Standards addition

In standard addition, known quantities of analyte are added to the unknown. From the increase in signal, we deduce how much analyte was in the original unknown. This method requires a linear response to analyte. 

Standard addition is especially appropriate when the sample composition is unknown or complex and affects the analytical signal. The matrix is everything in the unknown, other than analyte. A matrix effect is a change in the analytical signal caused by anything in the sample other than analyte. 

Different groundwaters have different concentrations of many anions, so there is no way to construct a calibration curve for this analysis that would apply to more than one specific groundwater. Hence, the method of standard addition is required. When we add a small volume of concentrated standard to an existing unknown, we do not change the concentration of the matrix very much. 

Consider a standard addition in which a sample with unknown initial concentration of analyte [X] s gives a signal intensity 7X. Then a known concentration of standard, S, is added to an aliquot of the sample and a signal 7S+X is observed for this second solution. Addition of standard to the unknown changes the concentration of the original analyte because of dilution. Let s call the diluted concentration of analyte [X]f, where f stands for final. We designate the concentration of standard in the final solution as [S]f. (Bear in mind that the chemical species X and S are the same.) 

The matrix affects the magnitude of the analytical signal. In standard addition, all samples are in the same matrix. 

The standard addition method [35] represents a combination of calibration with the aid of both external and internal standards. In ion chromatography, it is used predominantly for the analysis of samples with difficult matrices. Matrix problems may lead to an increase in nonprecision and/or express themselves as constant or proportional systematic deviations of the analytical results. Matrix influence can be identified via calculation of the recovery function. In constant systematic deviation, the error is independent of the analyte component. Such a deviation will cause a parallel shift of the calibration line. A possible origin for this deviation might be a codetection of a matrix component. In proportional systematic deviations, the error depends on the concentration of the analyte component. This type of deviation results in a change of the slope of the calibration line. Deviations of this kind can be caused by individual sample preparation steps such as sample digestion and sample extraction, and also by matrix effects. Systematic deviations can be identified by standard addition and/or calculation of the recovery function. 

The recovery or recovery rate is the ratio of the measured mean value under repeating conditions to the so-called true value of the analyte in the sample  

The ideal value for W is 100%. With the aid of the recovery rate, the complete process can be assessed. If the true value is found, selectivity, accuracy, and robustness for this concentration level and this matrix under the given experimental conditions are proven. To identify a potential matrix influence, the sample matrix to be analyzed (which does not contain the analyte component) is divided into 10 equal sized portions and spiked with concentrated standard solutions, so that the component concentrations in the spiked samples and in the aqueous cahbration standards are the same. The spiked matrix samples are then analyzed with the corresponding analytical method. Ideally, the recovery function is a straight line with a residual standard deviation corresponding to the process standard deviation of the basic analytical method. In case a proportional systematic or constant systematic deviation is the result of the investigation of the matrix influence, the calibration function obtained with aqueous standards cannot be used for data evaluation the standard addition method has to be applied. 

After analyzing the analyte sample under suitable chromatographic conditions, a known amount of the component of interest is added and the sample is chromatographed again. In the calculation of the concentration, the volume change has to be taken into account. A peak that is not of interest serves as the internal standard to compensate for the dosing error. Calculation is performed according to Eq. (9.50)  

The standard addition method is relatively little used in chromatography mainly because several analyses are needed per sample, and this is quite time consuming. In the standard addition method, the sample is divided into several aliquots, to 

The concentration of the analyte A in a sample is to be determined by a chromatographic method. Analyses of the calibration samples and three replicates of the sample are compiled. 

Note that in this example, the concentration of IS in sample and calibration samples is different. 

The concentration of the analyte ion may also be determined graphically. As seen in Fig. 8-7, the peak area of the compound of interest is plotted versus the added concentration. A linear correlation exists if the measuring quantity (electric conductance, UV absorption, etc.) is proportional to the analyte ion concentration. The concentration of the ion is obtained by extrapolating the straight line to the abscissa. 

The method of using an internal standard, useful whenever the detector response has to be checked continually, can be implemented by the pre- 

Standard addition is another technique where zone penetration is useful. A sample containing an unknown level of analyte is injected as zone A, while a selected concentration of a standard is injected as zone B. By adjusting a suitable zone overlap a composite zone will be obtained, which may be evaluated by taking the readout either at the equidispersion point (tAf), in which case a formula equivalent to (2.32) can be used for calculations, or it may be taken at any other point along the interface of the two gradients, provided that the ratio of the dispersion coefficients at each selected delay time is known. This is readily accomplished using the same approach as described for selectivity measurement. 

Hgure 4.5 Schematic diagram of a standard addition calibration with the x-axis intercept giving the analyte concentration in the unspiked sample this can also be calculated with the equation of the regression line. 

Inductively Coupled Plasma Mass Spectrometry Handbook 

Standard addition calibration is more robust and reliable than conventional external calibration, but is more time consuming and costly if it is applied separately for every sarr5 le. It is however possible to utilise the calibration generated from only one sample to quantify analytes in subsequent samples of the same type. For example, Pb in blood is often measured in this way in high throughput clinical laboratories, using a known, low Pb level blood sample as the calibration matrix. Successive analyses of the unspiked blood sample in this case can also serve as one mechanism by which to validate the method. 

A recent study demonstrated that using just a single spiked sample was sufficient for ICP-MS and that a bracketing approach (i.e. unknown sample - spike sample - unknown sample) was helpful for drift reduction. More details on standard addition in general can be found in the literature. °  

Allowance for any dilution due to addition of the standard amount has to be made. The main difficulty with this method concerns the reproducibility of the sample injection. A precision of better than 1% should be achieved if valid quantitative results are to be obtained. 

A frequently encountered situation is that of no blank matrix being available for spiking at levels below the expected ( nominal ) level. 

The only recourse is to modify the recovery experiments above in the sense that the sample to be tested itself is used as a kind of blank, to which further analyte is spiked. This results in at least two measurements, namely untreated sample and spiked sample, which can then be used to establish a calibration line from which the amount of analyte in the untreated sample 

Amount Spiked Signal Levels Used Conventional Estimate (Extrapolation) Alternative Estimate (Interpolation) 

The trade-offs between direct calibration and standard addition are treated in Ref 103. The same recovery as is found for the native analyte has to be obtained for the spiked analyte (see Section 3.2). The application of spiking to potentiometry is reviewed in Refs. 104 and 105. A worked example for the application of standard addition methodology to FIA/AAS is found in Ref 106. Reference 70 discusses the optimization of the standard addition method. 

Example 34 The test sample is estimated, from a conventional calibration, to contain the analyte in question at a level of about 0.8 mg/ml the measured GC signal is 58 376 area units. (See Table 2.10)  

---

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. 

It also is possible to make a standard addition directly to the sample after measuring Ssamp (Figure 5.6). In this case, the final volume after the standard addition is Vo + Vs and equations 5.5-5.7 become... 

Colorplate 2 shows an example of a set of standard additions and their corresponding standard additions calibration curve. 

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. 

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... 

Figure 5.7(b) shows the relevant relationships when Sspike is plotted versus the concentrations of the spiked standards after dilution. Standard addition calibration curves based on equation 5.8 are also possible. 

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. 

In a standard addition the analyte s concentration is determined by extrapolating the calibration curve to find the x-intercept. In this case the value of X is... 

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. 

Standardization—External standards, standard additions, and internal standards are a common feature of many quantitative analyses. Suggested experiments using these standardization methods are found in later chapters. A good project experiment for introducing external standardization, standard additions, and the importance of the sample s matrix is to explore the effect of pH on the quantitative analysis of an acid-base indicator. Using bromothymol blue as an example, external standards can be prepared in a pH 9 buffer and used to analyze samples buffered to different pHs in the range of 6-10. Results can be compared with those obtained using a standard addition. 

An appropriate standard additions calibration curve based on equation 5.8 plots Sspi elVo + Vs) on they-axis and CsVs on the x-axis. Clearly explain why you cannot plot Sspike on the y-axis and Cs[ Vs/( Vo Vj)] on the x-axis. Derive equations for the slope and y-intercept, and explain how the amount of analyte in a sample can be determined from the calibration curve. 

To determine the concentration of analyte in a sample, a standard additions was performed. A 5.00-mL portion of the sample was analyzed and then successive 0.10-mL spikes of a 600.0-ppb standard of the analyte... 

Construct an appropriate standard additions calibration curve, and use a linear regression analysis to determine the concentration of analyte in the original sample and its 95% confidence interval. 

Franke and co-workers evaluated a standard additions method for a voltammetric determination of Tl. A summary of their results is tabulated here. 

Renman, L., Jagner, D. Asymmetric Distribution of Results in Galibration Gurve and Standard Addition Evaluations, Anal. Chim. Acta 1997, 357, 157-166. 

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

Bader, M. A Systematic Approach to Standard Addition Methods in Instrumental Analysis, /. Chem. Educ. 1980, 57, 703-706. 

Nimura, Y. Carr, M. R. Reduction of the Relative Error in the Standard Additions Method, Analyst 1990, 115, 1589-1595. The following paper discusses the importance of weighting experimental data when using linear regression Karolczak, M. To Weight or Not to Weight An Analyst s Dilemma, Curr. Separations 1995, 13, 98-104. 

Ophardt, G. E. Acid Rain Analysis by Standard Addition Titration, /. Chem. Educ. 1985, 62, 257-258. 

This experiment describes a method for determining the acidity, reported as an equivalent molarity of H2SO4, of rain water. Because the volume of standard base needed to titrate a sample of rain water is small, the analysis is done by a standard addition. A 10.00-mL sample of nominally 0.005 M H2SO4 is diluted with 100.0 mL of distilled water and standardized by titrating with 0.0100 M NaOH. A second 10.00-mL sample of the sulfuric acid is mixed with 100.0 mL of rain water and titrated with the same solution of NaOH. The difference between the two equivalence point volumes... 

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. 

The generalized standard addition method (GSAM) extends the analysis of mixtures to situations in which matrix effects prevent the determination of 8x and 8y using external standards.When adding a known concentration of analyte to a solution containing an unknown concentration of analyte, the concentrations usually are not additive (see question 9 in Chapter 5). Conservation of mass, however, is always obeyed. Equation 10.11 can be written in terms of moles, n, by using the relationship... 

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 ... 

A standard addition calibration curve of emission versus the concentration of added sodium gives, by linear regression, an equation of... 

The concentration of sodium in the standard addition samples is determined from the absolute value of the x-intercept (see Figure 5.7b) thus, substituting zero for the emission intensity gives the concentration of sodium as 1.44 ppm. The concentration of sodium in the salt substitute, therefore, is... 

Quantitative Determination of Cr(lll) and Co(ll) Using a Spectroscopic H-Point Standard Addition, /. Chem. Educ. 1997, 74, 848-850. 

Another nice example of a multicomponent analysis based on current research is presented in this experiment. Although the H-point standard addition is not discussed in this text, this paper provides adequate theory and references to the original literature. 

Raymond, M. Jochum, C. Kowalski, B. R. Optimal Multicomponent Analysis Using the Generalized Standard Addition Method, /. Chem. Educ. 1983, 60, 1072-1073. 

This experiment demonstrates the application of the generalized standard additions method for the analysis of mixtures of K2Cr207 and KMn04. 

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

Trace metals in sea water are preconcentrated either by coprecipitating with Ee(OH)3 and recovering by dissolving the precipitate or by ion exchange. The concentrations of several trace metals are determined by standard additions using graphite furnace atomic absorption spectrometry. 

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. 

---