Page 156 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

4 ERRORS AND STATlSTlCS

glassware, and other instruments; the attack of reagents upon glassware,
porcelain, etc., resulting in the introduction of foreign materials; volatilisation
of platinum at very high temperatures; and the use of reagents containing
impurities.
3. Errors of method. These originate from incorrect sampling and from
incompleteness of a reaction. In gravimetric analysis errors rnay arise owing
to appreciable solubility of precipitates, CO-precipitation, and post-precipitation,
decomposition, or volatilisation of weighing forms on ignition, and precipitation
of substances other than the intended ones. In titrimetric analysis errors rnay
occur owing to failure of reactions to proceed to completion, occurrence of
induced and side reactions, reaction of substances other than the constituent
being determined, and a difference between the observed end point and the
stoichiometric equivalence point of a reaction.
4. Additive and proportional errors. The absolute value of an additive error is
independent of the amount of the constituent present in the determination.
Examples of additive errors are loss in weight of a crucible in which a
precipitate is ignited, and errors in weights. The presence of this error is
revealed by taking samples of different weights.
The absolute value of a proportional error depends upon the amount of
the constituent. Thus a proportional error rnay arise from an impurity in a
standard substance, which leads to an incorrect value for the molarity of a
standard solution. Other proportional errors rnay not Vary linearly with the
amount of the constituent, but will at least exhibit an increase with the
amount of constituent present. One example is the ignition of aluminium
oxide: at 1200 OC the aluminium oxide is anhydrous and virtually non-
hygroscopic; ignition of various weights at an appreciably lower temperature
will show a proportional type of error.
Random (indeterminate) errors. These errors manifest themselves by the slight
variations that occur in successive measurements made by the same observer
with the greatest care under as nearly identical conditions as possible. They are
due to causes over which the analyst has no control, and which, in general, are
so intangible that they are incapable of analysis. If a suficiently large number
of obseroations is taken it can be shown that these errors lie on a curve of the
form shown in Fig. 4.1 (Section 4.9). An inspection of this error curve shows:
(a) small errors occur more frequently than large ones; and (b) positive and
negative errors of the same numerical magnitude are equally likely to occur.

4.3 ACCURACY
The accuracy of a determination rnay be defined as the concordance between
it and the true or most probable value. It follows, therefore, that systematic
errors cause a constant error (either too high or too low) and thus affect the
accuracy of a result. For analytical methods there are two possible ways of
determining the accuracy; the so-called absolute method and the comparative
method.
Absolute method. A synthetic sample containing known amounts of the
constituents in question is used. Known amounts of a constituent can be obtained
by weighing out pure elements or compounds of known stoichiometric
composition. These substances, primary standards, rnay be available commercially