calibration of pipets
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Calibration of Pipets
A Statistical Point of View
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Types of Pipets
Two Main Types
- TC (to contain)
- TD (to deliver)
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Purpose of Calibration
To determine the random error introducedby human error. Then to determinesystematic error introduced due to poor
manufacturing tolerances in either thebalance or the pipet itself.
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Gravimetric Titration
Conventional volumetric calibrationprocedure using gravimetry i.e. bytransferring aliquots of known density from
the pipet to a weighing vessel andmeasuring the masses transferred.
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Gravimetric Calibrations
Gravimetric calibration uses an assumedcorrect and working balance to give aparticular amount of a fluid at a known
weight using a standard such a H2O.
Experimental conditions used in calibrationshould match as closely as possible the
conditions of the experiment itself
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Advantage to GravimetricTitration
Easy to set up
Distilled H2O is easy to acquire
Cheap
Can be done with very few aliquots
Calibration of volumetric devices bygravimetry is simple, effective, and well-
known and under ordinary circumstancesthis procedure and associated dataanalysis are straight forward
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Disadvantages to GravimetricCalibration
Not an accurate procedure
Assumes low error and a preciselycalibrated balance
The balance MUST be properly calibrated
To improve accuracy, many aliquots must
be taken Taring can be time consuming depending
on vessel
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Analysis
Plot large amounts of aliquots and see ifthey drift aimlessly about the mean, if theydont then some other systematic error
must be found and corrected. The smaller the aliquot, the larger and
easier errors are to introduce. Tocounteract this taring is best doneperformed as well as containment ofevaporation along with large numbers ofaliquots measured.
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EXPERIMENTAL PROCEDURES
Two procedures: tared and untared Same equipment and materials used for both procedures
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Amount of trials: 40 aliquots
Each aliquot: 20.0% capacity
Mean: 0.19069 g
Standard deviation: 0.0032 g
Standard error: 0.00051 g
System Correction: -0.0084 mL
EXPERIMENT 1(TARED)
The temperature of the water was measured to be 21.7 degreesCelsius +/- 0.2 degrees, and the density of the water wascalculated to be 0.9978 g/mL. With a mean of 0.1906 g and astandard error of 0.0005 g, the nominal volume delivered by themicropipette was 0.1911 g.
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Amount of trials: 40 aliquots
Each aliquot: 20.0% capacity
Mean: 0.19064 g
Standard deviation: 0.0034 g Standard error: 0.0006 g
System Correction: -0.0094 mL
EXPERIMENT 2(UNTARED)
Values for mean, standard deviation, and standard error werecalculated through extrapolation of a residual plot trend.
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Results
Experiment One vs. Experiment
Two vs. Lab1 (Calibration ofglassware)
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Experiment One
Weighed 40 aliquots , tared immediatelybefore each weighing .
Standard deviation- .0032g
Volume change of -.0084 +- .0005
The .0005 being rate of water evaporation
* time interval.
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Experiment One (Cont.)
The independent random component can be found by
the residual variable being subtracted from the
previous residual.
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Experiment One (Cont.)
Volumetric Variance - S= 1.02x10^-5ml^2 based on 39 degrees of freedomwhich leads to a volumetric standard
deviation of Sv=.0032 mL based on 39degrees
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Experiment Two
Weighed 40 aliquots , Did not tare beforeeach weighing .
Standard deviation- .0034
Volume change of-.00094 +- .0006
The .0006 being rate of water evaporation
* time interval.
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Experiment Two (Cont.)
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Experiment Two (Cont.)
Volumetric Variance - S= 1.16x10^-5ml^2 based on 37 degrees of freedomwhich leads to a volumetric standard
deviation of Sv=.0034 mL based on 37degrees.
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Lab 1 (Calibration of Glassware)
Used measurements of 10ml , 20ml ,30ml , 40ml and 50ml of distilled water.
Measured mass of water
From mass and density we found thevolume .
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Lab One ( cont.)
Graphed experimental amount of
water vs. the theoretical amount of
water.
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Discussion (Cont.)
For the volumetric variances we take theratio (1.16x10^-5)mL / (1.04x10^-5) mL
The ratio of the volumetric varianceestimates gives us 1.14 which is lessthan the tabulated F- statistic for any
reasonable confidence interval
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Discussion (Cont.)
Thus we may accept the null hypothesisand the two variances are from thestatistical population and conclude that the
volumetric standard deviations of .0032and .0034 mL are consistent.
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Works Cited
Calibration of pipettes A statistical view(Lowell M. Schwartz)- dept of chemistry ,University of Massachusetts , Boston. (
Via ACS.com. Anal. Chem . 1989 61,1080-1083
Meyer , S. L Data for Analysis for scientist and
Engineers ; Willey : New York 1975 chapter 33 Mandel , J.J Am. Statist. Assoc. 1957 , 52 , 552-566 Mandel , J.J the statistical Analysis of Experimental Data
; Willey ; New York, 1964 , Sections 12.7 , 12.8
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Resource and Discussion
Statistical uncertainties and accuracies Matching experimental conditions
Properly calibrated weighing machine
The pipet maybe used to contain or deliverthe aliquot
Two Ways Calibrated series of vessel (tared)
Using single vessel (Untered)
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Tared Vs Untared
Tared
Taring vessel is timeconsuming and
troublesome Evaporation of liquid
negligible
Data analysis is simpler
Untared
No need to tare thevessel each time
Must account evaporationof liquid
Data analysis verycumbersome
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Two Errors
Systematic error Denote by v
Partly comes from the manufacture tolerance
Partly result from the fluctuation of dispensingtechnique between manufacture and analyst
Random error: Denote v
Result from successive aliquot delivered Magnitude depending on the operation sill of theanalyst
Taking weighing data of the aliquot
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Points of Interest
The density of the liquid be known
The liquid must be equilibrated at STPcondition
When plotting the data, make sure theweighing data scattered randomly aboutthe mean.
Balance must be able to operate withminimal mechanical and electricalfluctuation
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Comparison with Our 1st Lab
Calibration of Pipet
1. Assumed the balance iscalibrated
2. Based on volumetriccalculation
3. Uses Single or series ofvessel
4. Condition STP5. Statistical replications 30
times or more
Calibration of glassware
1. Same
2. same
3. Used only one vessel4. Condition STP
5. Statistical replicationsonly five times
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Compression Continued
Calibration of pipets
7. Evaporation considered
8. Calibration of Micro pipet
(1 micro liters)9. Data analysis is time
consuming andcomplicated
Calibration of glassware
7. Evaporation neglected
8. Calibration of mL
glassware's (difference1000 times)
9. Data analysis is lesscomplicated and straight
forward
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Conclusion
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Error Reduction
Calibration of pipets is a delicateprocedure where much care must betaken to assure as little human error as
possible is introduced, and all systematicerrors are taken into account.
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Effectiveness
Gravimetric titration is an easy to perform,lost cost/high value procedure to ensuremeasurement precision.
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Availibility
Almost universally available due to allequipment being easy to procure. IEbalance, distilled water, and pipets.
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Reliability
Can be very reliable when care is takenand large amounts of aliquots are used toreduce the human error introduced.
Reliability is low with less aliquotsmeasured; Also assumes workingbalance.
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Questions