Standard addition calculations

Table 8.10 shows the results obtained using the nitrous oxide combustion techniques. For the Boscan sample there was a pronounced difference in the quality of data between the iron and copper analyses. The linearity of the standard addition curves for copper is reflected by the precision and the agreement with the expected value. The absorbance value obtained for iron, on the other hand, yielded erratic data points when plotted for the standard addition calculation. 

The concentration of copper in a sample of sea water is determined by anodic stripping voltammetry using the method of standard additions. When a 50.0-mL sample is analyzed, the peak current is 0.886 )J,A. A 5.00-)J,L spike of 10.0-ppm Cu + is added, giving a peak current of 2.52 )J,A. Calculate the parts per million of copper in the sample of sea water. 

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

The result may be checked by adding four successive portions (2mL) of standard solution C to the test solution of which the e.m.f. has already been determined, and measuring the e.m.f. after each addition the calculation for this standard addition procedure is as described above. 

Example 6-2 The following standard addition plot was obtained for a competitive electrochemical enzyme immunoassay of the pesticide 2,4-D. A ground water sample (diluted 1 20 was subsequently assayed by the same protocol to yield a current signal of 65 nA. Calculate the concentration of 2,4-D in the original sample. 

The problem asks for a yield, so we identify this as a yield problem. In addition, we recognize this as a limiting reactant situation because we are given the masses of both starting materials. First, identify the limiting reactant by working with moles and stoichiometric coefficients then carry out standard stoichiometry calculations to determine the theoretical amount that could form. A table of amounts helps organize these calculations. Calculate the percent yield from the theoretical amount and the actual amount formed. 

Once we have estimated the unknown parameters that appear in an algebraic or ODE model, it is quite important to perform a few additional calculations to establish estimates of the standard error in the parameters and in the expected response variables. These additional computational steps are very valuable as they provide us with a quantitative measure of the quality of the overall fit and inform us how trustworthy the parameter estimates are. 

The above system of directly sensing a process stream without more is often not sufficiently accurate for process control so, robot titration is preferred in that case by means of for instance the microcomputerized (64K) Titro-Analyzer ADI 2015 (see Fig. 5.28) or its more flexible type ADI 2020 (handling even four sample streams) recently developed by Applikon Dependable Instruments20. These analyzers take a sample directly from process line(s), size it, run the complete analysis and transmit the calculated result(s) to process operation (or control) they allow for a wide range of analyses (potentiometric, amperometric and colorimetric) by means of titrations to a fixed end-point or to a full curve with either single or multiple equivalent points direct measurements with or without (standard) addition of auxiliary reagents can be presented in any units (pH, mV, temperature, etc.) required. 

Walters [24] examined the effect of chloride on the use of bromide and iodide solid state membrane electrodes, and he calculated selectivity constants. Multiple linear regression analysis was used to determine the concentrations of bromide, fluorine, and iodide in geothermal brines, and indicated high interferences at high salt concentrations. The standard curve method was preferred to the multiple standard addition method because of ... 

Garcia-Monco Carra et al. [296] have described a hybrid mercury film electrode for the voltammetric analysis of copper (and lead) in acidified seawater. Mercury plating conditions for preparing a consistently reproducible mercury film electrode on a glassy carbon substrate in acid media are evaluated. It is found that a hybrid electrode , i.e., one preplated with mercury and then replated with mercury in situ with the sample, gives very reproducible results in the analysis of copper in seawater. Consistently reproducible electrode performance allows for the calculation of a cell constant and prediction of the slopes of standard addition plots, useful parameters in the study of copper speciation in seawater. 

Because of this complexation capacity, any standard addition performed at high pH will not return 100% of the spike, so a true value for the copper concentration cannot be calculated. Therefore, after an initial measurement at high pH the sample was acidified to pH 1.0 with 0.5 ml acid and another trace obtained. This compared the amount of copper released at low pH with the labile fraction at high pH. Standard additions were performed on the sample at low pH so almost all of the spike was returned. This allowed an estimate to be made of the percentage of total copper that was labile at high pH, and the quantification of this fraction in pg/1. This is illustrated graphically in Fig. 5.9. 

This method of using an internal standard to deal with matrix and background effects has, of course, been used for ages in analytical chemistry. Equally useful would be another analytical method, namely that of standard additions. In this latter approach, the sample is spiked with successively increasing amounts of the pure analyte, and the intercept in the response-concentration curve is used to calculate the amount of analyte in the original sample. 

First the responses Rq are measured for the sample. Thereafter K is determined by fitting the changes in the concentrations of the analytes in the sample, brought about by the standard additions, to the changes in the responses. Once all elements in the calibration matrix, K, have been determined, the concentration vector of the analytes in the sample is calculated. The method has been successfully applied to absorption spectrophotometry , anodic stripping voltametry and ICP-atomic emission spectrophotometry Attractive features of the method are that automation is very easy and automatic drift compensation is possible . A drawback is that all interferents should be known and be corrected for. 

Since the m/niR ratio is constant and known, the mass fraction of A in the material rA can be calculated from Eq. 4.26 by inserting the abscissa at the H-point obtained from a standard addition experiment. 

Data in Table 4.2 corresponds to the application of the H-point standard addition method to a mixture of a commercial madder pigment diluted with silica, using morin as a reference compound. Calculations were performed by taking m/niR = 10.246, using square-wave voltammetric currents measured for sample-modified PIGEs in contact with an acetate buffer of pH 4.90. Linear plots of ii/ip(R) (squares) and i2/ip(R) (solid squares) vs. mA/mp for additions of purpurin are shown in Fig. 4.17. 

Table 4.3 Comparison of the percentages of Sn and Pb calculated upon apphcation of the H-point standard addition method to three commercial ceramic frits (F-1 to F-3) and an archaeological sample (A-1)—a medieval glazed piece produced in the second half of the 15th century in Manises (Valencia, Spain)...

Standard Addition. The sample is analyzed with and widioul the addition of a known umuunl or a compound that is also in the sample (spiking). The concentration is calculated from the observed increase in area. 

Alternatively, the analysis may be performed by standard addition method (see Chapter 1.9) in which no calibration curve is required. Prepare an NH3 standard solution that is about 10 times as concentrated as the estimated concentration of NH3-N in the sample. Determine the electrode slope following the instruction manual. To 100 mL sample, add 1 mL 10 A NaOH and immerse the electrode and stir the solution. Record the millivolt value Ex when the reading is stable. Add 10 mL of standard solution into the sample. Mix thoroughly and record the stable millivolt reading E2. Calculate the millivolt difference AE as E2 - E and determine the concentration, Cx mg NH3-N/L, from the following expression ... 

One simple approach to the preparation of appropriate standards where the gross activity of the sample may be large with respect to the activity of interest is to use the method of standard addition. In this technique a number of aliquants of the sample are spiked with varying amounts of the element to be determined and irradiated along with a similar sized unspiked sample. The specific activities of the spiked and unspiked samples are then plotted vs. the weight of added element as illustrated in Fig. 12. Extrapolation of this curve to zero specific activity will easily permit calculation of the unknown amount (x) of the element... 

Internal standards could be used in external calibration, matrix-matched external calibration, and standard addition calibration [2], However, the use of internal standards in LC-MS quantitative methods should not be confused with internal calibration in which an internal standard is employed as a calibrant and the concentration of a unknown sample is calculated from the concentration of this internal standard and its analyte/IS signal ratio, i.e., the concentration of the unknown sample is calculated without the need for a calibration curve [3], The use of internal standards in most LC-MS quantitative methods belongs to signal-ratio calibration or internal standardization [2,4], In fact, the majority of bioanalytical LC-MS methods use matrix-matched signal-ratio external calibration. 

The principle of this method is that the extra signal produced by the addition of standard is proportional to the original signal. Equations can be used to make the necessary calculations, but the principle is more easily seen graphically. Figure 7.11 shows a typical standard addition calibration plot. Note that a signal is present when no standard is added it represents the original concentration, which is to be determined. As... 

Exact matrix matching is not always feasible for example, the precise matrix composition may be unknown for various reasons. In such a case the standard additions method may be employed. The sample is spiked with at least two additions of known amounts of determinant in such a way that the matrix is not significantly altered, and the absorbance of spiked and unspiked samples is measured compared to that of aqueous standards, as shown in Figure 1. By extrapolation back to the negative extension of the concentration axis, the unknown concentration may be calculated. 

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