Random and Systematic Errors

The titration example oversimplifies the accumulation of random errors in titrations. It is worth a more complete examination in order to clarify what is meant by multiple sources of variation and additive errors. Making a volumetric titration, as one does to measure alkalinity, involves a number of steps:

1. Making up a standard solution of one of the reactants. This involves (a) weighing some solid material, (b) transferring the solid material to a standard volumetric flask, (c) weighing the bottle again to obtain by subtraction the weight of solid transferred, and (d) filling the flask up to the mark with reagent-grade water.

2. Transferring an aliquot of the standard material to a titration flask with the aid of a pipette. This involves (a) filling the pipette to the appropriate mark, and (b) draining it in a specified manner into the flask.

3. Titrating the liquid in the flask with a solution of the other reactant, added from a burette. This involves filling the burette and allowing the liquid in it to drain until the meniscus is at a constant level, adding a few drops of indicator solution to the titration flask, reading the burette volume, adding liquid to the titration flask from the burette a little at a time until the end point is adjudged to have been reached, and measuring the final level of liquid in the burette.

The ASTM tolerances for grade A glassware are ±0.12 mL for a 250-mL flask, ±0.03 mL for a 25-mL pipette, and ± 0.05 mL for a 50-mL burette. If a piece of glassware is within the tolerance, but not exactly the correct weight or volume, there will be a systematic error. Thus, if the flask has a volume of 248.9 mL, this error will be reflected in the results of all the experiments done using this flask. Repetition will not reveal the error. If different glassware is used in making measurements on different specimens, random fluctuations in volume become a random error in the titration results.

The random errors in filling a 250-mL flask might be ± 0.05 mL, or only 0.02% of the total volume of the flask. The random error in filling a transfer pipette should not exceed 0.006 mL, giving an error of about 0.024% of the total volume (Miller and Miller, 1984). The error in reading a burette (of the conventional variety graduated in 0.1-mL divisions) is perhaps ± 0.02 mL. Each titration involves two such readings (the errors of which are not simply additive). If the titration volume is about 25 mL, the percentage error is again very small. (The titration should be arranged so that the volume of titrant is not too small.)

In skilled hands, with all precautions taken, volumetric analysis should have a relative standard deviation of not more than about 0.1%. (Until recently, such precision was not available in instrumental analysis.)

Systematic errors can be due to calibration, temperature effects, errors in the glassware, drainage errors in using volumetric glassware, failure to allow a meniscus in a burette to stabilize, blowing out a pipette that is designed to drain, improper glassware cleaning methods, and "indicator errors." These are not subject to prediction by the propagation of error formulas.

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