Instant Notes: Analytical Chemistry

Calibration dataare generally used to construct a calibration graph, where

detector response is plotted on the ordinate axis (y-values) and massor concen-

trationof the analyte on the abscissa axis (x-values) as shown in Figure 1.

The graphs are often linear, being defined by the equation

y=bx+a (1)

where bis the slope and athe intercept on the y-axis. In some cases, it is prefer-

able to plot a logarithmic function of the detector response or analyte concentra-

tion to obtain a linear calibration curve.

Unknown levels of the analyte are determined from the graph by interpola-

tion. Where a linear relation has been established, a calibration factor can be

used to convert detector response to mass or concentration of analyte when

analyzing samples.

Theoretically, the graph should pass through the origin, but frequently in

practice there is a small positive intercept due to traces of analyte in the reagent

blank or contributions to the detector signal by other components in the

standards. Calibration points also show a degree of scatter due to the effects of

experimental errors in preparing the standards, or noise in the measuring

circuitry. A line of best fitthrough the points, known as a regression line, is

therefore drawn or computed.

Calibration graphs may show curvature, particularly at higher mass or

concentration levels, but this does not invalidate their use if the data are repro-

ducible. However, it is advisable to prepare additional standards to define the

curve more closely, and the use of a factor to compute analyte levels in samples

is precluded.

Statistical methods are used to assess calibration data

● for linearity or otherwise;

● to calculate the parameters defining a calibration curve;

● to assess the effects of determinate and indeterminate errors on standards

and samples.

42 Section B – Assessment of data

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Detector response

Sample response

Interpolated sample

mass/concentration

Analyte mass/concentration

Fig. 1. A typical calibration graph.

The correlation coefficient, r, indicates the degree of linearitybetween xand y

and is given by the expression

Correlation
coefficient