Calibration curve - wikipedia Calibration curve hide This article has multiple issues. Please help improve it or discuss these issues on the talk page. ( Learn how and when to remove these template messages ) This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. ( October 2008 ) This article 's lead section may be too long for the length of the article. Please help by moving some material from it into the body of the article. Please read the layout guide and lead section guidelines to ensure the section will still be inclusive of all essential details. Please discuss this issue on the article 's talk page. ( November 2017 ) This article may be in the wrong category or belong in further categories. Please re-categorize this article to list it with similar topics or add further categories if required. If you are satisfied that the article is in the correct category please remove this tag. ( November 2017 ) A calibration curve plot showing limit of detection ( LOD ), limit of quantification ( LOQ ), dynamic range, and limit of linearity ( LOL ). In analytical chemistry, a calibration curve, also known as a standard 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. A calibration curve is one approach to the problem of instrument calibration ; other standard approaches may mix the standard into the unknown, giving an internal standard. The calibration curve is a plot of how the instrumental response, the so - called analytical signal, changes with the concentration of the analyte ( the substance to be measured ). The operator prepares a series of standards across a range of concentrations near the expected concentration of analyte in the unknown. The concentrations of the standards must lie within the working range of the technique ( instrumentation ) they are using. Analyzing each of these standards using the chosen technique will produce a series of measurements. For most analyses a plot of instrument response vs. concentration will show 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. Contents 1 General use 2 Error in calibration curve results 3 Applications 4 Notes 5 Bibliography 6 References General use In more general use, a calibration curve is a curve or table for a measuring instrument which measures some parameter indirectly, giving values for the desired quantity as a function of values of sensor output. For example, a calibration curve can be made for a particular pressure transducer to determine applied pressure from transducer output ( a voltage ). Such a curve is typically used when an instrument uses a sensor whose calibration varies from one sample to another, or changes with time or use ; if sensor output is consistent the instrument would be marked directly in terms of the measured unit. The data - the concentrations of the analyte and the instrument response for each standard - can be fit to a straight line, using linear regression analysis. This yields a model described by the equation y = mx + y, where y is the instrument response, m represents the sensitivity, and y is a constant that describes the background. The analyte concentration ( x ) of unknown samples may be calculated from this equation. Many different variables can be used as the analytical signal. For instance, chromium ( III ) might be measured using a chemiluminescence method, in an instrument that contains a photomultiplier tube ( PMT ) as the detector. The detector converts the light produced by the sample into a voltage, which increases with intensity of light. The amount of light measured is the analytical signal. Most analytical techniques use a calibration curve. There are a number of advantages to this approach. First, the calibration curve provides a reliable way to calculate the uncertainty of the concentration calculated from the calibration curve ( using the statistics of the least squares line fit to the data ). Second, the calibration curve provides data on an empirical relationship. The mechanism for the instrument 's response to the analyte may be predicted or understood according to some theoretical model, but most such models have limited value for real samples. ( 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, by analysis of one or more reference standards ; a calibration curve is a convenient extension of this approach. The calibration curve for a particular analyte in a particular ( type of ) sample provides the empirical relationship needed for those particular measurements. The chief disadvantages are ( 1 ) that the standards require a supply of the analyte material, preferably of high purity and in known concentration, and ( 2 ) that the standards and the unknown are in the same matrix. Some analytes - e.g., particular proteins - are extremely difficult to obtain pure in sufficient quantity. Other analytes are often in complex matrices, e.g., heavy metals in pond water. In this case, the matrix may interfere with or attenuate the signal of the analyte. Therefore, a comparison between the standards ( which contain no interfering compounds ) and the unknown is not possible. The method of standard addition is a way to handle such a situation. Error in calibration curve results As expected, the concentration of the unknown will have some error which can be calculated from the formula below. This formula assumes that a linear relationship is observed for all the standards. It is important to note that the error in the concentration will be minimal if the signal from the unknown lies in the middle of the signals of all the standards ( the term y u n k − y  ̄ ( displaystyle y_ ( unk ) - ( \bar ( y ) ) ) goes to zero if y u n k = y  ̄ ( displaystyle y_ ( unk ) = ( \bar ( y ) ) ) ) s x = s y m 1 n + 1 k + ( y u n k − y  ̄ ) 2 m 2 ∑ ( x i − x  ̄ ) 2 ( displaystyle s_ ( x ) = ( \frac ( s_ ( y ) ) ( m ) ) ( sqrt ( ( \frac ( 1 ) ( n ) ) + ( \frac ( 1 ) ( k ) ) + ( \frac ( ( y_ ( unk ) - ( \bar ( y ) ) ) ^ ( 2 ) ) ( m ^ ( 2 ) sum ( ( x_ ( i ) - ( \bar ( x ) ) ) ^ ( 2 ) ) ) ) ) ) ) s y ( displaystyle s_ ( y ) ) is the standard deviation in the residuals = ∑ ( y i − m x i − b ) 2 n − 2 ( displaystyle = ( sqrt ( \frac ( sum ( ( y_ ( i ) - mx_ ( i ) - b ) ) ^ ( 2 ) ) ( n - 2 ) ) ) ) m ( displaystyle m ) is the slope of the line b ( displaystyle b ) is the y - intercept of the line n ( displaystyle n ) is the number of standards k ( displaystyle k ) is the number of replicate unknowns y u n k n o w n ( displaystyle y_ ( unknown ) ) is the measurement of the unknown y  ̄ ( displaystyle ( \bar ( y ) ) ) is the average measurement of the standards x i ( displaystyle x_ ( i ) ) are the concentrations of the standards x  ̄ ( displaystyle ( \bar ( x ) ) ) is the average concentration of the standards 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 This section is empty. You can help by adding to it. ( January 2018 ) Bibliography Harris, Daniel Charles ( 2003 ). Quantitative chemical analysis. San Francisco : W.H. Freeman. ISBN 0 - 7167 - 4464 - 3. Skoog, Douglas A. ; Holler, F. James ; Crouch, Stanley R. ( 2007 ). Principles of Instrumental Analysis. Pacific Grove : Brooks Cole. p. 1039. 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. Bibcode : 2007MSRv... 26... 1L. doi : 10.1002 / mas. 20100. PMID 16788893. Analytical chemistry Instrumentation Atomic absorption spectrometer Flame emission spectrometer Gas chromatograph High - performance liquid chromatograph Infrared spectrometer Mass spectrometer Melting point apparatus Microscope Spectrometer Spectrophotometer Techniques Calorimetry Chromatography Electroanalytical methods Gravimetric analysis Mass spectrometry Spectroscopy Sampling Coning and quartering Dilution Dissolution Filtration Masking Pulverization Sample preparation Separation process Sub-sampling Calibration Chemometrics Calibration curve Matrix effect Internal standard Standard addition Isotope dilution Prominent publications Analyst Analytica Chimica Acta Analytical and Bioanalytical Chemistry Analytical Chemistry Analytical Biochemistry Chemistry References Jump up ^ `` Worksheet for analytical calibration curve ''. umd.edu. Jump up ^ http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM070107.pdf Jump up ^ ASTM : Static Calibration of Electronic Transducer - Based Pressure Measurement Systems Example of calibration curve for instrumentation. Jump up ^ The details for this procedure may be found in D.A. Skoog ; et al. ( 2006 ). Principles of Instrumental Analysis., as well as many other textbooks. Jump up ^ `` Statistics in Analytical Chemistry - Regression ( 6 ) ''. utoronto.ca. 4 September 2008. Jump up ^ http://alpha.chem.umb.edu/chemistry/ch361/Salter%20jchem%20ed%201.pdf Retrieved from `` https://en.wikipedia.org/w/index.php?title=Calibration_curve&oldid=830162166 '' Categories : Analytical chemistry Hidden categories : Articles lacking in - text citations from October 2008 All articles lacking in - text citations Wikipedia introduction cleanup from November 2017 All pages needing cleanup Articles covered by WikiProject Wikify from November 2017 All articles covered by WikiProject Wikify Articles with multiple maintenance issues Category needs checking Articles to be expanded from January 2018 All articles to be expanded Articles with empty sections from January 2018 All articles with empty sections Articles using small message boxes Talk Contents About Wikipedia Català Español Bahasa Indonesia Nederlands 日本 語 Română Edit links This page was last edited on 13 March 2018, at 03 : 34. 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Question: what is the purpose of constructing a calibration curve
Answer: determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration