Estimation of measurement uncertainty in chemical analysis

Self test 9.7

Here you can test your understanding of where to obtain data for estimating measurement uncertainty contributions of different uncertainty sources and how to obtain uncertainty estimates from these data, as well as how to combine the standard uncertainty estimates.

An analyst started to implement an analysis for determining phosphorous content in a gaseous drink with UV-Vis spectrophotometric method. For this, he had to perform a 200 times dilution from the sample. The analyst thought about 3 different ways, how to perform the dilution (diluent is water-based mixture containing the photometric reagents):

-1- Pipetting 0.5 ml of sample into a 100 mL volumetric flask and adding the diluent to the mark

An automatic pipette with variable range (see the table) can be used.

Model	Volume range (μl) Color code	Testing volume	Error limits by the manufacturer
			Systematic error		Random error
			±%	±μl	±%	±μl
100 – 1000 μl Increment: 1 μl	100 – 1000 Blue	100 μl	3.0	3.0	0.6	0.6
		500 μl	1.0	5.0	0.2	1.0
		1000 μl	0.6	6.0	0.2	2.0

100ml flask

Flask filling uncertainty can be estimated as ± 1 drop (±0.03 ml) and temperature is not different from calibration temperature more than 4 °C.

-2- Pipetting 5 ml of sample into a 1000 mL volumetric flask and adding the diluent to the mark

Glassware shown here can be used:

5ml pipette tolerance +/-0.015ml
Pipetting repeatability with 5 ml glass pipette in this lab was estimated previously from repeated measurements and estimated as 0.011 ml.
1L flask
Flask filling uncertainty can be estimated as ± 2 drops (±0.06 ml) and temperature is not different from calibration temperature more than 4 °C.

-3- Pipetting 50 μl of sample and 9.95 ml of diluent

Two automatic pipettes (see information in the table) can be used.

Model	Volume range Color code	Testing volume	Error limits by the manufacturer
			Systematic error		Random error
			±%	±μl	±%	±μl
10 – 100 μl Increment: 0.1 μl	10 – 100 μl Yellow	10 μl	3.0	0.3	1.0	0.1
		50 μl	1.0	0.5	0.3	0.15
		100 μl	0.8	0.8	0.2	0.2
1 – 10 ml Increment: 0.01 ml	1 – 10 ml Turquoise	1.0 ml	3.0	30	0.6	6
		5.0 ml	0.8	40	0.2	10
		10 ml	0.6	60	0.15	15

Temperature did not differ from calibration temperature more than 4 °C.

Please help analyst to decide, which of the abovementioned procedures has the smallest uncertainty estimate. For this, please calculate the uncertainty estimate of dilution factor (DF) for each of the procedure and present the results in the table below. Please use dots instead of comma for decimals separator and keep in mind the rule of reasonable significant digits (see section 4.5).

	Absolute u_c of dilution factor (ml/ml)	Relative u_c of dilution factor (%)
-1- 0.5 ml → 100 ml flask
-2- 5 ml → 1000 ml flask
-3- 50 μl + 9.95 ml into a vial

According to the table with results, which of the procedure has the smallest uncertainty estimate?

Which of the proposed procedures would be best to use for the sample preparation?

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