Method Errors

The nonideal chemical or physical behavior of the reagents and reactions on which an analysis is based often introduce systematic method errors. Such sources of nonideality include the slowness of some reactions, the incompleteness of others, the instability of some species, the lack of specificity of most reagents, and the possible occurrence of side reactions that interfere with the measurement process. As an example, a common method error in volumetric analysis results from the small excess of reagent required to cause an indicator to change color and signal the equivalence point. The accuracy of such an analysis is thus limited by the very phenomenon that makes the titration possible.

Another example of method error is illustrated by the data in Figure 1.1 in which the results by analysts 3 and 4 show a negative bias that can be traced to the chemical nature of the sample, nicotinic acid. The analytical method used involves the decomposition of the organic samples in hot concentrated sulfuric acid, which converts the nitrogen in the samples to ammonium sulfate. Often a catalyst, such as mercuric oxide or a selenium or copper salt, is added to speed the decomposition. The amount of ammonia in the ammonium sulfate is then determined in the measurement step. Experiments have shown that compounds containing a pyridine ring such as nicotinic acid  are incompletely decomposed by the sulfuric acid. With such compounds, potassium sulfate is used to raise the boiling temperature.

Samples containing NiO or NiN linkages must be pretreated or subjected to reducing conditions.3 Without these precautions, low results are obtained. It is highly likely the negative errors, (x₃^-- x_t) and (x₄^-- x_t) in Figure 1.1 are systematic errors resulting from incomplete decomposition of the samples. Errors inherent in a method are often difficult to detect and are thus the most serious of the three types of systematic error.

Figure 1.1 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. (Data from C. O. Willits and C. L. Ogg, J. Assoc. Offic. Anal. Chem., 1949, 32, 561.)