Calibration of Pipets

7/31/2019 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

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Calibration of Pipets