Calibration curve analysis

The choice between X-ray fluorescence and the two other methods will be guided by the concentration levels and by the duration of the analytical procedure X-ray fluorescence is usually less sensitive than atomic absorption, but, at least for petroleum products, it requires less preparation after obtaining the calibration curve. Table 2.4 shows the detectable limits and accuracies of the three methods given above for the most commonly analyzed metals in petroleum products. For atomic absorption and plasma, the figures are given for analysis in an organic medium without mineralization. 

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). 

Standardizations using a single standard are common, but also are subject to greater uncertainty. Whenever possible, a multiple-point standardization is preferred. The results of a multiple-point standardization are graphed as a calibration curve. A linear regression analysis can provide an equation for the standardization. 

Construct an appropriate standard additions calibration curve, and use a linear regression analysis to determine the concentration of analyte in the original sample and its 95% confidence interval. 

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. 

Chemical Limitations to Beer s Law Chemical deviations from Beer s law can occur when the absorbing species is involved in an equilibrium reaction. Consider, as an example, an analysis for the weak acid, HA. To construct a Beer s law calibration curve, several standards containing known total concentrations of HA, Cmt, are prepared and the absorbance of each is measured at the same wavelength. Since HA is a weak acid, it exists in equilibrium with its conjugate weak base, A ... 

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. 

Sensitivity The sensitivity of a molecular absorption analysis is equivalent to the slope of a Beer s-law calibration curve and is determined by the product of the analyte s absorptivity and the pathlength of the sample cell. Sensitivity is improved by selecting a wavelength when absorbance is at a maximum or by increasing the pathlength. 

Sensitivity Sensitivity in flame atomic emission is strongly influenced by the temperature of the excitation source and the composition of the sample matrix. Normally, sensitivity is optimized by aspirating a standard solution and adjusting the flame s composition and the height from which emission is monitored until the emission intensity is maximized. Chemical interferences, when present, decrease the sensitivity of the analysis. With plasma emission, sensitivity is less influenced by the sample matrix. In some cases, for example, a plasma calibration curve prepared using standards in a matrix of distilled water can be used for samples with more complex matrices. 

In the process of performing a spectrophotometric determination of Ee, an analyst prepares a calibration curve using a single-beam spectrometer, such as a Spec-20. After preparing the calibration curve, the analyst drops the cuvette used for the method blank and the standards. The analyst acquires a new cuvette, measures the absorbance of the sample, and determines the %w/w Ee in the sample. Will the change in cuvette lead to a determinate error in the analysis Explain. 

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 ... 

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

The next step is to show that the response for the analysis of any target compound is linear. This step is known as the initial calibration and is achieved by the analysis of standards for a series of specified concentrations to produce a five-point calibration curve (Figure 41.2a, b). On subsequent days, a continuing calibration must be performed on calibration check compounds to evaluate the calibration precision of the GC/MS system. 

Figure 6.21 shows the calibration curves of the SB-800 HQ series using standard pullulan. Because a high molecular weight standard sample is not available, the calibration curves of 805 and 806 are partly estimates (dotted lines). The difference in the conformation between polyethylene oxide (PEO) and pullulan in the solvent causes a shift of the calibration curves of pullulan slightly higher than those of PEO. The OHpak SB-800HQ series is better suited for the analysis of hydrophilic samples than the Asahipak GS/GE series. 

The linear column (PSS SDV 5 /mm linear) has a wider molar mass fractionation range while keeping the analysis time roughly the same. Therefore the slope of the calibration curve is much steeper and the resolution will be poorer in this case. The second column with a single pore size (PSS SDV 5 /mm 1000 A) separates only below 50,000 Da, but does this very efficiently in the same time. 

For proteins, the most useful columns are those with pores of 100-500 A, as seen in Fig. 10.2, because most proteins elute on the linear portions of the calibration curves. Figure 10.5 illustrates an analysis of a protein mixture on SynChropak GPC100. Small peptides can be analyzed on the 50-A SynChro-pak GPC Peptide column with appropriate mobile-phase modifications. Many peptides have poor solubility in mobile phases standardly used for protein analysis, as discussed later in this chapter. 

The use of hexafluoroisopropanol (HFIP) as an SEC eluent has become popular for the analysis of polyesters and polyamides. Conventional PS/DVB-based SEC columns have been widely used for HFIP applications, although the relatively high polarity of HFIP has led to some practical difficulties (1) the SEC calibration curve can exhibit excessive curvature, (2) polydisperse samples can exhibit dislocations or shoulders on the peaks, and (3) low molecular weight resolution can be lost, causing additive/system peaks to coelute with the low molecular weight tail of the polymer distribution... 

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. 

An alternative elution technique is to transfer the powder (e.g. for bromophenol blue) to a glass column fitted with a glass-wool plug or glass sinter, and elute the dye with ethanol containing a little ammonia. The eluted solution, made up to a fixed volume in a small graduated flask, may be used for colorimetric/ spectrophotometric analysis of the recovered dye (see Chapter 17). A calibration curve must, of course, be constructed for each of the individual compounds. 

The procedure comprises the addition of a constant amount of internal standard to a fixed volume of several synthetic mixtures which contain varying known amounts of the component to be determined. The resulting mixtures are chromatographed and a calibration curve is constructed of the percentage of component in the mixtures against the ratio of component peak area/standard peak area. The analysis of the unknown mixture is carried out by addition of the same amount of internal standard to the specified volume of the mixture from the observed ratio of peak areas the solute concentration is read off using the calibration curve. 

Protein concentration can be determined using a method introduced by Bradford,4 which utilises Pierce reagent 23200 (Piece Chemical Company, Rockford, IL, USA) in combination with an acidic Coomassie Brilliant Blue G-250 solution to absorb at 595 nm when the reagent binds to the protein. A 20 mg/1 bovine serum albumin (Piece Chemical Company, Rockford, IL, USA) solution will be used to prepare a standard calibration curve for determination of protein concentration. The sample for analysis of SCP is initially homogenised or vibrated in a sonic system to break down the cell walls. 

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.

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