Experiment # 1
Calibration of volumetric glass wares:
cylinder
pipette, burette and measuring
Introduction
Two important, though often neglected, parts of an analysis are ‘error analysis’ and
‘correct results’ reporting. Results should always be reported along with some
estimation of the error involved. The best way to do this is to report the most likely
value along with confidence interval. The confidence interval gives the range of
values thought to contain the ‘true’ value. The statistical treatment of data involves
basing the error estimation on firm theoretical principle. This laboratory exercise
on treatment of data should help you understand and apply these principles.
The proper treatment of error in data is critical in any experimental science. The
mere reporting of numbers without any indication of how reliable the numbers are
is useless. The application of any of the statistical procedures depends on acquiring
multiple data for any process or phenomenon measured. Without at least three
trials for each result, error analysis is reduced to a tedious and often phony
recitation of possible error sources that is boring to write and even more boring to
read. In order to perform a scientifically valid error analysis, measurements at least
three times is required.
Theory
The results of volumetric analyses are based on accurate measurement of volumes
of solution that react with one another. To achieve accuracy one must employ
accurate measuring tools. Burettes, pipettes of wide range and variety are used in
normal volumetric analysis. Therefore pipettes, burettes and measuring cylinder
should be properly calibrated to achieve accurate results. Calibration of pipettes,
burettes and measuring cylinder may be done by measuring weight of water
delivered by particular glassware. Then with the density of water or the volume of
1 gram of water at a measured temperature, the correct volume is calculated. If
w is the weight water delivered, then
Volume water delivered = w×v mL
where v is the volume of 1 gm of water in mL at toC.
Calibration of volumetric glass wares © Raja Ram Pradhananga
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Mean of finite number of measurements x1,x2 -------------xn is obtained by
averaging the individual results
∑𝑖=𝑛 𝑥
𝑥 + 𝑥2 + − − − − − − + 𝑥𝑛
𝑥̅ = 𝑖=𝑜 𝑖 = 1
𝑛
𝑛
where x1, x2 etc. are individual results and n is number of observations and 𝑥̅ is the
mean.
Error is numerical difference between a measured value and true value.
Accuracy is the extent to which the average value of series of measurements
differs from the true value. That means accuracy is closeness with which the test
result cluster round the true value. The smaller the error, the greater is the
accuracy. The accuracy as relative error is calculated as:
Absolute error
| Measured value – True value |
Relative error = -------------------- x 100 % = -------------------------------- x 100 %
True value
True value
The true value is never known to the degree of 100% accuracy. Accurate results
are assumed to be those measured value which have been determined by skilled
experimentalists using best quality instruments. The accuracy can be measured
quantitatively with the help of the standard deviation, the deviation of the results
being calculated from true value not from the average. The smaller the standard
deviations the higher is the accuracy.
Precision is the extent to which the repeat measurements repeat its results. That
means precision is the closeness with which the repeat measurements cluster
around the average value. Precision does not by any means imply accuracy – it is
used to describe the reproducibility of the results. The precision is quantitatively
measured with the help of standard deviation. The standard deviation is calculated
from the arithmetic mean of observed values. The smaller the standard deviation,
the higher is the precision.
The standard deviation is a root mean square deviation of values from their average
and calculated using the equations
∑i=n
(xi -x̅)2
s = √ i=0
n-1
Confidence interval is the termed used to define the numerical interval on either
side of the mean within which the true mean can be expected to lie with a given
probability. It is calculated by the formula,
Calibration of volumetric glass wares © Raja Ram Pradhananga
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Here s is the standard deviation, 𝑥̅ is the mean, n is the number of observations and
t is the statistical factor. The value of t is obtained from a table at a given
probability level and a given degree of freedom. For a five observations (i-e for a 4
degree of freedom at 95% confidence level), the value of t is 2.776.
Apparatus
One 25 mL volumetric pipette, one 50 mL burette, one 50 mL measuring cylinder
and two 50 mL beakers
Chemicals
200 mL distilled water
Procedure
(a) Cleanliness check:
Fill the pipette to slightly above the mark. Place the tip against the side of a
beaker and let the pipette drain until empty. Examine the inner surface of the
pipette to ensure it is clean (any water droplets indicate that the pipette walls
are contaminated). If necessary, clean the pipette or obtain another one.
(b) Dispensing time:
Fill the pipette to the mark. The bottom of the meniscus should touch the top of
the graduated mark. The adjustment should be made with your eye at the same
level as the graduation mark. Measure the time required to deliver the definite
volume of the water from volumetric pipette, with the tip touching inside of a
beaker. Note this time in your laboratory note book.
Calibration of a Pipette
1. Weigh a clean and dry 50 mL beaker on a top loading balancing to 1 mg
and record the weight. (Once you pick a balance, use the same one for all
weighing)
2. Fill the pipette to above the mark and remove any water adhering to the
outside of the pipette.
3. Place the tip of the pipette in contact with the inside of beaker and slowly
lower the meniscus to the mark. Do not remove any more water from
outside of the pipette.
Calibration of volumetric glass wares © Raja Ram Pradhananga
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4. Touch the top to the side of the weighed beaker and dispense the water until
holding the pipette vertically.
5. After the water has ceased flowing, wait 2 seconds, and then remove the
pipette from the container.
6. Reweigh the beaker, and calculate the weight of water in beaker. Record the
water temperature in your laboratory note-book.
7. Repeat the procedure until you have 5 separate measurements for the same
pipette.
Calibration of Burette
Take 50mL burette for this experiment. Carry out the experiment following
the procedure similar to the calibration of pipette. For gravimetric calibration drain
25mL of water from the burette and determine the weight. Repeat the
measurement until you have 5 separate measurements. Analyze the data as given
in the calibration of pipette.
Calibration of Measuring Cylinder
Take 50mL measuring cylinder for this experiment. For the gravimetric
calibration, weigh 25mL of water transferred from the measuring cylinder. Repeat
the measurement for five times. Analyze the data as given in the calibration of the
pipette.
Calibration of volumetric glass wares © Raja Ram Pradhananga
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Results:
Temperature oC
Volume of 1 gram of water at oC = mL
Calibration of pipette.
Nominal volume of volumetric pipette = 25 mL
First
Second
Third
Fourth
Fifth
Beaker weight
Total weight
Weight of water
Volume of water
Mean volume
=
Relative error =
Standard deviation
=
Confidence limit
=
at 95% confidence level
Calibration of burette.
Nominal Volume delivered by the burette = 25 mL
First
Second
Third
Fourth
Fifth
Beaker weight
Total weight
Weight of water
Volume of water
Mean volume
=
Relative error =
Standard deviation
=
Confidence limit
=
at 95% confidence level
Calibration of measuring cylinder.Volume deliv. by measuring cylinder=25 mL
First
Second
Third
Fourth
Fifth
Beaker weight
Total weight
Weight of water
Volume of water
Mean volume
=
Relative error =
Standard déviation
=
Confidence limit
=
at 95% confidence level
Conclusion:
Calibration of volumetric glass wares © Raja Ram Pradhananga
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Appendix
Volume of 1 g of water at different temperature
Temp, oC
Vol, mL
16
18
20
1.0021 1.0023 1.0027
22
24
26
28
1.0033 1.0037 1.0044 1.0047
30
1.0053
Value of “t” at 95% confidence level at different degree of freedom
Deg. of
1
2
3
reedom
Value of t 12.706 4.303 3.182
4
5
6
7
8
9
2.776
2.571
2.447
2.365
2.306
2.306
Calibration of volumetric glass wares © Raja Ram Pradhananga
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