Concentration of analyte

The detection limits in the table correspond generally to the concentration of analyte required to give a net signal equal to three times the standard deviation of the background in accordance with lUPAC recommendations. 

Since equimolar concentrations of analyte and interferent were used (Ca = Cl), we have... 

Another way to narrow the choice of methods is to consider the scale on which the analysis must be conducted. Three limitations of particular importance are the amount of sample available for the analysis, the concentration of analyte in the sample, and the absolute amount of analyte needed to obtain a measurable signal. The first and second limitations define the scale of operations shown in Figure 3.6 the last limitation positions a method within the scale of operations. ... 

Diagonal lines connecting the two axes show combinations of sample size and concentration of analyte containing the same absolute amount of analyte. As shown in Figure 3.6, for example, a 1-g sample containing 1% analyte has the same amount of analyte (0.010 g) as a 100-mg sample containing 10% analyte or a 10-mg sample containing 100% analyte. 

Concentration methods frequently have both lower and upper limits for the amount of analyte that can be determined. The lower limit is dictated by the smallest concentration of analyte producing a useful signal and typically is in the parts per million or parts per billion concentration range. Upper concentration limits exist when the sensitivity of the analysis decreases at higher concentrations. 

A material available from the National Institute of Standards and Technology certified to contain known concentrations of analytes. 

Effect of a constant determinate error on the reported concentration of analyte. 

A method s detection limit is the smallest amount or concentration of analyte that can be detected with statistical confidence. The International Union of Pure and Applied Chemistry (lUPAC) defines the detection limit as the smallest concentration or absolute amount of analyte that has a signal significantly larger than the signal arising from a reagent blank. Mathematically, the analyte s signal at the detection limit, (Sa)dl, is... 

The simplest way to determine the value of k in equation 5.2 is by a singlepoint standardization. A single standard containing a known concentration of analyte, Cs, is prepared and its signal, Sjtand) is measured. The value of k is calculated as... 

Example showing how an improper use of a single-point standardization can lead to a determinate error in the reported concentration of analyte. 

The most commonly employed standardization method uses one or more external standards containing known concentrations of analyte. These standards are identified as external standards because they are prepared and analyzed separately from the samples. 

A quantitative determination using a single external standard was described at the beginning of this section, with k given by equation 5.3. Once standardized, the concentration of analyte, Ca, is given as... 

Equation 5.7 can be solved for the concentration of analyte in the original sample. 

The successful application of an external standardization or the method of standard additions, depends on the analyst s ability to handle samples and standards repro-ducibly. When a procedure cannot be controlled to the extent that all samples and standards are treated equally, the accuracy and precision of the standardization may suffer. For example, if an analyte is present in a volatile solvent, its concentration will increase if some solvent is lost to evaporation. Suppose that you have a sample and a standard with identical concentrations of analyte and identical signals. If both experience the same loss of solvent their concentrations of analyte and signals will continue to be identical. In effect, we can ignore changes in concentration due to evaporation provided that the samples and standards experience an equivalent loss of solvent. If an identical standard and sample experience different losses of solvent. 

A single-point internal standardization has the same limitations as a singlepoint normal calibration. To construct an internal standard calibration curve, it is necessary to prepare several standards containing different concentrations of analyte. These standards are usually prepared such that the internal standard s concentration is constant. Under these conditions a calibration curve of (SA/Sis)stand versus Ca is linear with a slope of K/Cis-... 

Table 5.2 demonstrates how an uncorrected constant error affects our determination of k. The first three columns show the concentration of analyte, the true measured signal (no constant error) and the true value of k for five standards. As expected, the value of k is the same for each standard. In the fourth column a constant determinate error of +0.50 has been added to the measured signals. The corresponding values of k are shown in the last column. Note that a different value of k is obtained for each standard and that all values are greater than the true value. As we noted in Section 5B.2, this is a significant limitation to any single-point standardization. 

How do we find the best estimate for the relationship between the measured signal and the concentration of analyte in a multiple-point standardization Figure 5.8 shows the data in Table 5.1 plotted as a normal calibration curve. Although the data appear to fall along a straight line, the actual calibration curve is not intuitively obvious. The process of mathematically determining the best equation for the calibration curve is called regression. 

A calibration curve shows us the relationship between the measured signal and the analyte s concentration in a series of standards. The most useful calibration curve is a straight line since the method s sensitivity is the same for all concentrations of analyte. The equation for a linear calibration curve is... 

Equations 5.13 and 5.14 are written in terms of the general variables x and y. As you work through this example, remember that x represents the concentration of analyte in the standards (Cs), and that y corresponds to the signal (Sjneas)- We begin by setting up a table to help in the calculation of the summation terms Ex , Ey , Ex, and Exy which are needed for the calculation of bo and bi... 

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... 

Three replicate determinations are made of the signal for a sample containing an unknown concentration of analyte, yielding values of 29.32, 29.16, and 29.51. Using the regression line from Examples 5.10 and 5.11, determine the analyte s concentration, Ca, and its 95% confidence interval. 

That all four methods give a different result for the concentration of analyte underscores the importance of choosing a proper blank but does not tell us which of the methods is correct. In fact, the variation within each method for the reported concentration of analyte indicates that none of these four methods has adequately corrected for the blank. Since the three samples were drawn from the same source, they must have the same true concentration of analyte. Since all four methods predict concentrations of analyte that are dependent on the size of the sample, we can conclude that none of these blank corrections has accounted for an underlying constant source of determinate error. 

Three replicate determinations of the signal for a standard solution of an analyte at a concentration of 10.0 ppm give values of 0.163, 0.157, and 0.161 (arbitrary units), respectively. The signal for a method blank was found to be 0.002. Calculate the concentration of analyte in a sample that gives a signal of 0.118. 

II. 5 (arbitrary units). A second 50-mL aliquot of the sample, which is spiked with 1.00-mL of a 10.0-ppm standard solution of the analyte, gives a signal of 23.1. What is the concentration of analyte in the original sample ... 

A standard sample was prepared containing 10.0 ppm of an analyte and 15.0 ppm of an internal standard. Analysis of the sample gave signals for the analyte and internal standard of 0.155 and 0.233 (arbitrary units), respectively. Sufficient internal standard was added to a sample to make it 15.0 ppm in the internal standard. Analysis of the sample yielded signals for the analyte and internal standard of 0.274 and 0.198, respectively. Report the concentration of analyte in the sample. 

To determine the concentration of analyte in a sample, a standard additions was performed. A 5.00-mL portion of the sample was analyzed and then successive 0.10-mL spikes of a 600.0-ppb standard of the analyte... 

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. 

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