Curve calibration

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. 

The calibration curve of each rosetta strain gauge was so obtained and ftg.5 shows the sum of the principal stresses at the measuring points versus pressure inside the vessel. Further tests were carried out to obtain the calibration factor and to check that it remained constant on the whole scan area of the test surface. This was achieved through additional measurements using the SPATE system on fixed points on the surface located very close to the applied rosetta strain gauges. This procedure gave the following results ... 

Fig. 6 Error of measuring limit length crack depth by using calibration curve for infinitely long crack.

Fig. 7 Error of measuring crack depth in plate by using calibration curve for crack in half space.

A measurement procedure has been developed that allows to determine the mass of the inclusions as well as their locations with respect to radius, angle, and depth (2). For the depth determination use is made of the approximate 1/R dependence of the magnetic field strength from the distance R to the inclusion When in a first measurement at a small lift off an inclusion is detected, the measurement is repeated at an increased lift off From the signal ratio the depth can be calculated or seen from a diagram like fig. 5a which was generated experimentally. After that, from calibration curves like fig. 5b the absolute value of the signal leads to the mass of the inclusion. 

Repeat the boiling point determination with the following pure liquids (a) carbon tetrachloride, A.R. (77°) (6) ethylene dibromide (132°) or chlorobenzene (132°) (c) aniline, A.R. (184-6°) and (d) nitrobenzene, A.R. (211°). An air condenser should be used for (c) and (d). Correct the observed boiling points for any appreciable deviation from the normal pressure of 760 mm. Compare the observed boiling points with the values given in parentheses and construct a calibration curve for the thermometer. Compare the latter with the curve obtained from melting point determinations (Section 111,1). 

In addition to the orthodox method, just described, for the determination of the boiling points of liquids, the student should determine the boiling points of small volumes (ca. 0 5 ml.) by Siwolobofifs method. Full details are given iri Section 11,12. Determine the boiling points of the pure liquids listed in the previous paragraph. Observe the atmospheric pressure and if this differs by more than 5 mm. from 760 mm., correct the boiling point with the aid of Table II,9,B. Compare the observed boiling points with the accepted values, and draw a calibration curve for the thermometer. 

Determination of melting points (a-naphthylamine, a-naphthol, benzoic acid, succinic acid and p-nitrobenzoic acid). Use the apparatus shown in Fig. II, 10, 2, a. Construction of calibration curve for thermometer. Determination of m.p. of unknown compound. 

Determination of boiling points. Distillation method (Fig. II, 12, 1) for carbon tetrachloride (25 nil. distillation flask and small water condenser), and SiwoloboflF s method (Fig. II, 12, 2) for carbon tetrachloride, aniline and nitrobenzene. Calibration curve for thermometer. Determination of b.p. of unknown liquid. 

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

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. 

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... 

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. 

Examples of calibration curves for the method of standard additions. In (a) the signal is plotted versus the volume of the added standard, and in (b) the signal is plotted versus the concentration of the added standard after dilution. 

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... 

Figure 5.7(b) shows the relevant relationships when Sspike is plotted versus the concentrations of the spiked standards after dilution. Standard addition calibration curves based on equation 5.8 are also possible. 

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. 

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-... 

When the internal standard s concentration cannot be held constant the data must be plotted as (SA/Sis)stand versus Ca/Cis, giving a linear calibration curve with a slope of K. 

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. 

C.I Linear Regression of Straight-Line Calibration Curves... 

---