D. Harvey - Modern Analytical Chemistry (794078), страница 15
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The difference between the obtained result and the expected result isusually divided by the expected result and reported as a percent relative error% Error =obtained result – expected result× 100expected result1400-CH03 9/8/99 3:51 PM Page 39Chapter 3 The Language of Analytical ChemistryAnalytical methods may be divided into three groups based on themagnitude of their relative errors.3 When an experimental result iswithin 1% of the correct result, the analytical method is highly accurate.
Methods resulting in relative errors between 1% and 5%are moderately accurate, but methods of low accuracy produce relative errors greater than 5%.The magnitude of a method’s relative error depends on howaccurately the signal is measured, how accurately the value of k inequations 3.1 or 3.2 is known, and the ease of handling the samplewithout loss or contamination. In general, total analysis methodsproduce results of high accuracy, and concentration methods rangefrom high to low accuracy. A more detailed discussion of accuracyis presented in Chapter 4.5.85.96.0ppm K+6.16.25.85.96.0ppm K+6.16.239(a)(b)3D.2 PrecisionWhen a sample is analyzed several times, the individual results are rarely the same.Instead, the results are randomly scattered.
Precision is a measure of this variability.The closer the agreement between individual analyses, the more precise the results.For example, in determining the concentration of K+ in serum, the results shown inFigure 3.5(a) are more precise than those in Figure 3.5(b). It is important to realizethat precision does not imply accuracy. That the data in Figure 3.5(a) are more precise does not mean that the first set of results is more accurate.
In fact, both sets ofresults may be very inaccurate.As with accuracy, precision depends on those factors affecting the relationshipbetween the signal and the analyte (equations 3.1 and 3.2). Of particular importance are the uncertainty in measuring the signal and the ease of handling samplesreproducibly. In most cases the signal for a total analysis method can be measuredwith a higher precision than the corresponding signal for a concentration method.Precision is covered in more detail in Chapter 4.Figure 3.5Two determinations of the concentration ofK+ in serum, showing the effect of precision.The data in (a) are less scattered and,therefore, more precise than the data in (b).precisionAn indication of the reproducibility of ameasurement or result.3D.3 SensitivityThe ability to demonstrate that two samples have different amounts of analyte is anessential part of many analyses.
A method’s sensitivity is a measure of its ability toestablish that such differences are significant. Sensitivity is often confused with amethod’s detection limit.4 The detection limit is the smallest amount of analytethat can be determined with confidence. The detection limit, therefore, is a statistical parameter and is discussed in Chapter 4.Sensitivity is the change in signal per unit change in the amount of analyte andis equivalent to the proportionality constant, k, in equations 3.1 and 3.2. If ∆SA isthe smallest increment in signal that can be measured, then the smallest differencein the amount of analyte that can be detected is∆nA =∆S Ak(total analysis method)∆C A =∆S Ak(concentration method)Suppose that for a particular total analysis method the signal is a measurementof mass using a balance whose smallest increment is ±0.0001 g.
If the method’ssensitivityA measure of a method’s ability todistinguish between two samples;reported as the change in signal per unitchange in the amount of analyte (k).detection limitA statistical statement about the smallestamount of analyte that can bedetermined with confidence.1400-CH03 9/8/99 3:51 PM Page 4040Modern Analytical Chemistrysensitivity is 0.200, then the method can conceivably detect a difference of aslittle as±0.0001 g∆nA == ±0.0005 g0.200in the absolute amount of analyte in two samples. For methods with the same ∆SA,the method with the greatest sensitivity is best able to discriminate among smalleramounts of analyte.3D.4 SelectivityAn analytical method is selective if its signal is a function of only the amount of analyte present in the sample.
In the presence of an interferent, equations 3.1 and 3.2can be expanded to include a term corresponding to the interferent’s contributionto the signal, SI,selectivityA measure of a method’s freedom frominterferences as defined by the method’sselectivity coefficient.selectivity coefficientA measure of a method’s sensitivity foran interferent relative to that for theanalyte (KA,I).Ssamp = SA + SI = kAnA + kInI(total analysis method)3.3Ssamp = SA + SI = kACA + kICI(concentration method)3.4where Ssamp is the total signal due to constituents in the sample; kA and kI are thesensitivities for the analyte and the interferent, respectively; and nI and CI are themoles (or grams) and concentration of the interferent in the sample.The selectivity of the method for the interferent relative to the analyte is defined by a selectivity coefficient, KA,IK A,I =kIkA3.5which may be positive or negative depending on whether the interferent’s effect onthe signal is opposite that of the analyte.* A selectivity coefficient greater than +1 orless than –1 indicates that the method is more selective for the interferent than forthe analyte.
Solving equation 3.5 for kIkI = KA,I × kA3.6substituting into equations 3.3 and 3.4, and simplifying givesSsamp = kA(nA + KA,I × nI)(total analysis method)3.7Ssamp = kA(CA + KA,I × CI)(concentration method)3.8The selectivity coefficient is easy to calculate if kA and kI can be independentlydetermined. It is also possible to calculate KA,I by measuring Ssamp in the presenceand absence of known amounts of analyte and interferent.EXAMPLE 3.1A method for the analysis of Ca2+ in water suffers from an interference in thepresence of Zn2+. When the concentration of Ca2+ is 100 times greater thanthat of Zn2+, an analysis for Ca2+ gives a relative error of +0.5%.
What is theselectivity coefficient for this method?*Although kA and kI are usually positive, they also may be negative. For example, some analytical methods work bymeasuring the concentration of a species that reacts with the analyte. As the analyte’s concentration increases, theconcentration of the species producing the signal decreases, and the signal becomes smaller. If the signal in the absenceof analyte is assigned a value of zero, then the subsequent signals are negative.1400-CH03 9/8/99 3:51 PM Page 41Chapter 3 The Language of Analytical ChemistrySOLUTIONSince only relative concentrations are reported, we can arbitrarily assignabsolute concentrations.
To make the calculations easy, let CCa = 100 (arbitraryunits) and CZn = 1. A relative error of +0.5% means that the signal in thepresence of Zn2+ is 0.5% greater than the signal in the absence of zinc. Again,we can assign values to make the calculation easier. If the signal in the absenceof zinc is 100 (arbitrary units), then the signal in the presence of zinc is 100.5.The value of kCa is determined using equation 3.2kCa =SCa100==1CCa100In the presence of zinc the signal isSsamp = 100.5 = kCaCCa + kZnCZn = (1)(100) + kZn(1)Solving for kZn gives a value of 0.5. The selectivity coefficient, therefore, isKCa / Zn =0.5kZn== 0.51kCaKnowing the selectivity coefficient provides a useful way to evaluate an interferent’s potential effect on an analysis. An interferent will not pose a problem aslong as the term KA,I × nI in equation 3.7 is significantly smaller than nA, or KA,I × CIin equation 3.8 is significantly smaller than CA.EXAMPLE 3.2Barnett and colleagues 5 developed a new method for determining theconcentration of codeine during its extraction from poppy plants.
As part oftheir study they determined the method’s response to codeine relative to thatfor several potential interferents. For example, the authors found that themethod’s signal for 6-methoxycodeine was 6 (arbitrary units) when that for anequimolar solution of codeine was 40.(a) What is the value for the selectivity coefficient KA,I when6-methoxycodeine is the interferent and codeine is theanalyte?(b) If the concentration of codeine is to be determined with anaccuracy of ±0.50%, what is the maximum relative concentrationof 6-methoxycodeine (i.e., [6-methoxycodeine]/[codeine]) thatcan be present?SOLUTION(a) The signals due to the analyte, SA, and the interferent, SI, areSA = kACASI = kICISolving these two expressions for kA and kI and substituting into equation3.6 givesS /CK A,I = I IS A /CA411400-CH03 9/8/99 3:51 PM Page 4242Modern Analytical ChemistrySince equimolar concentrations of analyte and interferent were used(CA = CI), we haveK A,I =SI6== 0.15SA40(b) To achieve an accuracy of better than ±0.50% the term KA,I × CI inequation 3.8 must be less than 0.50% of CA; thus0.0050 × CA ≥ KA,I × CISolving this inequality for the ratio CI/CA and substituting the value forKA,I determined in part (a) givesCI0.00500.0050≤== 0.033CAK A,I0.15Therefore, the concentration of 6-methoxycodeine cannot exceed 3.3% ofcodeine’s concentration.Not surprisingly, methods whose signals depend on chemical reactivity are oftenless selective and, therefore, more susceptible to interferences.
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