Empirical calibration curve

Subsequently, the difference Ad(U0) (in A) is calculated from the theoretical value and the measured d value of the (1 1 0) reflection. Using the empirical calibration curve (a second- order polynomial, Eq.(6)), the pyrolusite concentration can be calculated or it may be taken from a diagram, as shown in Fig. 5. 

Theoretically, the absorbance must be proportional to concentrations, however, deviations from linearity usually take place. Therefore, it is necessary to prepare an empirical calibration curve (ECC). For this, the standard solutions of the element(s) to be determined are employed to plot the ECC from which the contents in the test solutions may be measured conveniently. 

In the text which follows we shall examine in numerical detail the decision levels and detection limits for the Fenval-erate calibration data set ( set-B ) provided by D. Kurtz (17). In order to calculate said detection limits it was necessary to assign and fit models both to the variance as a function of concentration and the response (i.e., calibration curve) as a function of concentration. No simple model (2, 3 parameter) was found that was consistent with the empirical calibration curve and the replication error, so several alternative simple functions were used to illustrate the approach for calibration curve detection limits. A more appropriate treatment would require a new design including real blanks and Fenvalerate standards spanning the region from zero to a few times the detection limit. Detailed calculations are given in the Appendix and summarized in Table V. 

Usually, the analytical chemist needs to determine the concentration of the ion of interest rather than its activity. The obvious approach to converting potentiometric measurements from activity to concentration is to make use of an empirical calibration curve, such as the one shown in Figure 5.3. Electrodes potentials of standard solutions are thus measured and plotted (on a semilog paper) versus the concentration. Since the ionic strength of the sample is seldom known, it is often useful to add a high concentration of an electrolyte to the standards and the sample to maintain approximately the same ionic strength (i.e., the same activity coefficient). The ionic strength adjustor is usually a buffer (since pH control is also desired for most ISEs). The empirical calibration plot thus yields results in terms of concentration. Theoretically,... 

Q=k/t+Q where is a constant. Generally, an empirical calibration curve is used. A tall jacketed cylinder with two fine marks, a micro-pipette delivering drops of-uniform size, and a stop-watch, are required. 

The conventional methods (Hottman and Johnson 1965 Pennebaker, 1968 Eaton, 1969) of relating velocity to pore pressure are via empirical calibration curves based on well log velocity data and in situ... 

When electrolyte concentrations are not too great, it is often useful to swamp both samples and standards with a measured excess of an inert electrolyte. The added effect of the electrolyte from the sample matrix becomes negligible under these circumstances, and the empirical calibration curve yields results in terms of concentration. This approach has been used, for example, in the potentiometric determination of fluoride ion in drinking water. Both samples and standards are diluted with a solution that contains sodium chloride, an acetate buffer, and a citrate buffer the diluent is sufficiently concentrated so that the samples and standaids have essentially identical ionic strengths. This method provides a rapid means of measuring fluoride concentrations in the part-per-million range with an accuracy of about 5% relative. 

The temperature of solid specimens in the plasma was determined by means of an infrared radiation thermometer (Infrascope Model 3-1C00, Huggins Laboratories Inc., Sunnyvale, Calif.) attached to a chart recorder. This device employs a lead sulfide detector and suitable filters to permit remote measurement of 1.2 to 2.5/x radiation emitted by the specimen. Line filters and electrostatic shielding were employed to minimize interaction of the radiofrequency field with the infrared thermometer. To compensate for variations in emissivity and inhomogeneity in the optical field, empirical calibration curves were constructed based on measurements of new and partially oxidized graphite pellets in a con-... 

Poteniiometric measurements e in he corrected to give results in terms of concentration using an empirical calibration curve such as the lower curve in Figure 2.3-17. For this approach to be successful, however, it is essential that the ionic composition of the standards approx-... 

In order to overcome these difficulties, an empirical calibration curve (value found by titrimetry a volume y) as a function of the known concentrations of the solute x is drawn. The same determination for the sample under study as those already done to construct the calibration curve is then achieved. Reporting the found value y on the curve gives the sought after value x (Fig. 7.1). 

Despite their interest, using empirical calibration curves is not recommended. A doubt always persists regarding the possible occurrence of a singularity in the... 

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