External standard calibration

True profile analysis requires scanning over the whole mass range for the acquisition of all data on excreted compounds. Quantitation has been more challenging on a quadrupole instrument because total ion current peaks are seldom a single component and extracted-ion chromatograms (EICs) when recovered from scanned data are of poor quality due to the lower sensitivity of scanning GC-MS. Thus, we developed profile analysis based on SIM of selected analytes but tried to ensure the components of every steroid class of interest were included. For ion traps the fundamental form of data collection (in non-MS/MS mode must be full -scans). Thus, the quantitative data produced are EICs obtained from scanned data. The EICs are of the same ions used for SIM in quadrupole instruments and the calibration external standards are the same. 

Prerequisites for the Calibration Types. It depends on the design of the analytical procedure as to which regression parameters are meaningful and which results are acceptable. In other words, the model to be used for quantitation must be justified. For a singlepoint calibration (external standardization), a linear function, zero intercept, and the homogeneity of variances are required. The prerequisites for a linear multiple-point calibration are a linear function and in case of an unweighted calibration also the homogeneity of variances. A non-linear calibration requires only a continuous function. With respect to the 100%... 

Three primary methods are used for calibration external standard calibration, internal standard calibration, and standard addition. Figs. 1-3 show the typical response curves for each method. 

The most commonly used quantification methods in purge and trap are external standard calibration and internal standard calibration. External standards refer to target compounds of known concentrations that are prepared and analyzed separately from the samples. A calibration curve or calibration factor (CF) is obtained by plotting the peak area count (or height) of the analyte versus its concentration in the standards. The analyte concentration in the sample is equal to its peak area divided by the CF. External standard calibration works well for relatively clean samples where matrix has no or little effects on analyte recovery. 

Calibration External standard Based on 1L samples from a SUMMA... 

Calibration External standard Range 0.10-4.00 mg/L, matrix spike... 

Calibration External standard Target compounds spiked into blank samples... 

A calibration curve prepared using several external standards. 

Colorplate i shows an example of a set of external standards and their corresponding normal calibration curve. 

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. 

Since a standard additions calibration curve is constructed in the sample, it cannot be extended to the analysis of another sample. Each sample, therefore, requires its own standard additions calibration curve. This is a serious drawback to the routine application of the method of standard additions, particularly in laboratories that must handle many samples or that require a quick turnaround time. For example, suppose you need to analyze ten samples using a three-point calibration curve. For a normal calibration curve using external standards, only 13 solutions need to be analyzed (3 standards and 10 samples). Using the method of standard additions, however, requires the analysis of 30 solutions, since each of the 10 samples must be analyzed three times (once before spiking and two times after adding successive spikes). 

The method of standard additions can be used to check the validity of an external standardization when matrix matching is not feasible. To do this, a normal calibration curve of Sjtand versus Cs is constructed, and the value of k is determined from its slope. A standard additions calibration curve is then constructed using equation 5.6, plotting the data as shown in Figure 5.7(b). The slope of this standard additions calibration curve gives an independent determination of k. If the two values of k are identical, then any difference between the sample s matrix and that of the external standards can be ignored. When the values of k are different, a proportional determinate error is introduced if the normal calibration curve is used. 

Using the Regression Equation Once the regression equation is known, we can use it to determine the concentration of analyte in a sample. When using a normal calibration curve with external standards or an internal standards calibration curve, we measure an average signal for our sample, Yx, and use it to calculate the value of X... 

The equation for a normal calibration curve using external standards is... 

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. 

Samples of car exhaust are collected using a 4-L glass bottle evacuated to a level of less than 2 torr. A normal calibration curve using external standards of known Pco is used to determine the Pco in the exhaust samples. 

In the absence of Fe +, the membrane is colorless, but when immersed in a solution of Fe + and C, the membrane develops a red color as a result of the formation of a Fe +-bathophenanthroline complex. A calibration curve determined using a set of external standards with known molar concentrations of Fe + gave a standardization relationship of... 

The purity of a sample of K3Fe(CN)6 was determined using linear-potential scan hydrodynamic voltammetry at a glassy carbon electrode using the method of external standards. The following data were obtained for a set of calibration standards. 

Calibration curves are usually constructed by analyzing a series of external standards and plotting the detector s signal as a function of their known concentrations. As long as the injection volume is identical for every standard and sample, calibration curves prepared in this fashion give both accurate and precise results. Unfortunately, even under the best of conditions, replicate injections may have volumes that differ by as much as 5% and often may be substantially worse. For this... 

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. 

Janusa and co-workers report the determination of chloride by CZE. Analysis of a series of external standards gives the following calibration curve. 

Curve-Fitting Methods In the direct-computation methods discussed earlier, the analyte s concentration is determined by solving the appropriate rate equation at one or two discrete times. The relationship between the analyte s concentration and the measured response is a function of the rate constant, which must be measured in a separate experiment. This may be accomplished using a single external standard (as in Example 13.2) or with a calibration curve (as in Example 13.4). 

Color plate i shows ai external standards and th normal calibration ci... 

External standard method (linear calibration curve of peak areas)... 

In many cases when methods involve internal or external standards, the solutions used to construct the calibration graph are made up in pure solvents and the signal intensities obtained will not reflect any interaction of the analyte and internal standard with the matrix found in unknown samples or the effect that the matrix may have on the performance of the mass spectrometer. One way of overcoming this is to make up the calibration standards in solutions thought to reflect the matrix in which the samples are found. The major limitation of this is that the composition of the matrix may well vary widely and there can be no guarantee that the matrix effects found in the sample to be determined are identical to those in the calibration standards. 

A matrix extract was prepared from poison-free scallop and spiked at the level of 200 ngg of scallop hepatopancreas. The toxins were determined by using LC-MS with calibration employing external standards prepared in methanol. The matrix extract was then spiked further with 300 ngg of each of the toxins and redetermined. The results obtained for each analyte are summarized in Table 5.17 and show that, when using the external calibration method, the values obtained range from 138 to 170 ngg a reduction in accuracy of between 15... 

The amounts of EMA and HEMA (derivatized as MEMA) are determined based upon external standard calibration. A nonweighted linear least-squares estimate of... 

The amount of NIPA is determined based upon external standard calibration. A non-weighted linear least-squares estimate of the calibration curve is used to calculate the amount of NIPA in the unknowns. The response of any given sample must not exceed the response of the most concentrated standard. If this occurs, dilution of the sample will be necessary. 

The concentration of the analyte in the injected sample is determined based on the height or area of the analyte peak and interpolation of the internal or external standard linear calibration curve according to the following equation ... 

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