Estimation of measurement uncertainty in chemical analysis

Self-test 4.2

1. After calibrating the 10 mL pipette it turned out, that the correction of the pipette is 0.03 mL. Manufacturer has indicated on the pipette that the uncertainty is ±0.03 mL. Is it allowed to use this pipette?

Absolutely not!

Yes, it is allowed.

2. Which two of the followings uncertainty sources are the most important by calibrating a pipette?

Possible difference of the temperature in case of calibration and measuring

Repeatability

Uncertainty of the content of dissolved gases from air in the water used for calibration

Density of the water at particular temperature

3. Which equations can be used for calculating the repeatability uncertainty of titration (n – number of the measurements, x_i– i-th measured value, x_m – arithmetic mean of the values)?

4. You have to assess the data of the purple automatic pipette (volume range 0.5 – 5 ml) calibration that your colleague has performed. Which of the following datasets obtained from calibration represents reliable experimental results, assuming that the pipette conforms to specifications? All volumes are presented in milliliters. The manufacturer specifications are given in the table.

The pipette was adjusted to 5.000 ml and the following volumes were obtained by repeated pipetting (all in ml): 4.910, 4.887, 4.890, 4.892, 4.876, 4.882, 4.887, 4.896, 4.895, 4.890

The pipette was adjusted to 2.500 ml and the following volumes were obtained by repeated pipetting (all in ml): 2.503, 2.489, 2.494, 2.507, 2.504, 2.500, 2.493, 2.497, 2.500, 2.496 ml

The pipette was adjusted to 0.500 ml and the following volumes were obtained by repeated pipetting (all in ml): 0.484, 0.510, 0.519, 0.501, 0.511, 0.492, 0.517, 0.491, 0.479, 0.512

The pipette was adjusted to 5.000 ml and the following volumes were obtained by repeated pipetting (all in ml): 4.999, 5.001 ml

5. How can we calculate the standard uncertainty of a quantity Y, which has several uncertainty sources, which all have been expressed by the respective standard uncertainties (all of them have the same units)?

6. Which is more accurate titration procedure, gravimetric or volumetric titration?

Gravimetric

Volumetric

7. Which could be the minimal number of parallel measurements in the case of correct pipette calibration or in the case of repeatability determination?

8. In the lab a 10 ml pipette was calibrated by repeatedly pipetting 10 ml of water and weighing it. The following results were obtained (all in ml): 9.9978; 10.0062; 10.0020; 10.0047; 9.9998; 9.9982; 10.0023; 10.0034; 10.0012; 9.9994. Please provide four decimal places after the decimal point.

What is the mean pipetted volume (with unit)? Please present the answer with 4 decimal places.

What is the volume that is reasonable to assign to the pipette after calibration (with unit)? Please present the answer with 4 decimal places.

What is the repeatability standard deviation of pipetting with this pipette (with unit)? Please present the answer with 4 decimal places.

9. Which equations can be used for calculating the repeatability uncertainty of single pipetting (n – number of the measurements, xi – i-th measured value, xm – arithmetic mean of the values)?

Course introduction
1. The concept of measurement uncertainty (MU)
- Self-test 1
2. The origin of measurement uncertainty
- Self-test 2
3. The basic concepts and tools
4. The first uncertainty quantification
5. Principles of measurement uncertainty estimation
6. Random and systematic effects revisited
- Self-test 6
7. Precision, trueness, accuracy
- Self-test 7
8. Overview of measurement uncertainty estimation approaches
- Self-test 8
9. The ISO GUM Modeling approach
10. The single-lab validation approach
11. Comparison of the approaches
- Self-test 11
12. Comparing measurement results
13. Additional materials and case studies
14. Tests and Exercises
Frequently asked questions
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