The steps involved in sampling
Constructing a representative sample
A chemical analysis is meaningless unless you begin with a meaningful sample.
Sampling is a process of selecting representative material to analyse.
A chocolate bar does not present the same difficulty in obtaining a sample for chemical analysis as a substance whose composition is not the same throughout. We say that a substance is homogeneous if its composition is the same everywhere. By contrast, a heterogeneous substance has a different composition from one place to another. For example, the graph below shows how the aluminum concentration varies as a function of depth at one location in the Atlantic Ocean. If you wanted to know how much aluminum is in ocean water, you could not simply take a sample from one depth or one location. Even a shallow lake is likely to be heterogeneous, with the topmost layer in equilibrium with the atmosphere and the bottom in equilibrium with sediments. Temperature and density gradients in the lake prevent rapid mixing of the layers.
Many analytical problems begin with objects that are not suitable for a laboratory experiment. The object might be human tissue, a 2,000-year-old urn, a lake full of water, or a trainload of ore. To perform a meaningful chemical analysis, we must obtain a small homogeneous sample whose composition is representative of the larger object.
The flow diagram below summarises the steps in going from a real object to individual samples that can be analysed. A lot is the total material (the tissue, the urn, the lake, etc.) from which samples are taken. A bulk sample (also called a gross sample) is taken from the lot for analysis or archiving (storing for future reference). The bulk sample must be representative of the lot, and the choice of bulk sample is critical to producing a valid analysis. The statistics of the sampling process are also important.
From the representative bulk sample, a smaller, homogeneous laboratory sample is formed that must have the same composition as the bulk sample. For example, we might obtain a laboratory sample by grinding an entire solid bulk sample to a fine powder, mixing thoroughly, and keeping one bottle of powder for testing. Small test portions (called aliquots) of the laboratory sample are used for individual analyses. Sample preparation is the series of steps needed to convert a representative bulk sample into a form suitable for chemical analysis. In the case of a chocolate bar, we assumed that the bar was homogeneous. Sample preparation would consist of removing fat and dissolving the desired analytes.
To construct a representative sample from a heterogeneous material, you can first visually divide the material into segments. A random sample is collected by taking portions from the desired number of segments chosen at random. For example, if you want to measure the magnesium content of the grass in the 10-metre x 20-metre field (below), you could divide the field into 20 000 small patches that are 10 cm on a side. After assigning a number to each small patch, you could use a computer program to pick 100 numbers at random from 1 to 20 000. Then harvest and combine the grass from each of these 100 patches to construct a representative bulk sample for analysis.
For segregated materials (in which different regions have different compositions), a representative composite sample must be constructed. For example, the field shown below has three different types of grass segregated into regions A, B, and C. You could draw a map of the field on graph paper and measure the area in each region. In this case, 66% of the area lies in region A, 14% lies in region B, and 20% lies in region C. To construct a representative bulk sample from this segregated material, take 66 of the small patches from region A, 14 from region B, and 20 from region C. You could do this by drawing random numbers from 1 to 20 000 to select patches until you have the desired number from each region.