Calibration data hypothetical

Table 13.1. Some hypothetical analytical calibration data.

Figure 13.2 Plot of hypothetical calibration data from the results in Table 13.1.

Hypothetical calibration data showing replicate standard analyses with (a) constant and (b) nonconstant variance. 

Normal calibration plot of hypothetical data from Table 5.1. 

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

Schwartz has published some hypothetical data for the titration of a 1.02 X ICr" M solution of a monoprotic weak acid (pXa = 8.16) with 1.004 X ICr M NaOH. " A 50-mL pipet is used to transfer a portion of the weak acid solution to the titration vessel. Calibration of the pipet, however, shows that it delivers a volume of only 49.94 ml. Prepare normal, first-derivative, second-derivative, and Gran plot titration curves for these data, and determine the equivalence point for each. How do these equivalence points compare with the expected equivalence point Comment on the utility of each titration curve for the analysis of very dilute solutions of very weak acids. 

Figure E5. Influence plot for a hypothetical data set showing, E, a probable oudier F and G, questionable outliers and, H, a probable atypical but important calibration sample.

We have recently reported (1 )) the use of this technique for characterization of various compounds. Experimental data obtained for a number of compounds are shown in Figure 2. We calculated the "size factors" for a number of small molecules and oligomers. This factor is a measure of the deviation of the elution volume of a given species from the calibration curve for n-alkanes which is assigned a size factor of 1. This size factor, F, is defined to be equal to A/M, where M is the molecular weight of the compound and A is the molecular weight of a real or hypothetical n-alkane which will elute at the same retention volume as the compound. Size factors for a number of... 

Figure 4.24 Studentised residuals leverage plot to detect outlier samples on the calibration set (a) general rules displayed on a hypothetical case and (b) diagnostics for the data from the worked example (Figure 4.9, mean centred, four factors in the PLS model).

When a = 1, My = M, so that My is usually close to M, but its value depends on the parameter a, and hence one observes a range of My (as shown in the graph. Figure 3.4). However, My will approach M , only if one predicts a hypothetical value for a = -1. The parameters K and a, for each pair of polymer-solvent (at a given temperature), are found by calibrating with narrowly distributed polymer samples (fractions), for which M (prefer M ) is given. Much data can be found in handbooks. 

To illustrate the operation of some of the equations and calibration principles earlier outlined, consider the data from the following hypothetical chromatogram summarized in Table 11.1. This is for a capillary GC column, 30 m long, with a diameter of 0.25 mm, operated at a constant temperature of 200°C under a helium pressure of 20 psi above atmospheric pressure, resulting in an average linear flow rate of 31.3 cm/s. We measured the time for an unretained component to pass through the column as 1.6 min. We determined the typical number of theoretical plates on the column to be 30,000. (How would you easily measure and/or calculate these last two values ) If the column is 30 m, or 30,000 mm, long, it is trivial to see that the HETP is 1 mm. This is a very efficient column ... 

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