The Method of Standard Additions

FIGURE 9-19. Standard addition method for the determination of the concentration of an unknown. [From W. G. Schrenk, in Flame Emission and Atomic Absorption Spectroscopy, Vol. 2, Edited by J. A. Dean and T. C. Rains, Marcel Dekker, New York (1971), Chapter 12. Used by permission of Marcel Dekker Inc.] 

Since both a and h are subject to error (Section 5.5) the calculated concentration is cleariy subject to error as well. In this case, however, the amount is not predicted from a singie measured value of y, so the formula for the standard deviation, of the extrapoiated x-value (x ) is not the same as that in equation (5.9). 

Increasing the value of n again improves the precision of the estimated concentration in general at least six points shouid be used in a standard-additions experiment. Moreover, the precision is improved by maximizing so the 

The siiver concentration in a sample of photographic waste was determined by atomic-absorption spectrometry with the method of standard additions. The foiiowing resuits were obtained. 

Determine the concentration of silver in the sample, and obtain 95% confidence iimits for this concentration. 

Although it is an elegant approach to the common problem of matrix interference effects, the method of standard additions has a number of disadvantages. The principal one is that each test sample requires its own calibration graph, in contrast to conventional calibration experiments, where one graph can provide concentration values for many test samples. The standard-additions method may also use larger quantities of sample than other methods. In statistical terms it is an extrapolation method, and in principle less precise than interpolation techniques. In practice, the loss of precision is not very serious. 

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The complication of matching the matrix of the standards to that of the sample can be avoided by conducting the standardization in the sample. This is known as the method of standard additions. The simplest version of a standard addi-... 

Illustration showing the method of standard additions in which separate aliquots of sample are diluted to the same final volume. One aliquot of sample is spiked with a known volume of a standard solution of analyte before diluting to the final volume. 

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. 

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. 

The successful application of an external standardization or the method of standard additions, depends on the analyst s ability to handle samples and standards repro-ducibly. When a procedure cannot be controlled to the extent that all samples and standards are treated equally, the accuracy and precision of the standardization may suffer. For example, if an analyte is present in a volatile solvent, its concentration will increase if some solvent is lost to evaporation. Suppose that you have a sample and a standard with identical concentrations of analyte and identical signals. If both experience the same loss of solvent their concentrations of analyte and signals will continue to be identical. In effect, we can ignore changes in concentration due to evaporation provided that the samples and standards experience an equivalent loss of solvent. If an identical standard and sample experience different losses of solvent. 

An analytical method is standardized by determining its sensitivity. There are several approaches to standardization, including the use of external standards, the method of standard addition. 

Two useful papers providing additional details on the method of standard additions are... 

Quantitative Analysis for a Single Analyte The concentration of a single analyte is determined by measuring the absorbance of the sample and applying Beer s law (equation 10.5) using any of the standardization methods described in Chapter 5. The most common methods are the normal calibration curve and the method of standard additions. Single-point standardizations also can be used, provided that the validity of Beer s law has been demonstrated. 

When possible, a quantitative analysis is best conducted using external standards. Unfortunately, matrix interferences are a frequent problem, particularly when using electrothermal atomization. Eor this reason the method of standard additions is often used. One limitation to this method of standardization, however, is the requirement that there be a linear relationship between absorbance and concentration. 

When possible, quantitative analyses are best conducted using external standards. Emission intensity, however, is affected significantly by many parameters, including the temperature of the excitation source and the efficiency of atomization. An increase in temperature of 10 K, for example, results in a 4% change in the fraction of Na atoms present in the 3p excited state. The method of internal standards can be used when variations in source parameters are difficult to control. In this case an internal standard is selected that has an emission line close to that of the analyte to compensate for changes in the temperature of the excitation source. In addition, the internal standard should be subject to the same chemical interferences to compensate for changes in atomization efficiency. To accurately compensate for these errors, the analyte and internal standard emission lines must be monitored simultaneously. The method of standard additions also can be used. 

Description of Method. Salt substitutes, which are used in place of table salt for individuals on a low-sodium diet, contain KCI. Depending on the brand, fumaric acid, calcium hydrogen phosphate, or potassium tartrate also may be present. Typically, the concentration of sodium in a salt substitute is about 100 ppm. The concentration of sodium is easily determined by flame atomic emission. Because it is difficult to match the matrix of the standards to that of the sample, the analysis is accomplished by the method of standard additions. 

What type of chemical interference in the sample necessitates the use of the method of standard additions ... 

The concentrations of iron, lead, tin, and aluminum are determined using the method of standard additions. 

Samples of urine are analyzed for riboflavin before and after taking a vitamin tablet containing riboflavin. Concentrations are determined using external standards or by the method of standard additions, fluorescence is monitored at 525 nm using an excitation wavelength of 280 nm. 

Quantitative Analysis Using the Method of Standard Additions Because of the difficulty of maintaining a constant matrix for samples and standards, many quantitative potentiometric methods use the method of standard additions. A sample of volume, Vx) and analyte concentration, Cx, is transferred to a sample cell, and the potential, (ficell)x) measured. A standard addition is made by adding a small volume, Vs) of a standard containing a known concentration of analyte, Cs, to the sample, and the potential, (ficell)s) measured. Provided that Vs is significantly smaller than Vx, the change in sample matrix is ignored, and the analyte s activity coefficient remains constant. Example 11.7 shows how a one-point standard addition can be used to determine the concentration of an analyte. 

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. 

The technique of hydrodynamic modulation voltammetry (HMV), in which the rate of stirring is pulsed between high and low values, is demonstrated in this experiment. The application of HMV for the quantitative analysis of ascorbic acid in vitamin C tablets using the method of standard additions also is outlined. 

Bohman and colleagues described a reverse-phase HPLC method for the quantitative analysis of vitamin A in food using the method of standard additions. In a typical example, a 10.067-g sample of cereal is placed in a 250-mL Erlenmeyer flask along with 1 g of sodium ascorbate,... 

Spike recoveries for samples are used to detect systematic errors due to the sample matrix or the stability of the sample after its collection. Ideally, samples should be spiked in the field at a concentration between 1 and 10 times the expected concentration of the analyte or 5 to 50 times the method s detection limit, whichever is larger. If the recovery for a field spike is unacceptable, then a sample is spiked in the laboratory and analyzed immediately. If the recovery for the laboratory spike is acceptable, then the poor recovery for the field spike may be due to the sample s deterioration during storage. When the recovery for the laboratory spike also is unacceptable, the most probable cause is a matrix-dependent relationship between the analytical signal and the concentration of the analyte. In this case the samples should be analyzed by the method of standard additions. Typical limits for acceptable spike recoveries for the analysis of waters and wastewaters are shown in Table 15.1. ... 

Note. The calibration procedure is, however, of limited accuracy and a more accurate result may be obtained using the method of standard addition (Section 9.4)... 

As an alternative to plotting a calibration curve, the method of standard addition may be used. The appropriate ion-selective electrode is first set up, together with a suitable reference electrode in a known volume (Ft) of the test solution, and then the resultant e.m.f. ( t) is measured. Applying the usual Nernst equation, we can say... 

Two procedures may be employed (1) that dependent upon wave height-concentration plots, and (2) the method of standard additions. The theory has been given in Section 16.5. 

The Method of Standard Additions to Overcome Matrix Effects... 

Adequate precision and accuracy are only likely to be achieved if some standardization procedure is employed and the nature of this, internal or external standards or the method of standard additions, needs to be chosen carefully. If internal standardization procedures are adopted then appropriate compound(s) must be chosen and their effect on the chromatographic and mass spectrometry methods assessed. The ideal internal standard is an isotopically labelled analogue of the analyte but, although there are a number of commercial companies who produce a range of such molecules, these are not always readily available. An analytical laboratory is then faced with the choice of carrying out the synthesis of the internal standard themselves or choosing a less appropriate alternative with implications on the accuracy and precision of the method to be developed. 

Table 5.17 Quantitative results obtained for the determination of four diarrhetic shellfish poisons (DSPs) using external standards and the method of standard additions. Reprinted from J. Chromatogr., A, 943, Matrix effect and correction by standard addition in quantitative liquid chromatographic-mass spectrometric analysis of diarrhetic shellfish poisoning toxins , Ito, S. and Tsukada, K., 39-46, Copyright (2002), with permission from Elsevier Science...

The fact that APCl and electrospray are soft ionization techniques is often advantageous because the molecular ion alone, in conjunction with HPLC separation, often provides adequate selectivity and sensitivity to allow an analytical method to be developed. Again, method development is important, particularly when more than one analyte is to be determined, when the effect of experimental parameters, such as pH, flow rate, etc., is not likely to be the same for each. Electrospray, in particular, is susceptible to matrix effects and the method of standard additions is often required to provide adequate accuracy and precision. 

The "method of standard additions" has been employed as a technique for standardization of atomic absorption analyses of metals In biological fluids (13,21) In this procedure, several concentrations of standard analyte are added to samples of the biological fluid to be analyzed The calibration curve which Is obtained after additions of the standard analyte to the biological fluid should parallel that obtained when aqueous standards are analyzed Extrapolation of the standard additions curve back to a negative Intercept on the abscissa furnishes an estimate of the concentration of the analyte In the original sample (21) This technique Is helpful In assessing the validity of methods of trace metal analysis (11,13,58) However, In the author s opinion, the "method of standard additions" Is neither practical nor reliable as a routine method for standardization... 

Currently, nutrient analytical methods development often utilizes the method of standard additions as an intrinsic aspect of the development process. Essentially, the analyte to be measured exists in the matrix to which an identical known pure standard is added. The spiked and non-spiked matrix is extracted and analysed for the nutrient of interest. By spiking at increasing levels the researcher can establish, to some degree of certainty, the recovery and linearity of the standard additions. One can also evaluate data to determine reproducibility, precision, and accuracy. Unfortunately, the method of standard additions does not allow the evaluation of the method at nutrient concentrations less than 100 % of the endogenous level. 

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