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# Calibration curve

In analytical chemistry, a calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration.

The calibration curve is a plot of how the instrumental response, the so-called “analytical signal,” changes with changing concentration of analyte (substance to be measured). The operator will create a series of standards across a range of concentrations near the expected unknown concentration. He or she must take care that these concentrations are in the working range of the technique (instrumentation) they are using. Analyzing each of these standards using the chosen technique will produce a series of readings. For most analyses a plot of response vs. concentration will create a linear relationship. The operator can measure the response of the unknown and, using the calibration curve, can interpolate to find the concentration of analyte.

## How to create a calibration curve

To find the best-fit straight line we use linear regression analysis. From the equation y = mx + b you substitute in the y value (response) and solve for x.

Many different variables can be used as the analytical signal, in Fig. 1 analysis was of Chromium(III) by chemiluminescence. The detector (PMT) detects light, voltage increases with intensity of light, this creates a peak and the peak area is the analytical signal.

For most analytical techniques, the ultimate goal is to obtain a calibration curve; and there are a number of advantages to this method:

The calibration curve not only gives you your answer it also gives you an idea about how good that answer is. Provided you are operating in the linear response range the plot should be a straight line, deviations from this straight line give a good indication about the precision of the result. That is to say, if the data points are spread out, there is less certainty in the result.

The calibration curve provides you with an empirical relationship, as opposed to a theoretical one. Instrumental response is usually highly dependent on the condition of the analyte, solvents used and impurities it may contain; it could also be affected by external factors such as pressure and temperature. Many theoretical relationships, such as fluorescence, require the determination of an instrumental constant anyway; in which case a calibration curve is the only way to do the determination. By making standards as similar as possible to the unknown and creating the calibration curve, what is created is a custom relationship, which takes into account all the above factors and many others for the specific conditions of the experiment.

The disadvantages are that a set of standards needs to be made, for which you must have a source of analyte material of known composition. This is a time-consuming process, may use significant quantities of expensive chemicals, and results in an increased amount of waste for disposal. Also, you need to make a rough estimate of the composition of your unknown sample, in order to enable interpolation the concentrations of the standards should fall above and below the expected unknown concentration.

In short, there is a lot of information about the analysis in a calibration curve and it is a simple way to account for all the influencing factors that could change the analytical signal.

## Applications

• Analysis of concentration
• Verifying the proper functioning of an analytical instrument or a sensor device such as an ion selective electrode
• Determining the basic effects of a control treatment (such as a dose-survival curve in clonogenic assay)

## Notes

1. ^ For a detailed discussion on how to find a numerical error from a calibration curve see any general analytical chemistry textbook. For example Principles of Instrumental Analysis by D.A. Skoog.

## Bibliography

• Harris, Daniel Charles (2003). Quantitative chemical analysis. San Francisco: W.H. Freeman. ISBN 0-7167-4464-3.
• Crouch, Stanley; Skoog, Douglas A.. Principles of Instrumental Analysis. Pacific Grove: Brooks Cole. ISBN 0-495-01201-7.
• Lavagnini I, Magno F (2007). "A statistical overview on univariate calibration, inverse regression, and detection limits: Application to gas chromatography/mass spectrometry technique". Mass spectrometry reviews 26 (1): 1–18. doi:10.1002/mas.20100. PMID 16788893.