Activity 1.1: Accuracy and ToleranceAn integral part of Chemistry is being able to accurately quantify chemical species in a variety of media and for a range of purposes. Historically, quantification was used to develop relationships between matter that gave rise to modern atomic theory. Today, analytical chemistry is used in medicine, industry and society to determine the quantity of certain chemicals for diagnosis of disease, the maintain quality of product, and to determine the health of the environment.Learning outcomes

Differentiate between precision and trueness

Compare the tolerance of various pieces of glassware

Classify data in terms of the trueness and precision

Goals

Interpret tables of volumetric glassware tolerances (Information Processing)

Infer based on tabulated data (Critical Thinking)

Collaborate with group members (Teamwork)

Assumed knowledge

Types of glassware for preparing solutions, including graduated cylinders, pipettes, burettes, and volumetric flasks

Calculate average and standard deviation for a set of data

Model 1: Calibrating a volumetric flask

Table 1 lists three measurements of the volume of water contained in a single 100.00 mL volumetric flask as measured by three students. These measurements were made by weighing the mass of water contained in the volumetric flask and correcting for buoyancy.

Table 1. Volume (mL) contained in 100-mL Class A Volumetric Flask

Trial Jicarilla Kerry Lorne

1

2

3

99.92 99.99 99.87

99.90 100.04 99.86

99.88 100.05 99.88

average / mL

standard deviation / mL

99.90 100.03 99.87

0.02 0.03 0.01

Critical Thinking Questions

1. Consider the average of the three trials for each student. Which student got closer to the known volume of 100.00 mL?

2. Consider the standard deviation of the three trials for each student. Which student had the lowest standard deviation?

Adapted from: Walczak, M., Nickels Dalton, C., & Lantz, J. M. (n.d.). Accuracy, Precision and Tolerance

Consider the following definitions:

? Trueness:1: exactness of adjustment; 2a: conformity to truth or to a standard or model2b: degree of conformity of a measure to a standard or a true value

? Precision:1: the quality or state of being precise2: the degree of refinement with which an operation is performed or a measurement stated

3. Explaining your answer, which of the students in Table 1 is the most true?

4. Explaining your answer, which of the students in Table 1 is the most precise?

5. In general, which statistic (average or standard deviation) is most useful for determining trueness, and which is the most useful for determining precision?

Table 2 lists data for four students using a 25.00 mL volumetric pipette. Each student used the pipette to deliver 25.00 mL of water three times. The reported values are corrected for buoyancy.

Table 2. Volume (mL) delivered by 25-mL Class A Volumetric Pipette

Trial Jicarilla Kerry Lorne Ming

1

2

3

24.94 24.91 25.15 25.10

24.88 24.96 24.88 25.02

24.81 24.94 25.07 25.12

average / mL

standard deviation / mL

24.88 24.94 25.03 25.08

0.07 0.03 0.14 0.05

Activity 1: Accuracy and tolerance 2

6. Divide the four students among group members. Examine each students trueness and precision. List the four students in order of increasing trueness assuming that the true volume of the flask is known to be 25.00 mL. List the four students in order of increasing precision.

7. Compare the precision of student data for volumetric flasks (Table 1) with that for pipettes(Table 2). Which has better precision? List reasons why this may be the case.

8. Is it possible to have high trueness and low precision? If so, give an example from Table 1 or 2. Is it more desirable to have high trueness or high precision? Explain.

9. How do trueness and precision collectively contribute to accuracy? Discuss among your group.

Activity 1: Accuracy and tolerance 3

Model 2: Glassware

Tolerance is the permissible deviation from a specified value of a structural dimension. All glassware has some tolerance for accuracy. That is, all glassware contains or delivers volumes that can be slightly different from the stated volume that is printed on the glassware. This tolerance in manufacturing is well-documented for each type and volume of glassware.

Volumetric flasks are calibrated by manufacturers to contain a specific volume. Volumetric flasks are marked with TC indicating to contain that volume at a stated temperature. Volumetric flasks also have manufacturing tolerances, the permissible deviation from a specified value. Table 3, below, specifies the tolerance for KIMAX Class A volumetric flasks.

Table 3. KIMAX Brand Volumetric Flasks with Standard Taper Glass Stopper, Class A, Serialized and Certified

Capacity / mL Tolerance / mL % Relative Tolerance

10 0.02

25 0.03

50 0.05 0.10

100 0.08 0.08

200 0.10 0.05

250 0.12

500 0.20 0.04

1000 0.30 0.03

2000 0.50

10. Consider the 50-, 100- and 200-mL volumetric flasks in Table 3. What are the maximum and minimum volumes that could be contained in each of these flasks?

11. One way to represent the uncertainty in the volume contained in the flask is to use the % relative tolerance. What is the formula for calculating % relative tolerance for the volumetric flasks?

12. Assign the missing entries from Table 3 to the group members and calculate the % relative tolerance of each flask. Write these values into Table 3.

Activity 1: Accuracy and tolerance 4

13. As a group, compare the % relative tolerance for different size volumetric flasks. What happens to the % relative tolerance as the volume of the flask increases?

14. For optimal accuracy, do you recommend choosing a larger or smaller sized flask? On what do you base this decision?

15. As a group brainstorm a list of experimental circumstances under which it would be advantageous to choose a smaller volumetric flask over a larger flask.

Activity 1: Accuracy and tolerance 5

Pipettes are calibrated by manufacturers to deliver a specific volume. Volumetric pipettes are marked with TD indicating to deliver that volume at a stated temperature. Table 4, below, specifies the tolerance for KIMAX Class A pipettes.

Table 4. KIMAX Brand Reusable Volumetric Pipettes, Class A

Capacity / mL Tolerance / mL % Relative Tolerance

0.5 0.006

1 0.006 0.6

2 0.01 0.5

3 0.01 0.3

4 0.01

5 0.02 0.4

10 0.03 0.3

15 0.03

20 0.03 0.2

25 0.05

50 0.08 0.2

16. True or False: The acceptable range of volume delivered by a KIMAX, Class A, 10-mL volumetric pipette is 9.98 to 10.02 mL. Explain your reasoning.

17. Assign the four missing % relative tolerance values in Table 4 to group members. Calculate the % relative tolerance and add the information to the Table.

18. What happens to the % relative tolerance as the volume delivered by the pipette increases?

Activity 1: Accuracy and tolerance 6

19. True or False: Volumetric glassware with the lowest tolerance will yield the most accurate measurement. Discuss this statement as a group and come to consensus. Explain your rationale in a complete and grammatically correct sentence.

20. Which pipette listed in Table 4 has the lowest tolerance? Which pipette has the lowest % relative tolerance? Which of these pipettes would you choose for an application that requires high precision?

21. State in your own words the definitions of trueness, precision and tolerance. Share your definitions with your group and discuss the variations. Agree upon a single set of definitions for these three terms.

22. State in your own words the definition of accuracy? Write a grammatically correct sentence reflecting the groups consensus.

Activity 1: Accuracy and tolerance 7

23. What do you think were the learning objectives for this activity?

24. What teamwork skill(s) did your group practice during this activity?

25. Thinking about this activity, what were its strengths?

26. Thinking about this activity, what areas need improvements?

27. Thinking about this activity, what were your groups insights?

Your workshop facilitator will assign you a piece of assessment for todays workshop, based on your answers to the preceding questions.

Activity 1: Accuracy and tolerance 8

Homework problems

1. Four students determined the concentration of a stock NaOH solution by titration of potassium hydrogen phthalate (KHP). The known concentration of this solution was 0.2023 M. The titration data is presented in Table 5. List the four students in order of increasing accuracy. List the four students in order of increasing precision.

Table 5. Sodium Hydroxide Concentration (M) as determined by titration

JicarillaJicarilla Kerry Lorne MingMing

0.1962 0.1969 0.1989 0.2010 0.0984 0.1121

0.1960 0.1954 0.1996 0.2013 0.0981 0.1144

0.1969 0.1939 0.1994 0.2013 0.0984 0.0975

0.1960 0.1937 0.1990 0.2016 0.0996 0.0956

0.1960 0.1927 0.2080 0.2018 0.1059 0.1038

0.1960 0.2093 0.2018 0.1157 0.1009

0.2023 0.1121 0.1003

0.2033

0.2037

2. a) Jicarilla needs to pipette 1 mL of bovine serum albumin solution into a test tube. Two options are available: a 1 mL volumetric pipette and a 1000 L micropipette. Refer to Table 4 for information about volumetric pipette tolerances. The micropipette has a volume of 1000 L, an accuracy of 8 L and a precision of 1.5 L. Which pipette will deliver the more accurate volume? Explain your reasoning.

b) Kerry is calibrating a 1000 L (1 mL) micropipette. The data appear below. Evaluate the data and make a statement about the accuracy of Kerrys use of the micropipette, assuming it is calibrated to deliver 1.000 x 103 L. Does Kerrys use of the micropipette fall within the manufacturers specifications?

Table 6. Kerrys Micropipette Calibration Data

Volume / mLVolume / mLVolume / mLVolume / mL

0.9953 0.9995 0.9772 0.9627

0.9951 1.0167 0.9965 1.0049

0.9951 1.0196 1.0015 1.0038

0.9951 1.0200 1.0041 0.9977

0.9911 1.0047 0.9945 1.0079

0.9925 1.0095 0.9677 0.9998

3. Ming has to decide between two micropipettes to deliver 500 L of lysozyme solution. One is a fixed 500-L micropipette, and the other is a 100-1000-L adjustable micropipette. The tolerances for both micropipettes appear in the table below. Determine the % relative tolerance for each micropipette. Based on this information, evaluate the utility of using each micropipette to deliver lysozyme solution.

Volume / L Tolerance / L

Fixed pipette

Adjustable pipetteAdjustable pipette

500 2

100 8

1000 1.5

Activity 1: Accuracy and tolerance 9

4. Jicarilla is going to pipette 10.00 mL of a sodium chloride solution. Accuracy and precision are critical to her work. She has both a 10-mL volumetric (transfer) pipette and a 10 mL measuring (Mohr) pipette. A Mohr pipette (shown below) has graduation marks on it and can be used to transfer various volumes.

a) The tolerances for Jicarillas 10-mL Mohr pipette are given in Table 8. Tolerances for volumetric pipettes are in Table 4. Which pipette has the lower tolerance? Which pipette should Ming use?

Table 8. KIMAX Brand Reusable Measuring (Mohr) Pipets, Class A, Colour Coded

Capacity / mL Subdivisions / mL Tolerance / mL

1 0.1 0.01

1 0.01 0.01

2 0.1 0.01

5 0.1 0.02

10 0.1 0.03

25 0.1 0.05

b) Jicarilla wanted to make sure she used the more precise pipet. Therefore, she used each pipet to deliver 10.00 mL of water, weighed each delivery, and converted to volume. Her results are shown in Table 9. Based on the data provided, which pipette should Jicarilla use for her laboratory work?

Table 9. Jicarillas pipetting data

TrialTrialVolume / mLVolume / mL

Volumetric pipette Mohr pipette

1

2

3

4

5

6

7

8

10.01 9.98

10.02 9.96

10.02 10.03

10.02 10.02

9.99 9.97

10.00 9.95

9.99 9.96

9.99 10.03

c) If your recommendations in parts (a) and (b) above are different suggest reasons why this might be the case.

5. Lorne and Kerry are working on preparing Copper Atomic Absorption standards in the 2-8 ppm range. They are working with a 100.000.01 ppm primary standard solution. Kerry decides to use volumetric pipets and flasks to make 100 mL of a 5 ppm Cu secondary standard. Lorne decides to make the solution gravimetrically using a top loader balance (0.01 g). Assuming that Kerry and Lorne use the equipment properly, which method results in a solution with better precision?

Activity 1: Accuracy and tolerance 10