Errors in Chemical Analyses

5 Errors in Chemical Analyses

Replicates: the same size samples are carried through an analysis in exactly the same way (2~5). Fig. 5-1 Results from six replicate determinations of iron in aqueous samples of a standard solution containing 20.0 ppm iron(III).

5A Some Important Terms

5A-1 The Mean and Median

Mean, arithmetic mean, and average( x ): Median: the middle value in a set of data

x = i =1 N

∑ Xi

N

Ex 5-1. Calculate the mean and median for the data: 19.4, 19.5, 19.6, 19.8, 20.1 and 20.3 (in Fig. 5-1). Mean = x =

19.4 + 19.5 + 19.6 + 19.8 + 20.1 + 20.3 = 19.78 ≈ 19.8 ppm Fe 6

Median = 19.6 + 19.8 = 19.7 ppm Fe 2

5A-2 Precision

Precision: the closeness of results to others that have been obtained in the same way. Deviation: di = | xi- x | Standard deviation Variance Coefficient of variation

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5A-3 Accuracy

Accuracy: the closeness of a measurement to the true or accepted value. Absolute error: E = xi - xt

x − xt Relative error: Er = i × 100% xt

Ex. Calculate the relative error of the data in ex.5-1 (true value =20.00)

Er =

19.8 − 20.00 × 100% = −1% or - 10 ppt 20.00

5A-4 Types of Errors in Experimental Data

Random, or indeterminate errors: affect the precision of measurement Systematic, or determinate error: affect the accuracy of results Gross errors: lead to outliers Fig. 5-3 Absolute error in the micro-Kjeldahl determination of nitrogen. Each dot represents the error associated with a single determination. Each vertical line labeled ( xi − xt ) is the absolute average deviation of the set from the true value.

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5B SYSTEMATIC ERRORS

5B-1 How do systematic errors arise?

Instrument Errors Method Errors Personal Errors

5B-2 The effects of systematic errors on analytical results

Constant errors: independent of the sample size Proportional errors: ↑ or ↓ ∝ sample size Ex. 5-2. Suppose that 0.50 mg of precipitate is lost as a result of being washed with 200 mL of wash liquid. If the ppt weights 500...