Normal calibration curve

Examples of (a) straight-line and (b) curved normal calibration curves. 

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

Effect of the sample s matrix on a normal calibration curve. 

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

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. 

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. 

Normal calibration curve for the hypothetical data in Table 5.1, showing the regression line. 

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... 

Weighted normal calibration curve for the data in Example 5.13. The lines through the data points show the standard deviation of the signal for the standards. These lines have been scaled by a factor of 50 so that they can be seen on the same scale as the calibration curve. 

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. 

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. 

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. 

The amount of caffeine in an analgesic tablet was determined by HPLC using a normal calibration curve. Standard solutions of caffeine were prepared and analyzed using a lO-pL fixed-volume injection loop. Results for the standards are summarized in the following table. 

Provide an SOP for the determination of cadmium in lake sediments by atomic absorption spectrophotometry using a normal calibration curve. 

An example of the determination of sodium in blood by flame spectrometry using lithium as an internal standard IS shown in Figure M2. The upper figure shows tlic normal calibration curve of sodium intensity versus sodium concentration in ppm, Although a fairly linear plot is obtained, quite a bit of scatter is observed, fhe lower plot shows the intensity ratio of sodium to lithium plotted against the sodium concentration in ppm. Note the improvemem in the calibration curve when the interna standard is used. 

The selectivity of a column [Eq. (8.11)] depends on the fraction of the column volume occupied by pores s, and the inverse slope of the normalized calibration curve ... 

The normal calibration curve is asymptotic to the value of (B), which represents the transmission of unabsorbed light. Unabsorbed light may be due to straylight or non-absorbing lines from the radiation source (cathode material or filler gas) which pass within the spectral bandwidth of the monochromator. The slope of the calibration graph is also dependent on the ratio of the half-widths of the emission line (zt e) and absorption line w (i) The curve is linear when wjw < l/5 (ii) The curve is slightly curved when /b < wjw < / (hi) The initial slope starts to decrease when > 1/1 ... 

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