Quantitation calibration curve

The relationship between concentration and secondary measurement is not always linear. Whether it is a straight line or a curved line that describes the calibration, an equation is needed to be able to predict concentrations for future samples. A quantitative calibration curve can also be used to calculate a number of important analytical properties (sensitivity, linearity, offset or baseline, detection limit [Currie 1995]). The calibration line would be... 

It proved impossible to derive consistent area or height information from repeat runs using either visual methods, or standard peak-picking algorithms. Reliable quantitative calibration curves could only be derived from evaluation of the slope of the phase angle difference curve as a function of time at a fixed arbitrary point near the beginning of the heat evolution. 

An LC-MS method with normal pressure Cl using negative-ion mode to detect nonsteroidal antiinflammatories (NSAIDs) and acetaminophen (ACE). Ion chromatograms for each species have been identified using full-scan fragmentation spectrograms. Linear quantitative calibration curves were obtained for the concentration range of 0.05-25.0 (xg/ml. Detection limits 0.05-1.0 pg/ml. Matrix detection limits 0.05 pg/ml for phenylbutazone miz 307) ... 

A second spectrophotometric method for the quantitative determination of Pb + levels in blood gives a linear normal calibration curve for which... 

An external standardization allows a related series of samples to be analyzed using a single calibration curve. This is an important advantage in laboratories where many samples are to be analyzed or when the need for a rapid throughput of samples is critical. Not surprisingly, many of the most commonly encountered quantitative analytical methods are based on an external standardization. 

A fifth spectrophotometric method for the quantitative determination of the concentration of Pb + in blood uses a multiple-point standard addition based on equation 5.6. The original blood sample has a volume of 1.00 mb, and the standard used for spiking the sample has a concentration of 1560 ppb Pb +. All samples were diluted to 5.00 mb before measuring the signal. A calibration curve of Sjpike versus Vj is described by... 

Equations 10.4 and 10.5, which establish the linear relationship between absorbance and concentration, are known as the Beer-Lambert law, or more commonly, as Beer s law. Calibration curves based on Beer s law are used routinely in quantitative analysis. 

Quantitative Analysis for a Single Analyte The concentration of a single analyte is determined by measuring the absorbance of the sample and applying Beer s law (equation 10.5) using any of the standardization methods described in Chapter 5. The most common methods are the normal calibration curve and the method of standard additions. Single-point standardizations also can be used, provided that the validity of Beer s law has been demonstrated. 

Standardizing the Method Equations 10.32 and 10.33 show that the intensity of fluorescent or phosphorescent emission is proportional to the concentration of the photoluminescent species, provided that the absorbance of radiation from the excitation source (A = ebC) is less than approximately 0.01. Quantitative methods are usually standardized using a set of external standards. Calibration curves are linear over as much as four to six orders of magnitude for fluorescence and two to four orders of magnitude for phosphorescence. Calibration curves become nonlinear for high concentrations of the photoluminescent species at which the intensity of emission is given by equation 10.31. Nonlinearity also may be observed at low concentrations due to the presence of fluorescent or phosphorescent contaminants. As discussed earlier, the quantum efficiency for emission is sensitive to temperature and sample matrix, both of which must be controlled if external standards are to be used. In addition, emission intensity depends on the molar absorptivity of the photoluminescent species, which is sensitive to the sample matrix. 

In most quantitative analyses we are interested in determining the concentration, not the activity, of the analyte. As noted earlier, however, the electrode s response is a function of the analyte s activity. In the absence of interferents, a calibration curve of potential versus activity is a straight line. A plot of potential versus concentration, however, may be curved at higher concentrations of analyte due to changes in the analyte s activity coefficient. A curved calibration curve may still be used to determine the analyte s concentration if the standard s matrix matches that of the sample. When the exact composition of the sample matrix is unknown, which often is the case, matrix matching becomes impossible. 

The slope of the calibration curve is found to be -57.98 mV per tenfold change in the concentration of F , compared with the expected slope of-59.16 mV per tenfold change in concentration. What effect does this have on the quantitative analysis for %w/w Snp2 in the toothpaste samples ... 

Quantitative Calculations Quantitative analyses are often easier to conduct with HPLC than GC because injections are made with a fixed-volume injection loop instead of a syringe. As a result, variations in the amount of injected sample are minimized, and quantitative measurements can be made using external standards and a normal calibration curve. 

If the rate is measured at a fixed time, then both k and are constant, and a calibration curve of (rate)f versus [A]o can be used for the quantitative analysis of the analyte. 

In a quantitative flow injection analysis a calibration curve is determined by injecting standard samples containing known concentrations of analyte. The format of the caK-bration curve, such as absorbance versus concentration, is determined by the method of detection. CaKbration curves for standard spectroscopic and electrochemical methods were discussed in Chapters 10 and 11 and are not considered further in this chapter. 

This, on the one hand, reduces the detection limit so that less sample has to be applied and, thus, the amounts of interfering substanees are reduced. On the other hand, the linearity of the calibration curves can also be increased and, hence, fewer standards need to be applied and scanned in routine quantitative investigations so that more tracks are made available for sample separations. However, the introduction of a large molecular group can lead to the equalization of the chromatographic properties. 

Kinetic methods. These methods of quantitative analysis are based upon the fact that the speed of a given chemical reaction may frequently be increased by the addition of a small amount of a catalyst, and within limits, the rate of the catalysed reaction will be governed by the amount of catalyst present. If a calibration curve is prepared showing variation of reaction rate with amount of catalyst used, then measurement of reaction rate will make it possible to determine how much catalyst has been added in a certain instance. This provides a sensitive method for determining sub-microgram amounts of appropriate substances. 

To use KBr discs for quantitative measurements it is best to employ an internal standard procedure in which a substance possessing a prominent isolated infrared absorption band is mixed with the potassium bromide. The substance most commonly used is potassium thiocyanate, KSCN, which is intimately mixed and ground to give a uniform concentration, usually 0.1-0.2 per cent, in the potassium bromide. A KBr/KSCN disc will give a characteristic absorption band at 2125 cm 1. Before quantitative measurements can be carried out it is necessary to prepare a calibration curve from a series of standards made using different amounts of the pure organic compound with the KBr/KSCN. A practical application of this is given in Section 19.9. 

It should be noted that the weighed amount of KBr/KSCN is constant and that although the problem of non-quantitative transfer of powder from the ball-mill grinder still exists it affects both the carrier and the organic compound equally. When the infrared spectra for the six discs have been obtained the calibration curve is prepared by plotting the ratio of the intensity of the selected... 

To determine die diffusion current, it is necessary to subtract the residual current. This can be achieved by extrapolating the residual current prior to the wave or by recording die response of the deaerated supporting electrolyte (blank) solution. Addition of a standard or a calibration curve are often used for quantitation. Polarograms to be compared for this purpose must be recorded in the same way. 

Figure 5.60 Calibration curves for the diarrhetic shellfish poisons in (i) standard solutions in methanol (O), and (11) standard solutions in poison-free scallop extract solutions ( ) (a) pectenotoxin-6 (b) okadaic acid (c) yessotoxin (d) dinophysistoxin-1. Reprinted from J. Chromatogr., A, 943, Matrix effect and correction by standard addition in quantitative liquid chromatographic-mass spectrometric analysis of diarrhetic shellfish poisoning toxins , Ito, S. and Tsukada, K., 39-46, Copyright (2002), with permission from Elsevier Science.

It is appropriate at this juncture to illustrate the power of chemiluminescence in an analytical assay by comparing the limits of sensitivity of the fluorescence-based and the chemllumlnescence-based detection for analytes in a biological matrix. The quantitation of norepinephrine and dopamine in urine samples will serve as an illustrative example. Dopamine, norepinephrine, and 3,4-dihydroxybenzy-lamine (an internal standard) were derivatized with NDA/CN, and chemiluminescence was used to monitor the chromatography and determine a calibration curve (Figure 15). The limits of detection were determined to be less than 1 fmol injected. A typical chromatogram is shown in Figure 16. 

Verification implies that the laboratory investigates trueness and precision in particular. Elements which should be included in a full validation of an analytical method are specificity, calibration curve, precision between laboratories and/or precision within laboratories, trueness, measuring range, LOD, LOQ, robustness and sensitivity. The numbers of analyses required by the NMKL standard and the criteria for the adoption of quantitative methods are summarized in Table 10. 

Quantitation is performed by the calibration technique. A new calibration curve with anilide standard solutions is constructed for each set of analyses. The peak area or peak height is plotted against the injected amount of anilide. The injection volume (2 pL) should be kept constant as the peak area or peak height varies with the injection volume. Before each set of measurements, the GC or HPLC system should be calibrated by injection of standard solutions containing about 0.05-2 ng of anilide. Recommendation after constructing the calibration curve in advance, standard solutions and sample solutions are injected alternately for measurement of actual samples. 

Instrument calibration is done during the analysis of samples by interspersing standards among the samples. Following completion of the samples and standards, a linear calibration curve is estimated from the response of the standards using standard linear regression techniques. The calibration constants obtained from each run are used only for the samples quantitated in that run. Drastic changes or lack of linearity may indicate a problem with the detector. 

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