular since tolerance levels are plus and minus. Thus only the trend of the curve should be called into question. The irregular trend can only be explained by the presence of determinate error. Such errors include not cleaning the buret properly to allow proper drainage and not waiting long enough for the drops of water sticking to the inside walls of the buret to drain down to provide an accurate reading. The meniscus level may not have been read correctly because it was slightly below eye level. In some of the dispersions, after delivering ~10 mL to the bottle a drop was still present at the tip of buret. This should have been collected to the bottle to be accounted for before massing which would increase the mass and the increase the actual volume which would decrease the correction a more moderate value. Another possible error is the difficulty in handling the bottle and the cap with just a paper towel so mass may have been added. There is also the possibility that water might have splashed out of the bottle. Calibrating the buret should be done again but with more care in making sure that no water is lost and that the mass of the weighing bottle is not altered by anything except for the water. Care must also be taken to make sure that the buret is fully washed. The ability to read the meniscus level and to interpolate between the marks must also get better to get more accurate results. Conclusion In this experiment, a buret was prepared and calibrated by determining the value of drops/mL and also finding the correction needed for a range of volumes delivered. The value of drops/volume was calculated to be 18.40 0.88 which fell within the range of uncertainty of the mean of the class data but was not within the range of frequently occurring values as shown in Table 9. In calibrating the buret an average correction value of 0.09 mL was calculated which seems too large to be tolerable. The calibration curve created (Table 13) also shows that the calibration is off. A proper re-calibration must be done again to get a curve where the correction value increases in magnitude.
References [1] Ian Ball. "Lecture 2" University of California San Diego, San Diego, CA. 8 February, 2006, pg. 1
Appendix: Table 14: Correction Factor values with respect to temperature Temperate (C) Correction Factor Temperate (C) 15 1.002 23 16 1.0021 24 17 1.0023 25 18 1.0025 26 19 1.0027 27 20 1.0029 28 21 1.0031 29 22 1.0033 30
Correction Factor 1.0035 1.0038 1.004 1.0042 1.0045 1.0047 1.005 1.0053
Figure 2: Spreadsheet for Part A and Part B Data
A B C 3 (A) Volume per drop (Use 40 drops) Vinit 4 Trial Number 5 (mL) 6 1 0.12 7 2 2.12 8 3 4.20 9 4 6.36 10 5 8.60 11 6 10.90 12 7 13.20 13 8 15.30 14 9 17.42 15 10 19.62 16 17 18 19 20 21 22 23 24 25 26 27 (B) Buret Calibration 28 29 Calibration 30 Buret volume (mL) 31 Initial buret reading (mL) 32 Final buret reading (mL) 33 Volume delivered (mL) 34 Initial container mass (g) 35 Final container mass (g) 36 Mass of water (g) 37 38 39 40 41 Temperature (oC) Actual volume (mL) Correction (mL) %error Average Correction (mL) D Vfinal (mL) 2.12 4.20 6.36 8.59 10.90 13.20 15.30 17.42 19.62 21.90 E Vused (mL) 2.00 2.08 2.16 2.23 2.30 2.30 2.10 2.12 2.20 2.28 range= mean= sd= Absolute uncertainty()= Relative uncertainty= % relative uncertainty= 90%CI= 99%CI= F V/drop (mL/drop) 0.0500 0.0520 0.0540 0.0558 0.0575 0.0575 0.0525 0.0530 0.0550 0.0570 0.0075 0.0544 0.0026 0.0026 0.0470 4.70% 0.0559 0.0529 0.0571 0.0518 G H Drop/V Plot V/Drop vs. Trial Number here. (drop/mL) 20.0 19.2 18.5 17.9 17.4 17.4 19.0 18.9 18.2 17.5 2.6 18.4 0.88 0.88 0.05 4.77% 18.9 17.9 19.3 17.5
10 0 - 10 0.00 10.02 10.02 14.3402 24.2683 9.9281 21.2 9.9579 0.06 0.62 0.09
20 ~10 - ~20 0.00 20.00 20.00 14.3402 34.2141 19.8739 21.2 19.9335 0.07 0.33
30 20 - 30 0.00 30.02 30.02 14.3402 44.1355 29.7953 21.2 29.8847 0.14 0.45
40 30 - 40 0.00 40.00 40.00 14.3402 54.0911 39.7509 21.2 39.8702 0.13 0.33
50 40 - 50 0.00 49.94 49.94 14.3402 64.0675 49.7273 21.2 49.8765 0.06 0.13
Figure 3: Class Data Statistis Spreadsheet
From all Drop/V n= max = min = mean = median = mode = sd = 90%CL = 99%CL = 1610 42.55 12.70 19.28 19.14 20 1.80 19.35 19.39 Bin range Drop/V 15 16 17 18 19 20 21 22 23 24 Bin 15 16 17 18 19 20 21 22 23 24 More Frequency 6 13 32 182 464 607 160 84 31 15 16
19.20 19.16
From all Means n= max = min = mean of means = median = mode = sd = 90%CL = 99%CL =
161 25.62 16.36 19.28 19.17 #N/A 1.28 19.44 19.54
19.11 19.02
Bin range mean 15 16 17 18 19 20 21 22 23 24
Bin 15 16 17 18 19 20 21 22 23 24 More
Frequency 0 0 2 15 53 63 18 4 2 3 1
Report results as sd: From all Drop/V From all Means
19.28 19.28
1.80 (drops/mL) 1.28 (drops/mL)
Report results as RSD%: From all Drop/V 19.28 From all Means 19.28
9.35 (drops/mL) 6.65 (drops/mL)