Standard multiple additions

Cx = (CsFo//xF3)(1-10- ) = Ac (1-10- ) (ASM). (5.20) The double and multiple addition methods are introduced in an attempt further to improve the measuring precision, because with three or more experimental potential values the slope value S need not be knowa Under the same assumptions and with the same symbols as above, provided the same volumes are always added, it holds for the nth addition of the determinand standard solution that... 

In potentiometry with ISEs, however, the second Gran method [46] has found especially wide use, not only in titrations, but also in multiple addition methods in general. In these methods, the concentration of the test substance is plotted against the volume of the titrant or of the standard solution and thus the curve is linearized. The end-point in the titration or the determinand concentration in a multiple addition method is found as the intercept of the straight line with the volume axis. Linearization is attained by taking the antilogarithm of the Nernst equation ... 

In the method of standard additions, a known amount of a standard solution of analyte is added to one portion of the sample. The responses before and after the addition are measured and used to obtain the analyte concentration. Alternatively, multiple additions are made to several portions of the sample. The standard additions method assumes a linear response. This should always be confirmed or the multiple additions method used to check linearity. 

We use the method of standard additions when it is difficult or impossible to duplicate the sample matrix. In general, the sample is spiked with a known amount or amounts of a standard solution of the analyte. In the single-point standard addition method, two portions of the sample are taken. One portion is measured as usual, but a known amount of standard analyte solution is added to the second portion. The responses for the two portions are then used to calculate the unknown concentration, assuming a linear relationship between response and analyte concentration (see Example 8-8). In the multiple additions method, additions of known amounts of standard analyte solution are made to several portions of the sample, and a multiple additions cahbration eurve is obtained. The multiple additions method gives some... 

The method of standard additions is quite powerful when used properly. First, there must be a good blank measurement so that extraneous species do not contribute to the analytical response. Second, the calibration curve for the analyte must be linear in the sample matrix. The multiple additions method provides a check on this assumption. A significant disadvantage of the multiple additions method is the extra time required for making the additions and measurements. The major benefit... 

The standard-addition method (see Section 8C-3) involves determining the potential of the electrode system before and after a measured volume of a standard has been added to a known volume of the analyte solution. Multiple additions can also be made. Often, an excess of an electrolyte is incorporated into the analyte solution at the outset to prevent any major shift in ionic strength that might accompany the addition of standard. It is also necessary to assume that the junction potential remains constant during the measurements. 

The standard addition method can take several forms as discussed in Section 8C-3 the single-point method was described in Example 8-8. The multiple additions method is often chosen for photometric or spectrophotometric analyses, and this method will be described here. This technique involves adding several increments of a standard solution to sample aliquots of the same size. Each solution is then diluted to a fixed volume before measuring its absorbance. When the amount of sample is limited, standard additions can be carried out by successive addition of increments of the standard to a single measured aliquot of the unknown. The measurements are made on the original solution and after each addition of standard analyte. This procedure is often more convenient for voltammetry. 

In this approach, small volumes (v or 2v or 3v etc.) of a concentrated standard are added to separate aliquots of the sample of volume V. After thorough mixing, the difference in absorbance between the amended sample and the unamended sample must have resulted from the added standard. Moreover, those interferences which modify the instrument response to the analj e in the sample will influence the added standard in identical fashion (see below). If the absorbance of sample itself and of each of the amended solutions are plotted versus the amount of added standard, a cahbration curve is obtained which does not pass though the origin but rather cuts the absorbance axis at some positive value (absorbance of the sample without added standard). Extrapolation of the cahbration curve back to the concentration axis provides a measure of the analyte originally present in the sample. However, the absorbance of each amended solution must be volume corrected (i.e., after one addition of standard, the observed absorbance Ai is multiplied by (V + lv)AT, after two additions the observed absorbance A2 is multiplied by (V + 2v)A etc.). The use of multiple additions demonstrates that, within the concentration range of interest, absorbance varies linearly with analyte concentration. 

Standard addition is a useful calibration method when the sample matrix cannot be reproduced well enough to prepare standard solutions for calibration. The sample itself is used to prepare calibration standards by addition of known amounts of the analyte to three or more aliquots of the sample. The amount of added standard should cover a range of about 10-100% of the sample concentration. When the instrument response is plotted against the concentration added, the sample concentration is determined by calculating the absolute value of the x intercept. See Fig. 2. This technique is often used in conjunction with internal standards, where the instrument response is then the ratio of the analyte to internal standard response. This is a very good reference method to cross-check a primary method. It is rarely used for routine analysis of multiple samples because each test article requires multiple sample preparations and analyses. 

Heat of atomization has been carefully studied experimentally and has been shown to be an additive property. For alkanes, using standard multiple linear regression statistics, it is possible to obtain a QSAR equation which possesses very good statistics. ... 

If the actual slope for the electrode is not known, then multiple additions of the standard should be made to determine the acmal shape. 

The choice of quantification in headspace analysis therefore depends on the sample and the analyte. Procedures include total vaporization, the use of matrix-matched standards, multiple extractions, and standard additions. A method using an internal standard may be used provided knowledge of the equiH-brium constants for the standard and the analyte can be determined. 

A close examination of the dotted curve and the saved output file shows that the fitted curve does not go exactly through the origin (the 0,0) point. The value is close to zero so the fit might be acceptable and no further improvement would be needed. However, in cases such as this where it is know that the curve should go through a particular point, the datafitQ function provides additional flexibility. As seen in Listing 7.16 a second parameter can be passed to the datafitQ function in addition to the y,x data. This second parameter can have one of two forms. The first and simplest form is simply a number which will be used as the number of interpolation points used in the data fit. This is useful when the standard multiple of 10 data points per interpolation point does not produce a good curve. With this parameter the user can experiment with varying numbers of interpolation data... 

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... 

Combine the modified probabilities to give the overall error probabilities for the task. The combination rules for obtaining the overall error probabilities follow the same addition and multiplication processes as for standard event trees (see last section). 

In addition, when installing multiple belts, it is imperative that the slack side of each belt be on the same side, either top or bottom. Tables 58.2 and 58.3 show the minimum movement below and above the standard center distance required between the pulleys. This movement allows the center distance to be shortened for new belt installation. It also allows the center distance to be increased to take up the slack and to maintain proper tension as the belt stretches (Figure 58.6). 

Gran-plot (multiple standard addition with 10iE/s vs. concentration) 0.1-3% 0-1-3% less accurate if interfering ions are present best results if many points between 30 and 80% of a titration curve are evaluated and discordant points are eliminated... 

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