Calibration of an Analytical Instrument

We mentioned in Section 6.2 that the response of an instrument used for chemical analysis is proportional to the concentration of the analyte in a solution. This proportionality can be expressed as follows  

We also indicated in Section 6.2 that the calibration of an instrument for quantitative analysis can utilize a single standard, resulting in a calibration constant, or a series of standards, resulting in a standard curve. If a single standard is used, the value of K is the calibration constant. It is found by determining the instrument response for a standard solution of the analyte and then calculating K  

The concentration of the unknown sample solution is then calculated from its instrument response and the K determined from Equation (6.4)  

In the above equations, Rs is the readout for the standard solution, Cs is the concentration of the analyte in the standard solution, R(J is the readout for the unknown sample solution, C, is the concentration of the analyte in the unknown solution, and the proportionality constant (K) is the calibration constant. 

There are two limitations with the above process 1) the analyst is putting all the eggs in one basket by comparing the sample to just one standard (not very statistically sound), and 2) the calibration constant, K, must truly be constant at the two concentration levels, Cs and Q, (possible, but not guaranteed). Because of these limitations, the concept of the standard curve is used most of the time. 

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Chemistry, and in particular physical and analytical chemistry, often requires a numerical or statistical approach. Not only is mathematical modelling an important aid to understanding, but computations are often needed to turn raw data into meaningful information or to compare them with other data sets. Moreover, calculations are part of laboratory routine, perhaps required for making up solutions of known concentration (see p. 170 and below) or for the calibration of an analytical instrument (see p. 171). In research, trial calculations can reveal what input data are required and where errors in their measurement might be amplified in the final result, e.g. flame atomic absorption spectrometer (see Chapter 27). Table 39.7 Sets of numbers and operations ... 

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