A study and evaluation of Uncertainty in Volumetric Measurement

 

Mukund   Nagarnaik,   Arun  Sarjoshi,  Ajay Bodkhe, Girish  Pandya*

Research and Development Division, Qualichem Laboratories, Near Gokulpeth Market, Nagpur 440010, India.

*Corresponding Author E-mail: pandyagh@rediffmail.com

 

ABSTRACT:

The present investigation deals with the experimental study carried out for a variety of volumetric wares such as fixed volume pipettes, graduated pipettes, graduated burettes, volumetric flasks and micropipettes used in various analytical and biological studies in our laboratory. It takes into account not only manufacturers tolerances for various types of glassware but attempts to estimate the systematic and random errors during their use. This leads to knowing the Inaccuracy and Imprecision of volumetric wares. A series of fill- and- weigh or fill-delivery- weigh operations using water are performed in the exercise to get the experimental standard deviation. Thus this experimental study is useful for knowing the uncertainty estimate of volumetric wares. Moreover it may be emphasized that systematic and random variation inherent in the volumetric glassware has not been really included in the stated tolerance of the glassware by the manufacturers. Hence evaluation of the same was essential and we have carried out the same in this study. The problem of uncertainty in the performance of laboratory glassware was analysed using cause-and – effect analysis. Uncertainty sources were identified and combined uncertainty was estimated.

 

KEYWORDS: Volumetric wares, Calibration, Pipettes, Micropipettes, Uncertainty

 

 

INTRODUCTION:

All chemistry students begin their laboratory exercises with simple volumetric operations such as preparation of a solution in a volumetric flask, transferring a fixed volume of liquid with a pipette, or delivering a known volume of liquid with a burette in a titration technique. These operations are a part of analytical procedures and are performed with volumetric wares. Today there is a pipette for virtually every requirement. Aqueous solutions, dense, viscous compounds, DNA sequencing, distributing aliquots, etc.

 

 

An important function of a good chemist is his ability to extract the best possible information from his or her equipment or volumetric wares. Ability to precisely measure volume of the solution is crucial for the accuracy of chemical analysis. Volumetric glasses – which are made according to known standards - are never perfect.  When using class a pipette, burette, one can safely assume its volume to fall within the range given by the standard specification, However, its range and differences between individual pipettes can be large.

 

To minimize problems one can calibrate the glass - that is, measure the real volume of solution delivered or contained - by weighing mass of the water. Weighing can be done with very good accuracy, and knowing water density we can calculate volume of the given water mass. Thus we can determine exact capacity of the glassware.

 

 

In recent years, it has become a requirement to include with the results of measurement a statement of its uncertainty to judge the results of measurement. This amounts to identifying problems, evaluating the uncertainty sources involved in the measurement and thus calculating the combined uncertainty. The detailed methodology was developed in a guidance document , Quantifying  Uncertainty in Analytical Measurements , issued by EURACHEM in 1995 and revised jointly with CITAC in 2000 (1) .Although uncertainty in volumetric measurement is relatively smaller compared to  other sources of uncertainty in analytical procedure, it needs to be properly determined and evaluated.

 

The present investigation deals with the experimental study carried out for a variety of volumetric wares such as fixed volume pipettes, graduated pipettes, graduated burettes, volumetric flasks and micropipettes used in various analytical and biological studies in our laboratory. Estimation of systematic and random errors during their use in experimental process is considered. The problem of uncertainty in the performance of laboratory glassware was analysed. Various uncertainty sources were identified and combined uncertainty was determined..

 

MATERIALS AND METHODS:

Following type of Volumetric wares have been analysed:                            

(a) one-mark volumetric flasks, (b) burettes, (c) one-mark pipettes, (d) graduated pipettes, (e) micro  pipettes.

For calibration of glassware one needs good analytical balance, and distilled (or DI) water

 

Cleaning Volumetric Glassware:

Cleaning of volumetric glassware is necessary to not only remove any contaminants, but to ensure its accurate use. The film of water which adheres to the inner glass wall of a container as it is emptied must be uniform. It is important that glassware is cleaned thoroughly before being used. After cleaning the walls are uniformly wetted and water will adhere to the glass surface in a continuous film. The liquids used for cleaning glassware are potassium/ sodium dichromate-sulphuric acid cleaning solution, nitric acid, alcohol and water. The choice of cleaning agent to be used depends on the nature of the contaminant. After cleaning with cleaning solution and thoroughly rinsing with water, the glassware is rinsed with distilled water. If the glassware is marked “to contain” it is additionally rinsed with ethyl alcohol and dried with clean air at room temperature.

 

Calibration of volumetric apparatus:

Calibration of capacity is carried out using a suitable, documented procedure. Detailed procedures for the calibration of volumetric glassware are given in IS 4787(2). The calibration of glassware is a skilled process, and carried out by trained personnel.

 

Volumetric capacity is normally determined gravimetrically, using water. Before starting, scrupulous care is taken to ensure that the glassware is clean. The amount of water that the vessel contains, or delivers at a measured temperature, is accurately weighed. The corrected volume is calculated at standard temperature for tropical country and at atmospheric pressure. All correction factors are referred from IS: 8897, 1978 (3). For burettes, and all types of pipettes normally encountered, analytical balance reading to 0.1 mg or less was used.

 

Pipettes

Pipette is used to transfer a volume of solution from one container to another. Most Volumetric Pipettes are calibrated To-Deliver (TD); with a certain amount of the liquid remaining in the tip and as a film along the inner barrel after delivery of the liquid. The liquid in the tip should not be blown-out. These are known as one mark pipettes. Another class of Measuring Pipettes are graduated in appropriate units. Once the pipette is cleaned and ready to use, make sure the outside of the tip is dry. Then rinse the pipette with the solution to be transferred. Insert the tip into the liquid to be used and draw enough of the liquid into the pipette to fill a small portion of the bulb. Hold the liquid in the bulb by placing your fore finger over the end of the stem. Withdraw the pipette from the liquid and gently rotate it at an angle so as to wet all portions of the bulb. Drain out and discard the rinsing liquid. Repeat this once more. To fill the pipette, insert it vertically in the liquid, with the tip near the bottom of the container. Apply suction to draw the liquid above the graduation mark. Quickly place a fore finger over the end of the stem. Withdraw the pipette from the liquid and use a dry paper to wipe off the stem. Now place the tip of the pipette against the container from which the liquid has been withdrawn and drain the excess liquid such that the meniscus is at the graduation mark.

 

Move the pipette to the receiving container and allow the liquid to flow out (avoiding splashing) of the pipette freely. When most of the liquid has drained from the pipette, touch the tip to the wall of the container until the flow stops.

 

Volumetric Flasks

The Volumetric Flask is used to prepare Standard Solutions or in diluting a sample. Most of these flasks are calibrated to-Contain (TC) a given volume of liquid. When using a flask, the solution or solid to be diluted is added and solvent is added until the flask is about two-thirds full. It is important to rinse down any solid or liquid which has adhered to the neck. Swirl the solution until it is thoroughly mixed. Now add solvent until the meniscus is at the calibration mark. If any droplets of solvent adhere to the neck, use a piece of tissue to blot these out. Stopper the flask securely and invert the flask at least 10 times. The meniscus is set so that the plane of the top edge of the graduation line is horizontally tangential to the lowest point of the meniscus, the line of sight being in the same plane.

 

The calibration of volumetric glassware is performed in a similar way as for pipettes and burettes. The basic idea is to weigh the flask empty and when filled. Calculate the difference in mass and then find the volume using the density of water at the relevant temperature.

 

Burettes

The Burette is used to accurately deliver a variable amount of liquid. Fill the burette to above the zero mark and open the stopcock to fill the tip. The air bubbles are driven out of the tip by rapidly squirting the liquid through the tip or tapping the tip while solution is draining.

 

The initial burette reading is taken after the drainage of liquid has ceased. The meniscus can be highlighted by holding a white piece of paper with a heavy black mark on it behind the burette.

 

Place the flask into which the liquid is to be drained on a white piece of paper. (This is done during a titration to help visualize color changes which occur during the titration.) The flask is swirled with the right-hand while the stopcock is manipulated with the left-hand.

 

The burette should be opened and allowed to drain freely until near the point where liquid will no longer be added to the flask. Smaller additions are made as the end-point of the addition is neared. Allow a few seconds after closing the stopcock before making any readings. At the end-point, read the burette in a manner similar to that above.

 

As with pipettes, drainage rates must be controlled so as to provide a reproducible liquid film along the inner barrel of the burette.

 

Method for micropipette calibration

Micropipette are classified as (1) Fixed volume and Variable Volume. These are also known as air- displacement pipettes Fixed volume are  designed and supplied by manufacturer to dispense a specific, fixed volume of liquid. This volume cannot be altered. Variable volume is those, in which the user can adjust the volume of liquid to be dispensed over a range specified by the manufacturer,

For calibrating micropipette, analytical balance is first properly set to record the weights accurately. To improve accuracy air displacement pipettes are usually pre-wetted by filling them several  times with the liquid being dispensed and expelled to the waste. This reduces the chance of air bubbles being aspirated. During filling of the micropipette the tip is immersed 2-3mm for pipette volume of 1μl to 100μl, 2-4mm for pipette of volume of 100μl to 1000μl and 2-5mm for volume of 1000μl to 5000μl into the distilled water reservoir vessel.

.

The calibration point is usually set at the minimum of 10%  and  50% of volume. Attach the tip to tip holder to suck the water from the reservoir vessel. Hold the pipette comfortably in one hand with thumb resting on plunger. Then press the plunger down smoothly to first top position, at this stage the pipette tip should not be immersed in the liquid. Immerse the tip of the pipette in the liquid to correct depth in a vertical position and release the plunger in a smooth and uniform manner to expel the liquid, ensure that the plunger extends fully to its upper top position and wait one or two seconds before withdrawing the tip of the pipette from the liquid. After withdrawing the tip from the liquid touch it against the edge of the reservoir to remove excess liquid. Touch the pipette against the wall of the receiving vessel at an angle of about 300 to 450 . Be careful not to immerse the tip in any liquid already in the receiving container. Carefully expel the liquid from the pipette by pressing the plunger down steadily and evenly to first top position while keeping the tip in contact with the wall of the vessel, push the plunger down to second top. This will force air through the tip to expel any remaining liquid. Remove the tip from the solution and release the plunger. Record the mass of water (take the reading after the balance has stabilized), if not stabilizing take the readings within 10 seconds and this should be kept constant in all other runs.

 

Volume measurement is an important step in most of the analytical measurements. Volumetric instruments are used in many fields like chemistry, biology and pharmacy. It is necessary that all laboratories engaged in analytical work must ensure that the results they obtain using these instruments are accurate, precise and reliable. In order to reduce and identify possible errors in liquid handling, it was necessary to calibrate volume instruments using correct methods. In this study   volumetric glassware such as fixed volume and graduated pipettes, fixed volume flasks and graduated burettes were calibrated .Micropipettes that extensively used in laboratory were also calibrated.   Uncertainty in these volumetric wares was subsequently determined.

 

 

 

Evaluation of accuracy

The specified accuracy is the limit to the systematic error, which is the difference between the mean volume of actual measurements and the true value of the volume set on instrument. The systematic error (E) is estimated as follows:

 

Where E is systematic error, V0 nominal volume, and       mean volume.

 

Where, Vi is the individually measured volume, n is the number of measurements.

 

The accuracy of the pipette is expressed as the percentage of nominal volume:

 

                                                                    

Evaluation of precision:

The specified precision is the limit to random error, which is the distribution of the measured values around a mean value For pipettes, precision refers to a within series group of data and therefore to repeatability. The random error is then quantified by the standard deviation of the measurements performed at a given volume setting under the same measuring conditions. The standard deviation SD or s is estimated as follows:

 

 

Where     is the mean volume, Vi is the individually measured volume.

 

The precision of the pipette can also be expressed as the percentage of the mean volume. This also known as Relative Standard Deviation (RSD) and estimated as follows:

 

 

The Standard limits for piston-operated pipettes (micropipettes) are defined in ISO 8655. (4) The standard characterizes both the maximum permissible systematic error, as well as the maximum permissible random error limits for a device at specific volumes ranging from

1-10,000uL. These errors are doubled for multichannel pipettes.

 

RESULTS AND DISCUSSION:

Fixed volume and variable volume micropipettes were calibrated as per the procedure discussed above. The results are summarized in Table 1.The systematic error E % and the random error Cv % were measured for various types of micropipettes available in the laboratory. The results of E % and Cv % are than compared with the permissible limits for micropipettes as per ISO  8655.(4)

               


Table 1.  Evaluation and Calibration of Micro Pipettes

Micro Pipette Information

Nominal volume, ml

Corrected Mean Volume, ml

Systematic Error   ±  E %

Random Error ,

CV %

Max. Permissible Systematic Error ISO 8655, E % ±

Max. Permissible Random Error ISO 8655, CV %

Model U46549,100ul

0.020

0.0201

0.35

0.5

1.0

0.5

0.050

0.0496

- 0.73

0.4

1.0

0.5

0.100

0.1002

0.17

0.1

0.8

0.3

Model U52124, 100ul

0.020

0.0200

-0.24

0.5

1.0

0.5

0.050

0.0501

0.13

0.2

1.0

0.5

0.100

0.0998

-0.22

0.3

0.8

0.3

Model U52809,1000ul

0.20

0.1995

-0.25

0.1

0.8

0.3

0.50

0.5019

0.39

0.2

0.8

0.3

1.00

1.0071

0.71

0.1

0.8

0.3

Model U20596, 5000ul

1.0

0.9941

-0.59

0.2

0.8

0.3

5.0

4.9871

-0.26

0.3

0.8

0.3

 

 

 

It is observed that systematic and random errors for the micropipettes under study were within permissible limits. It is observed that consistency in pipetting technique contributes significantly to the reproducibility of the results. Inexperienced or untrained technicians can cause substantial variations in pipette performance. The pipettes should be operated as per the instructions given in the user’s guide of the pipette under test. Care should be given to maintain a steady rhythm when aspirating and dispensing samples, speed and smoothness when pressing and releasing the push-button, and tip immersion depth.

Evaluation of Fixed volume and graduated pipettes

The pipettes which we routinely use in our laboratory are expected to deliver its nominal volume with good precision and good accuracy if it is used in the way recommended. In this investigation we studied the precision and accuracy of such fixed mark and graduated a pipette by making accurate determinations of the mass of water it delivers in repeated operations. The mean volume is determined from 3-5 tests.. The mean volume is calculated from the mean mass and the density of water at that temperature. Finally the volume is corrected to standard temperature of 27oC as per Tables in IS:8897(3 ). The corrected volumes for various glassware under study are summarized in Tables 1-4.The systematic error (measure of Inaccuracy) and random error (measure of Imprecision) was calculated from the relations discussed above in case of micropipettes. Normally the performance of the volumetric glassware is judged by comparison with the Tolerance value of the glassware as specified by the manufacturer. The capacity tolerances for volumetric glassware have been established and classified into class A and Class B respectively. It is felt that while performing volumetric experiment there are some inherent operational errors which contribute to the measurement procedure. It is observed that systematic and random errors for the micropipettes under study are within limits of ISO 8655(4). Hence the total error could be judged from the hand- eye – operated volumetric apparatus by incorporating the contribution due to systematic and random errors in the operating process. This has been done in this study and systematic and random errors for various glassware have been determined and results are summarized in Tables 1-4. For sake of comparison Tolerance values are also considered.

 

In case of single mark pipettes five 1 ml and five 2 ml fixed mark were calibrated. One 5 ml and one 10 ml graduated pipettes were evaluated. The results are illustrated in Table 2.The systematic and random errors are expressed in terms of Inaccuracy (E %) and Imprecision (CV%). For 1.ml pipette E% is in the range of -1.42 to 1.24 and Cv% in the range of 0.46 to 4.92 respectively. For sake of comparison if one expresses inaccuracy E in ml as shown in Table 2, and compares with the certified tolerance values of manufacturers in ml, it is observed that measured values of these pipettes are within the tolerance limits. Similarly the measured values for 2 ml, 5 ml and 10 ml pipettes are within the tolerance limits.

 

 

Table  2  Calibration of Single mark and  Graduated  Pipettes

S.No.

Nominal volume of pipette, ml

 

Weight of water, g

Corrected volume of water, ml

Standard Deviation

Systematic Error, (Inaccuracy)

  ±     E %

Random Error ,

( Imprecision)

CV %

Tolerance

 E,  ml

Certified

Manufacturers Tolerance, ml

1

1.0

1.0094

1.0124

0.0197

1.24

0.46

0.01

  ± 0.01   

2

1.0

0.9829

0.9858

0.0047

-1.42

0.47

-0.01

3

1.0

1.0002

1.0032

0.0494

0.32

4.92

0.00

4

1.0

0.9855

0.9885

0.0297

-1.15

3.0

-0.01

5

1.0

0.9931

0.9961

0.0094

-0.39

0.94

-0.00

6

2.0

2.0044

2.0104

0.0158

0.52

0.78

0.005

 

  ± 0.01   

7

2.0

1.9992

2.0052

0.0214

0.26

1.07

0.002

8

2.0

1.9846

1.9906

0.0184

-0.47

0.94

-0.004

9

2.0

1.9850

1.9909

0.0088

-0.45

0.44

-0.004

10

2.0

1.9899

1.9959

0.0171

-0.20

0.86

-0.002

11

2.0

1.9610

1.9870

0.0175

-0.65

0.88

-0.006

12

2.0

1.9958

2.0018

0.0178

0.09

0.89

-0.000

13

1.0

0.9953

0.9953

0.0052

-0.50

0.52

-0.005

 

  ±0.03

14

2.0

1.9865

1.9925

0.0177

-0.37

0.88

-0.003

15

3.0

3.0045

3.0135

0.01304

0.45

0.43

0.004

16

4.0

3.9741

3.9861

0.0374

-0.34

0.93

-0.003

17

5.0

5.0002

5.0152

0.0138

0.30

0.27

-0.003

18

1.0

0.9975

1.0005

0.0052

0.50

0.51

0.005

 

 

 

± 0.05   

19

2.0

1.9824

1.9884

0.0177

-0.58

0.89

-0.005

20

3.0

29748

2.9838

0.01304

-0.54

0.43

-0.005

21

4.0

4.0002

4.0122

0.0174

0.30

0.27

0.003

22

5.0

4.9865

5.0015

0.0138

0.03

0.32

0.000

23

6.0

5.9786

5.9966

0.0191

-0.05

0.25

-0.000

24

7.0

6.9378

6.9587

0.0172

-0.59

097

-0.005

25

8.0

7.9854

8.0094

0.0078

0.11

0.21

0.001

26

9.0

8.9955

9.0226

0.0187

0.25

0.61

0.002

27

10.0

9.9760

10.0060

0.0553

0.06

0.55

0.000

                                  

 

 

 

Table  3. Calibration of Burette

.No.

Nominal volume in Bureette ml

 

Mean Weight of water, g

N=3

Corrected volume of water, ml

Standard Deviation

N=3

Systematic Error,

(Inaccuracy)

  ±     E %

Random Error ,  (Imprecision)

CV %

Tolerance

 E,  ml

Certified  Manufacturers Tolerance ,  ml

1

1.0

1.0057

1.0088

0.0052

0.88

0.52

0.0088

 

 

 

 

 

 

  ±0.025    

 

2

2.0

1.9953

2.0013

0.0177

0.06

0.89

0.0006

3

3.0

2.9948

3.0038

0.0130

0.12

0.43

0.0012

4

4.0

3.9785

3.9904

0.0374

-0.24

0.93

-0.0024

5

5.0

4.9913

5.0063

0.0138

0.12

0.27

0.0012

6

6.0

5.9921

6.0101

0.0191

0.16

0.31

0.0016

7

7.0

6.9902

7.0112

0.0172

0.16

0.24

0.0016

8

8.0

7.9957

8.0198

0.0078

0.24

0.09

0.0024

9

9.0

8.9885

9.0156

0.0187

0.17

0.20

0.0017

10

10.0

9.9641

9.9941

0.0553

-0.59

0.55

-0.0059

11

11.0

10.9830

11.0163

0.0194

0.15

0.27

0.0015

12

12.0

11.9830

12.0190

0.0233

0.16

0.19

0.0016

13

13.0

12.9652

13.0042

0.0675

0.03

0.52

0.0003

14

14.0

13.9820

14.0241

0.0188

0.17

0.13

0.0017

15

15.0

14.9803

15.0253

0.0316

0.16

0.21

0.0016

16

16.0

15.9766

16.0247

0.0359

0.15

0.22

0.0015

17

17.0

16.9669

17.0180

0.0422

0.10

0.25

0.0010

18

18.0

17.9501

18.0041

0.0521

0.22

0.29

0.0022

19

19.0

18.9563

19.0134

0.0390

0.07

0.20

0.0007

20

20.0

19.9635

20.0235

0.0484

0.11

0.24

0.0011

21

21.0

20.9493

21.0123

0.0505

0.06

0.24

0.0006

22

22.0

21.9581

22.0241

0.0467

0.10

0.21

0.0010

23

23.0

22.9367

23.0058

0.0595

0.02

0.25

0.0002

24

24.0

23.9485

24.0206

0.0469

0.08

0.19

0.0008

25

25.0

24.9475

25.0226

0.0820

0.09

0.32

0.0009

 

 

                                                                                                                                          

Table  4.  Calibration of Fixed  mark Volumetric Flasks

S.No.

Nominal volume of  flask , ml

Weight of water, g

Corrected volume of water, ml

Standard Deviation

Systematic Error ,

(Inaccuracy)

  ±     E %

Random Error ,

( Imprecision)

CV %

  Tolerance

 E,  ml

Certified

Manufacturers Tolerance, ml

1.0

5.0

5.0105

5.0176

0.03882

0.352

0.030

0.0035

±0.02

2.0

5.0

4.9829

4.9900

0.04490

-0.020

0.90

-0.0002

 

3.0

5.0

4.9826

4.9897

0.00670

-0.206

0.134

-0.0020

 

4.0

5.0

5.0095

5.0166

0.04080

0.332

0.814

0.0033

 

 

 

 

 

 

 

 

 

 

5.0

10.0

9.9438

9.9798

0.07761

0.202

0.780

0.0020

±0.02

6.0

10.0

9.9561

9.9921

0.06408

-0.079

0.643

-0.00079

 

7.0

10.0

9.9758

10.018

0.00757

0.118

0.0758

0.0011

 

8.0

10.0

9.9742

10.0102

0.001222

0.102

0.0122

0.0010

 

9.0

10.0

9.9682

10.0042

0.04164

0.042

0.417

0.00042

 

 

 

 

 

 

 

 

 

 

10.0

25.0

24.90001

24.9911

0.0494

-0.035

0.198

-0.00035

±0.03

11.0

25.0

24.9001

24.9911

0.04948

-0.0356

0.1987

-0.00035

 

12.0

25.0

24.8974

24.9884

0.0838

-0.0464

0.337

-0.00046

 

13.0

25.0

24.9327

25.0237

0.05999

0.0948

0.240

0.00094

 

14.0

25.0

24.8920

24.9830

0.07772

-0.068

0.3122

-0.00068

 

 

 

 

 

 

 

 

 

 

15.0

100.0

99.6860

100.01

0.1399

0.01

0.14

0.0001

±0.08

16.0

100.0

99.6810

100.01

0.1002

0.01

0.10

0.0001

 

17.0

100.0

99.5982

99.93

0.3034

-0.07

0.30

-0.0007

 

18.0

100..0

99.7005

100.03

0.1193

0.03

0.11

-0.0003

 

19.0

100.0

99.6888

100.02

0.1032

-0.07

0.21

-0.0007

 

 

 

 

Referring Table 3 and Table 4 for calibration of Burettes and Volumetric flasks, the systematic and random errors for burettes are in range of -0.59 to 0.88 and 0.09 to 0.93 respectively. However, the tolerance value for 25 ml burette is within limit of ± 0.025 ml. In case of fixed volume volumetric flasks ( Table 4.), the accuracy E expressed as tolerance in ml for 5 ml, 10 ml, 25 ml and 100 ml volumetric flasks are within the tolerance limits of ±0.02, 0.03 and 0.08 respectively.

 

Identifying Uncertainty sources

In order to identify uncertainty source in the volumetric analysis, a cause and effect diagram has been prepared and summarized in Fig.  1   In this diagram various branches are depicted for which contributory cause factors are considered.

 

 

 

Temperature Effects

 

 

Figure 1. Cause- and - Effect   in volumetric operations.

 

 

The procedural contribution to total uncertainty involves several factors such as cleanliness of apparatus, setting and reading the meniscus, and drainage effects for the apparatus used to deliver the liquids. Temperature   effects are also considered as the liquid density and capacity of the vessel also changes with temperature. In the calibration procedure and temperature are also considered. One may also consider the effects due to mass determination by weighing. Balance performance in weighing is also necessary.

 

Identifying and analyzing uncertainty sources

In this study it has been observed that the two main steps that influence the uncertainty are:

(1). Uncertainty in Volume ( UB), and  (2) Uncertainty in  experimental process

 

 (1 )Uncertainty in Volume V

The volume has three major influences; calibration, repeatability and temperature effects.

 

(i) Calibration: Considering a volume of a 5.0 ml pipette as 5.0 ±0.02 ml, the value of the uncertainty is calculated assuming a triangular distribution by relation 0.02 / (6.0)˝    ml = 0.008196.

 

(ii) Repeatability: The uncertainty due to variations in filling was  estimated by performing   repeatability experiment   with a typical one mark 5.0 ml pipette. The  series of seven  fill and weigh experiments on this  5 ml pipette  gave a   standard deviation of 0.0137 ml.  RSD calculated was 0.002739. The standard uncertainty was obtained using the relation = [(RSD)2 / n] ˝. Which gives value of uncertainty as 0.001035

 

(iii)Temperature: According to the manufacturer the pipette are calibrated at a temperature  of 20 °C, whereas the laboratory temperature varies between the limits of ±4 °C. The uncertainty from this effect is calculated using the estimate of the temperature range and the coefficient of the volume expansion. The volume expansion of the liquid is considerably larger than that of the pipette, so only the former is considered. The coefficient of volume expansion for water is 2.1 x 10-4   °C–1, which leads to   

 

5 x 4x 2.1 x 10 -4. Hence expansion of glassware is  0.0042 / 3 ˝   = 0.0024.

 

The three contributions are combined to give the standard uncertainty u(V) of the volume V

 

u(V) =   [ (0.008) 2 +   (0.0024)  2 +  ( 0.0137 )2  ] 1/2    = 0.01609 ml. = UB

 

(2) Uncertainty in experimental measurements (UA)

An experimental exercise with the volumetric apparatus was carried for for repeatability. The experiment were repeated seven times and standard deviation and relative standard deviation was determined for each case .The Uncertainty in experimental measurements (UA) was calculated as follows:

 

UA   = √∑ RSD 2 /n

Total Expanded Uncertainty = 2 Ö UA2 + UB 2

 

The result of Uncertainty measurement with different volumetric wares were similarly carried out and the results are summarized in Table 5.

 

 

 

Table  5.Total Expanded Uncertainty for Volumetric wares                                                   

Volumetric ware

Volume

Standard Uncertainty

U B

Standard Uncertainty U A

Total Expanded Uncertainty ±

Fixed volume pipette

1.0

0.007353

0.01988

0.042

Graduated Pipette

5.0

0.001035

0.01609

0.032

Graduated pipette

10.0

0.002087

0.05993

0.121

Graduated Burette

25.0

0.001238

0.08593

0.171

Volumetric flask

5.0

0.01338

0.0007783

0.026

Volumetric flask

10.0

0.01216

0.0002867

0.024

Volumetric flask

25.0

0.02317

0.06626

0.140

Volumetric flask

100.0

0.1184            

0.0001478

0.23

 

 

CONCLUSION:                             

Care should be taken to ensure that volumetric glassware is used and maintained in a way that does not cause damage to it nor alter its calibration. Extremes of  temperature, including high temperature cleaning, and oven or hot air drying, which might lead to permanent changes in the capacity, shall be avoided. Certain solvents, strong acids/alkalis or surfactants may attack or alter the wetting characteristics of the glass, which in turn may affect draining properties. Machine washing should be avoided wherever possible since this is a common source of mechanical damage. Any contamination that is not water-soluble should be removed with an appropriate solvent before the glassware is washed. Any guidance available from the supplier should be followed. Before use, the tips of pipettes and burettes shall be examined for mechanical damage and possible obstructions. Individually calibrated items shall be readily identifiable against a record of the calibration results. Any items calibrated for a specific application should be segregated from the general stock of glassware.

 

 Proper calibration as per standard procedure and subsequently determination of uncertainty of  volumetric wares during use is necessary for  quality control in the laboratory.

                       

REFERENCES:

1.        EURACHEM/CITAC. Guide, Quantifying Uncertainty in Analytical Measurements, Second edition, 2000.

2.        IS 4787 Laboratory Glassware – Volumetric Instruments –Methods for Testing of capacity and for use, August, 2012.

3.        IS 8897 Correction factors for temperature, pressure, Tables for calibration and method of verification  of volumetric glassware, 1978.

4.       ISO 8655-6 Piston operated volumetric apparatus Part 6. Gravimetric method for the determination of measurement error, 2002

                                


 

 

 

Received on 19.05.2015         Modified on 17.06.2015

Accepted on 30.06.2015         © AJRC All right reserved

Asian J. Research Chem. 8(9): September 2015; Page 553-560

DOI: 10.5958/0974-4150.2015.00088.7