Page 181 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

SAMPLING AND PHYSICAL STATE 5.4

at the 95 per cent confidence level is 2.13.

Hence, from this test it has been shown that at least 41 samples are required
if the specifications given in the above example are to be satisfied.
The other major problem concerned with sampling is that of the sample size.
The size of the sample taken from a heterogeneous material is determined by
the variation in particle size, and the precision needed in the results of the
analysis.
The major source of error in sampling can arise from the taking of increments
from the bulk material. It can be shown from random sampling theory that the
accuracy of the sample is determined by its total size. Hence, the sampling
variance, K is inversely proportional to the mass of the sample. However, this
statement is not true if the bulk material consists of varying particle sizes; then
the number of increments taken will influence the sampling accuracy. The
sampling variance, K is inversely proportional to the number of sampling
increments (n):

where k is a constant dependent on the size of the increment and variation
within the bulk material.

5.4 SAMPLING AND PHYSICAL STATE
Many of the problems occurring during sampling arise from the physical nature
of the materials to be ~tudied.~ Although gases and liquids can, and do, present
difficulties, the greatest problems of adequate sampling undoubtedly arise with
solids.
Gases. Few problems arise over homogeneity of gas mixtures where the storage
vesse1 is not subjected to temperature or pressure variations. Difficulties may
arise if precautions are not taken to clear valves, taps and connecting lines of
any other gas prior to passage of the sample. Similarly care must be taken that
no gaseous components will react with the sampling and analytical devices.
Liquids. In most cases general stirring or mixing is sufficient to ensure
homogeneity prior to sampling. Where separate phases exist it is necessary to
determine the relative volumes of each phase in order to compare correctly the
composition of one phase with the other. The phases should in any case be
individually sampled as it is not possible to obtain a representative sample of
the combined materials even after vigorously shaking the separate phases
together.
Solids. It is with solids that real difficulties over homogeneity arise. Even
materials that superficially have every appearance of being homogeneous in fact
may have localised concentrations of impurities and Vary in composition. The
procedure adopted to obtain as representative a sample as possible will depend
greatly upon the type of solid. This process is of great importance since, if it is
not satisfactorily done, the labour and time spent in making a careful analysis