Method of standard addition

It may be found that E varies from one electrode to another, or with minor variations in the composition of the working medium. The labour 

Make up two solutions of AT in a medium as similar as possible to that in the test solution. Their concentrations must differ by a factor of 10 and must span the range within which the value to be measured is expected to lie. If this is unknown, do step 3 first. 

Insert the electrode pair, connected to a potentiometer, into one of the solutions, stir continuously until the reading becomes constant and record it. Repeat with the other solution. The slope of the calibration curve, 5, is the difference between the two readings, in millivolts. 

Make up a solution of the sample to be analysed at an appropriate concentration. Take a fairly large measured volume, e.g. 50 or 100 ml, insert the electrodes and take a reading as in step 2. 

Add a small measured volume of a solution of sufficient to cause an appreciable change in the concentration, say by a factor of at least 2. Take a reading as before. 

An alternate method of calibration is the Method of Standard Additions (MSA) calibration. This calibration method requires that known amounts of the analyte be added directly to the sample, which contains an unknown amount of analyte. The increase in signal due to the added analyte (e.g., absorbance, emission intensity) permits us to calculate the amount of analyte in the unknown. For this method of calibration to work, there must be a linear relationship between the concentration of analyte and the signal. 

MSA is often used if no suitable external calibration curve has been prepared. There may be no time to prepare calibration standards— for example, in an anergency situation in a hospital, it may be necessary to measure sodium rapidly in a patient s serum. It may not be possible to prepare a valid set of calibration standards because of the complexity of the sample matrix or due to lack of sufficient information about the sample. Industries often require the analysis of mystery samples when something goes wrong in a process. MSA calibration is very useful when certain types of interferences are present in the sample matrix. MSA permits us to obtain accurate results without removing the interferences by performing the calibration in the presence of the interferences. It is often used when only one sample must be analyzed and the preparation of external standards would be inefficient. 

A typical example of the use of MSA is the determination of sodium by atomic emission spectrometry in an industrial plant stream of unknown composition. A representative sample of the plant stream is taken and split into four aliquots of 100 mL each. The first aliquot is left untreated this is called the no add or zero add sample. To the second aliquot, 100 pg Na is added to the 100 mL sample in such a way as to not change the volume significantly. This can be done by adding a 10 pL volume of a 10,000 ppm Na solution to the sample. A 10,000 ppm Na solution contains 10,000 pg Na/mL, so a 10 pL portion contains 100 pg Na as shown  

Sample Aliquot Emission Intensity (Intensity Units) Corrected Intensity (Intensity Units) ppm Na Added 

The anission intensity increases by 1.3 units for every 1.0 ppm Na present. Therefore, the concentration of Na in the untreated sample is calculated from the following equation  

The two cases discussed thus far are obviously not best practice examples but such circumstances may arise on occasion also, the preceding discussion allowed demonstration of the benefits of matrix matched cahbrators over clean solutions of the analytical standard. In situations where neither a surrogate internal standard nor suitable blank matrix are available, the Method of Standard Additions (MSA) is a preferred analytical method it is included in this sub-category for convenience, although strictly speaking it involves a non-zero intercept for the experimental line that serves both as calibration and measurement. In this method the analytical sample itself is used as a kind of blank into which the calibration standard is spiked. As will become apparent, linearity of response is a prerequisite for accurate results and this implies that multiple experiments must be performed at 

This is a remarkably simple result but a few cautionary remarks are necessary. The MSA method has a great advantage in that, since the recovered spike and analyte from the sample are contained in the same sample extract solution, the volumes v and V are the same for both and thus do not appear explicitly in the final expression for Qa. An assumption that was glossed over in the derivation of Equation [8.66d] was that the reponse level to which the extrapolation should be done was indeed R = zero this is valid in the absence of any bias systematic errors (such as can arise if e.g., la 7 0). However, if any such error is present, extrapolation to a value of other than zero will be observed this possibility is considered later (see discussion leading to Equation [8.75]). 

Again F a can not be measured since is not known a priori, and in most cases it is assumed that F = F a in Equation [8.66d], thns leading to a potential proportional systematic error in the measured value of since generally Fjj,aa Fa as a result of occlusion effects. However, an estimate of F a can be obtained by noting from Equation [8.66b] that  

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. 

This approach is easier than it sounds provided that the instrument can display concentration ( with a sign) and has provision to automatically zero the readout (standard features of modern instruments). The sample (V mLs plus V mL of distilled water) is aspirated and the concentration mode readout is set to zero. A separate ahquot (V mL) of sample (plus v mL of added standard) is then aspirated and the concentration mode readout is set to the amount of standard added. Distilled water is then aspirated and the concentration mode readout will provide the amovuit of analyte present 

The method of standard additions will correct for physical and minor chemical interferences which are independent of concentration (i.e., interferences which influence the slope of the cahbration plot only). Concentration dependent chemical interferences and ionisation interferences cannot be ehminated since both influences result in cmwed cahbration plots (which are difficult to extrapolate back to zero concentration). Additionally, this cahbration technique cannot correct for background interferences since the two components of the net signal (true analjde absorbance and interference) cannot be separated. A deuterium background correction system can be used in combination with this technique to correct for background interferences. 

Since AAS is t5q)ically a trace technique, it might happen that the analyte content of certain samples are above the linear range of the response. The initial temptation to simply dilute the offending samples should be resisted in favour of a more efficient procedure. By simply rotating the burner head somewhat a portion of the flame is removed from the optical beam. The net effect is that the pathlength of the sample within the optical beam is shortened. Standards are simply rerun under the modified conditions and a new calibration plot is established. Since all manipulations of the sample(s) and/or standards increase uncertainty, it is to be anticipated that the linear range of the analyte response will be increased appreciably but that the anticipated precision should not be adversely affected. By contrast, having to dilute samples will probably decrease the precision as well. 

A number of flameless atomisation techniques have been developed to (i) increase the efficiency of production of analyte atoms within the optical beam of the instrument and/or (ii) exploit the volatility of analyte transformation products. 

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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... 

Method of standard addition. The polarogram of the unknown solution is first recorded, after which a known volume of a standard solution of the same ion is added to the cell and a second polarogram is taken. From the magnitude of the heights of the two waves, the known concentration of ion added, and the volume of the solution after the addition, the concentration of the unknown... 

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. 

Method of standard addition. The polarogram of the unknown solution will have been determined under (1). A new polarogram must now be recorded after the addition of a known volume of a standard solution containing the same ion, care being taken that in the resulting solution the concentrations of the supporting electrolyte and the suppressor are maintained constant. 

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. 

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