PART VI I

Chapter 35The Analysis of Real Samples

Chapter 36Preparing Samples for Analysis

Chapter 37Decomposing and Dissolving the Sample

Chapter 38Selected Methods of Analysis

practical aspects of Chemical analysis

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© Corbis

CHAPTER 35

Very early in this text (Section 1C), we pointed out that a quantitative analysis consists of a sequence of steps: (1) selecting a method, (2) sampling, (3) preparing a laboratory

sample, (4) defining replicate samples by mass or volume measurements, (5) preparing solu-tions of the samples, (6) eliminating interferences, (7) completing the analysis by performing measurements that are related in a known way to analyte concentration, and (8) computing the results and estimating their reliability. In Chapters 1 through 34, we have focused largely on steps 6, 7, and 8 and to a lesser extent on steps 2 and 4. We have chosen this emphasis not because the earlier steps are unimportant or easy. In fact, the preliminary steps may be more difficult and time consuming than the two final steps of an analysis and may be greater sources of error.

The reasons for postponing a discussion of the preliminary steps to this point are ped-agogical. Experience has shown that it is easier to introduce students to analytical tech-niques by having them first perform measurements on simple materials for which no method selection is required and for which problems with sampling, sample preparation, and sample dissolution are either nonexistent or easily solved. Thus, we have been largely concerned so far with measuring the concentration of analytes in simple aqueous solutions that have few interfering species.

35a real SampleSDetermining an analyte in a simple solution is often easier than in a complex solution because the number of variables that must be controlled is small and the tools available are numerous and easy to use. With simple systems, our knowledge of the chemical and measurement principles allows us to anticipate problems and to correct for them.

The analysis of real samples, such as the soil and rock samples brought back to the earth from the moon by the Apollo astronauts, is usually quite complex compared to the analysis of materials studied in laboratory courses. As discussed in this chapter, the choice of analytical method for real materials is not simple, often requiring consultation with the literature, modification of exist-ing methods, and extensive testing to determine method validity.

Shown in the photograph is one of the Apollo astronauts taking a core sample of the lunar soil. Such samples were valuable in determining the geological history of the moon and its relationship to the history of the earth.

the analysis of real Samples

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35A Real Samples  961

In fact, academic and industrial scientists are usually interested in materials that are not as a rule simple. To the contrary, most analytical samples are com-plex mixtures of components containing in some cases hundreds of species. Such materials are frequently far from ideal in matters of solubility, volatility, stability, and homogeneity, and many steps must precede the final measurement step. In-deed, the final measurement may be easier and less time consuming than any of the preceding steps.

For example, we showed in earlier chapters that the calcium ion concentration of an aqueous solution may be easily determined by titration with a standard EDTA solution or by potentiometry with a specific-ion electrode. Alternatively, the calcium content of a solution can be determined from atomic absorption or atomic emission measurements or by the precipitation of calcium oxalate followed by weighing or by titrating with a standard solution of potassium permanganate.

All of these methods can be used to determine the calcium content of a sim-ple salt, such as the carbonate. However, chemists are seldom interested in the calcium content of calcium carbonate. More likely, what is needed is the percent-age of this element in a sample of blood, animal tissue, a silicate rock, or a piece of glass. The analysis thus acquires a new level of complexity. None of these materials is soluble in water or in dilute aqueous reagents. Before calcium can be determined, therefore, the sample must be decomposed by high-temperature treatment with con-centrated reagents. Unless care is taken, we could lose some calcium during this step, or equally bad, we could introduce some calcium as a contaminant because of the relatively large quantities of reagent usually needed for sample decomposition.

Even after the sample has been decomposed to give a solution containing calcium ions, the procedures mentioned in the two previous paragraphs cannot ordinarily be applied immediately to complete the analysis because the reactions or properties used are not specific to calcium. Thus, a sample of animal tissue, silicate rock, or glass almost surely contains one or more components that also react with EDTA, act as a chemical interference in an atomic absorption measurement, or form a precipitate with oxalate ion. In addition, the high ionic strength resulting from the reagents used for sample decomposition would complicate a direct potentiometric measurement. Because of these difficulties, several additional operations are required to eliminate interferences before the final measurement is made.

We have chosen the term real samples to describe materials such as those in the preceding example. In this context, most of the samples encountered in an elementary quantitative analysis laboratory course definitely are not real but rather are homogeneous, stable, soluble, and chemically simple. Also, there are well- established and thoroughly tested methods for their analysis. There is much value in introducing analytical techniques with such materials because they permit you to focus on the mechanical aspects of an analysis. Even experienced analysts use such samples when learning new techniques, calibrating instruments, or standardizing solutions.

Determining the compositions of real samples frequently demands intellectual skill and chemical intuition in addition to mechanical aptitude. Frequently, a compromise must be struck between the available time and the accuracy required. We are often happy to settle for an accuracy of one or two parts per hundred instead of one or two parts per thousand, knowing that ppt accuracy may require several hours or even days of additional effort. In fact, with complex materials, even parts-per- hundred accuracy may be unrealistic.

The difficulties encountered in the analysis of real samples stem from their com-plexity. As a result, the literature may not contain a well-tested analytical route for the kind of sample under consideration. For such cases, an existing procedure must be

Real samples are far more complex than most of those that you encounter in the instructional laboratory.

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962  CHAPTER 35 The Analysis of Real Samples

modified to take into account compositional differences between the current sample and samples in the original publication. Alternatively, an entirely new analytical method might need to be developed. In either case, the number of variables that must be taken into account usually increases exponentially with the number of spe-cies contained in the sample.

As an example, contrast the problems associated with the inductively coupled plasma atomic emission analysis of calcium carbonate with those for a real calcium-containing sample. In the calcium carbonate case, the number of components is small, and only a few variables are likely to affect the results. The most important variables are the physical loss of analyte when carbon dioxide evolves as the sample is dissolved in acid, the effect of the anion of the acid and of the radio-frequency power on the intensity of the calcium emission line, the position of the plasma with respect to the spectrometer entrance slit, and the quality of the standard calcium solutions used for calibration.

Determining calcium in a real sample, such as a bone or a silicate rock, is far more complex since the sample is insoluble in ordinary solvents and contains a dozen or more components. The silicate rock sample, for example, can be dis-solved by fusing it at a high temperature with a large excess of a reagent such as sodium carbonate. Physical loss of the analyte is possible during this treatment unless suitable precautions are taken. Furthermore, we must be concerned that calcium could be introduced from the excess sodium carbonate or the fusion vessel. Following fusion, the sample and reagent are dissolved in acid. With this step, all the variables affecting the calcium carbonate sample are operating, but in addition, many new variables are introduced because of the dozens of com-ponents in the sample matrix. Now, we must take care to minimize instrumental and chemical interferences brought about by the presence of various anions and cations in the solution being introduced into the plasma. Thus, the analysis of a real substance is often a challenging problem and developing a procedure for such materials is a demanding task.

 35B ChoiCe of analytiCal methodThe choice of a method for the analysis of a complex substance requires good judg-ment based on sound knowledge of the advantages and limitations of the available analytical tools. In addition, a familiarity with the literature of analytical chemistry is essential. We cannot be very explicit concerning how an analytical method is selected because there is no single best way that applies under all circumstances. We can, however, suggest a systematic approach to the problem and present some generalities that can aid in making good decisions.

35B-1 Definition of the ProblemThe first step, which must precede any choice of method, is to clearly define the ana-lytical problem. The method selection will be mostly governed by the answers to the following questions:

■■ What is the concentration range of the analyte to be determined?■■ What degree of accuracy is desired?■■ What other components are present in the sample?■■ What are the physical and chemical properties of the gross sample?■■ How many samples will be analyzed?

The objectives of an analysis must be clearly defined before the work begins.

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35B Choice of Analytical Method  963

The concentration range of the analyte may well limit the number of feasible methods. For example, if we wish to determine an element present at the parts-per-billion or parts-per-million level, gravimetric or volumetric methods can be ruled out, and spectrometric, potentiometric, and other more sensitive methods become likely candidates. For components in the parts-per-billion and parts-per-million range, even small losses resulting from coprecipitation or volatility and contamina-tion from reagents and apparatus are major concerns. In contrast, if the analyte is a major component of the sample, these considerations are less important, and a classic analytical method may well be adequate for the task.

The accuracy required is vitally important in choosing a method and in the way it is performed because the time required to complete an analysis increases dramatically with demands for higher accuracy. Therefore, to improve the reliability of analytical results from, say, 2 to 0.2% relative may require an increase in the analysis time by a factor of 100 or more. Consequently, we should always carefully consider the degree of accuracy that is required before undertaking an analysis.

The demands for accuracy frequently dictate the procedure chosen for an analy-sis. For example, if the allowable error in the determination of aluminum is only a few parts per thousand, a gravimetric procedure is probably required. On the other hand, if an error of, say, 50 ppt can be tolerated, a spectroscopic or electroanalytical approach may be preferable.

The way in which an analysis is done is also affected by accuracy requirements. If precipitation with ammonia is chosen for the analysis of a sample containing 20% aluminum, the presence of 0.2% iron is of serious concern if accuracy in the parts-per-thousand range is demanded and if a preliminary separation of the two elements is necessary. If an error of 50 ppt is tolerable, however, the separation of iron is not necessary. This tolerance can also govern other aspects of the method. For example, 1-g samples can be weighed to perhaps 10 mg and certainly no closer than 1 mg. In addition, less care is needed in transferring and washing the precipi-tate and in other time-consuming operations of the gravimetric method. The wise use of shortcuts is not a sign of carelessness but a recognition of the importance of efficiency. The question of accuracy, then, must be clearly resolved before begin-ning an analysis.

To choose a method for the determination of one or more species in a sample, you frequently need to know what other elements or compounds are present. If such information is lacking, a qualitative analysis must be undertaken in order to iden-tify components that are likely to interfere in the various methods under consider-ation. As we have noted frequently, most analytical methods are based on reactions and physical properties that are shared by more than a single element or compound. Thus, measuring the concentration of a given element by a method that is simple and straightforward in the presence of one group of elements or compounds may require many tedious and time-consuming separations in the presence of others. A  solvent suitable for one combination of compounds may be totally unsatisfactory when used for another. It is very important to know the approximate chemical composition of the sample before selecting a method for the quantitative determination of one or more of its components.

We must also consider the physical state of the sample in order to determine whether it must be homogenized, whether volatility losses are likely, and whether its composition may change under laboratory conditions due to the absorption or the loss of water. We must also determine how to decompose or dissolve the sample without loss of analyte. Preliminary tests of one sort or another may be needed to provide this type of information.

The time required to carry out an analysis increases, often in an exponential manner, with the desired level of accuracy.

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Often, you can save considerable time by the use of permissible shortcuts in an analytical procedure.

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It is frequently necessary to identify the components of a sample before undertaking a quantitative analysis.

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964  CHAPTER 35 The Analysis of Real Samples

Finally, the number of samples to be analyzed is an important criterion in select-ing a method. If there are many samples, considerable time can be spent in calibrating instruments, preparing reagents, assembling equipment, and investigating shortcuts since the cost of these operations can be spread over the large number of samples. If, however, only few samples will be analyzed, a longer and more tedious procedure with few of these preparatory operations may be the wiser choice from an economic standpoint.

Once we have answered the preliminary questions, we can then consider possible approaches to the problem. Sometimes, experience provides a straightforward route for the analysis. In other instances, we must speculate on problems that are likely to be encountered in the analysis and how they can be solved. By the time these prob-lems have been considered, some methods probably will have been eliminated from consideration and others put on the doubtful list. Usually, however, we first turn to the analytical literature to profit from the experience of others.

35B-2 Investigating the LiteratureA list of reference books and journals covering various aspects of analytical chemistry appears in Appendix 1. This list is not exhaustive but rather one that is adequate for most work. It is divided into several categories. In many instances, the division is arbitrary since some works could be logically placed in more than one category.

We usually begin a search of the literature by referring to one or more of the treatises on analytical chemistry or to those devoted to the analysis of specific types of materials. In addition, it is often helpful to consult a general reference work relating to the compound or element of interest. From this survey, a clearer picture of the problem at hand may develop, including the steps that are likely to be diffi-cult, the separations that must be made, and the pitfalls to be avoided. Occasionally, all the answers needed or even a set of specific instructions for the analysis may be found. Alternatively, journal references that lead directly to this information may be discovered. Sometimes, we find only a general notion of how to proceed. Several possible methods may appear suitable; others may be eliminated. At this point, it is often helpful to consider reference works concerned with specific substances or spe-cific techniques. If these works do not provide the desired information, the various analytical journals may be consulted. Monographs on methods for completing the analysis are often valuable in deciding among several possible techniques.

The most difficult aspect of using analytical journals is locating articles pertinent to the problem at hand. The various reference books can be useful since most con-tain many references to the original journals. The key to a thorough search of the literature, however, is Chemical Abstracts, which was published in print form from 1907 through 2009. As personal computers became available, manual literature searches were replaced by computer-based searches. Two major electronic databases available through Chemical Abstracts are CAplus and CAS REGISTRY. In 2011, the CAplus database contained some 34 million references to the scientific litera-ture and to patents. The CAS REGISTRY is the authoritative source for chemical names and structures and uniquely identifies chemical substances through a CAS Registry Number. These databases and several others can be accessed by computer with SciFinder and STN software. SciFinder is a web-based program with a graphical interface that permits scientists to search the large bibliographic, structure, and reac-tion databases. The STN software is intended primarily for information profession-als and features a command-language interface. Computer-aided literature searches through such programs have reduced dramatically the time required for a careful literature search—from months or days to hours or even minutes.

A little extra time spent in the library can save a tremendous amount of time and effort in the laboratory.

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The technology for computer-based scientific information retrieval provides an efficient means of surveying the analytical literature. For example, complete archives of all American Chemical Society journals are available online.

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35B Choice of Analytical Method  965

35B-3 Choosing or Devising a MethodAfter defining the problem and investigating the literature for possible approaches, we must next decide on the laboratory procedure. If the choice is simple and obvi-ous, analysis can be undertaken directly. Frequently, however, the decision requires the exercise of considerable judgment and ingenuity. In addition, experience, an understanding of chemical principles, and perhaps intuition all come into play.

If the substance to be analyzed occurs widely, the literature survey usually yields several alternative methods for the analysis. Economic considerations may dictate a method that will yield the desired reliability with the least expenditure of time and effort. As mentioned earlier, the number of samples to be analyzed is often a deter-mining factor in the choice.

In many cases, existing instrumentation and expertise in particular methods may play a large role in the choice of methods. There is no reason to consider a mass spec-trometric approach if a mass spectrometer is not available in the laboratory or in the vicinity. Likewise, appropriate expertise may not be at hand for a newly purchased instrument until weeks after installation. Hence, choices may be limited because of the laboratory environment.

Investigation of the literature does not always reveal a method designed specifi-cally for the type of sample in question. Ordinarily, however, we will find procedures for materials that are at least similar in composition to ours. We must then decide whether the variables introduced by the differences in composition are likely to have any influence on the results. This judgment can be difficult, and we may still be uncertain as to the effects. Experiments in the laboratory may be the only way of making a wise decision.

If we conclude that existing procedures are not applicable, consideration must be given to modifications that may overcome the problems imposed by the variation in composition. Again, the complexity of the chemical system may dictate that we can propose only tentative alterations. Whether these modifications will accomplish their purpose without introducing new difficulties can be determined only in the laboratory.

After considering existing methods and their modifications, we may decide that none fits the problem and an entirely new procedure must be developed. For this approach, all the facts on the chemical and physical properties of the analyte must be organized and considered. Several possible ways of performing the desired mea-surement may become evident from this information. Each possibility must then be examined critically, while considering possible influences of the other components in the sample as well as to the reagents that must be used for solution or decomposition. At this point, we must try to anticipate sources of error and possible interferences due to interactions among sample components and reagents. It may be necessary to devise strategies to circumvent such problems. The conclusion of such a preliminary survey generally produces one or more tentative methods worth testing. Usually, the feasibility of some of the steps in the procedure cannot be determined without pre-liminary laboratory testing. Certainly, critical evaluation of the entire procedure can come only from careful laboratory work.

35B-4 Testing the ProcedureOnce a procedure for an analysis has been selected, we must decide whether it can be applied directly to the problem at hand or it must be tested. The answer to this question is not simple and depends on a number of considerations. If the method chosen is the subject of a single, or at most a few, literature references, there may

Preliminary laboratory testing may be needed to evaluate proposed changes to established methods.

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966  CHAPTER 35 The Analysis of Real Samples

be real value in a preliminary laboratory evaluation. With experience, we become more and more cautious about accepting claims regarding the accuracy and applica-bility of a new method. All too often, statements found in the literature tend to be overly optimistic. A few hours spent in testing the procedure in the laboratory may be enlightening.

Whenever a major modification of a standard procedure is undertaken or an attempt is made to apply it to a type of sample different from that for which it was designed, a preliminary laboratory test is again recommended. The effects of such changes simply cannot be predicted with certainty.

Finally, a newly devised procedure must be extensively tested before it is adapted for general use. We now consider the means by which a new method or a modifica-tion of an existing method can be tested for reliability.

The Analysis of Standard SamplesThe best way to evaluate an analytical method is to analyze one or more standard samples whose analyte composition is reliably known. For this technique to be effective, however, it is essential that the standards closely resemble the samples to be analyzed with respect to both the analyte concentration range and the overall composition.

Occasionally, standards suitable for method testing can be synthesized by thor-oughly homogenizing weighed quantities of pure compounds. Such a procedure is generally inapplicable, however, when the samples to be analyzed are complex, such as biological materials, soil samples, and many forensic samples.

Section 8E-3 discusses the general methods for validation of analytical results. The National Institute of Standards and Technology sells a variety of standard refer-ence materials (SRM) that have been specifically prepared for validation purposes.1

Most standard reference materials are substances commonly encountered in industry or in governmental and academic studies. Over 1200 standard reference materials are available, in categories such as engineering, food and agriculture, health and clinical, environmental, high-purity, and industrial materials. Specific substances include fer-rous and nonferrous metals; ores, ceramics, and cements; environmental gases, liq-uids, and solids; primary and secondary chemicals; clinical, biological, and botanical samples; fertilizers; and glasses. The concentration of one or more components in these SRMs is certified by the Institute based on measurements using (1) a previously vali-dated reference method; (2) two or more independent, reliable measurement methods; or (3) results from a network of cooperating laboratories, technically competent and thoroughly familiar with the material being tested. Several industrial concerns also offer various kinds of standard materials designed for validating analytical procedures.

When standard reference materials are not available, the best we can do is to prepare a solution of known concentration whose composition approximates that of the sample after it has been decomposed and dissolved. Such a standard gives no information at all concerning the fate of the substance being determined during the important decomposition and solution steps.

Using Other MethodsThe results of an analytical method can sometimes be evaluated by comparing them with data obtained from an entirely different method, particularly if we know the

The National Institute of Standards and Technology is an important source for standard reference materials. For literature describing standard reference materials and other standards, see http://www.nist.gov.

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1 See U.S. Department of Commerce, NIST Standard Reference Materials Catalog, 2011 ed., NIST Special Publication 260, Washington, D.C.: U.S. Government Printing Office, 2011. The catalog can be downloaded from the NIST web site at http://www.nist.gov.

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35C Accuracy in the Analysis of Complex Materials   967

reliability of the reference method. The second method should be based on chemical or instrumental principles that differ as much as possible from the method being considered. Because it is unlikely that the same errors influence both methods, if we obtain results comparable to the reference method, we can usually conclude that our new method is satisfactory. Such a conclusion does not apply to those aspects of the two methods that are similar.

Standard Addition to the SampleWhen standard reference materials and different analytical methods are not appli-cable, the standard addition method may prove useful. In addition to being used to analyze the sample, the proposed procedure is tested against portions of the sample to which known amounts of the analyte have been added. The effectiveness of the method can then be established by evaluating the extent of recovery of the added quantity. The standard addition method may reveal errors arising from the way the sample was treated or from the presence of the other elements and/or compounds in the matrix.

 35C

aCCuraCy in the analySiS of Complex materialS

To provide a clear idea of the accuracy that can be expected for the analysis of a com-plex material, data on the determination of four elements in a variety of materials are presented in Tables 35-1 to 35-4. These data were taken from a much larger set of results collected by W. F. Hillebrand and G. E. F. Lundell of the National Bureau of Standards (now NIST) and published in the first edition of their classical book on inorganic analysis.2

The materials analyzed were naturally occurring substances and items of com-merce. They were specially prepared to give uniform and homogeneous samples and were distributed among chemists who were, for the most part, actively engaged in the analysis of similar materials. The analysts were allowed to use the methods they considered most reliable and best suited for the analysis. In most instances, special

The standard addition method is described in Section 8D-3. Applications of standard additions methods are presented in Chapters 21, 26, and 28.

2 W. F. Hillebrand and G. E. F. Lundell, Applied Inorganic Analysis, New York: Wiley, 1929, pp. 874–87.

taBle 35-1Determination of Iron in Various Materials*

Materials

Iron, %

Number of Analysts

Average Absolute Error

Average Relative Error, %

Soda-lime glass 0.064 (Fe2O3) 13 0.01 15.6Cast bronze 0.12 14 0.02 16.7Chromel 0.45 6 0.03 6.7Refractory 0.90 (Fe2O3) 7 0.07 7.8Manganese bronze 1.13 12 0.02 1.8Refractory 2.38 (Fe2O3) 7 0.07 2.9Bauxite 5.66 5 0.06 1.1Chromel 22.8 5 0.17 0.75Iron, ore 68.57 19 0.05 0.07

W. F. Hellebrand and G.E.F. Lundell, Applied Inorganic Analysis, (New York: Wiley, 1929), p. 878. Reprinted by permission of the Lundell Estate.

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968  CHAPTER 35 The Analysis of Real Samples

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precautions were taken, and the results are consequently better than can be expected from the average routine analysis.

The numbers in the second column of Tables 35-1 through 35-4 are best values, obtained by the most painstaking determination of the measured quantity. Each is considered to be the true value for calculating the absolute and relative errors shown in the fourth and fifth columns. The fourth column was computed by discarding extremely divergent results, determining the deviation of the remaining individual

taBle 35-2Determination of Manganese in Various Materials*

Material

Manganese, %

Number of Analysts

Average Absolute Error

Average Relative Error, %

Ferro-chromium 0.225 4 0.013 5.8Cast iron 0.478 8 0.006 1.3

0.897 10 0.005 0.56Manganese bronze 1.59 12 0.02 1.3Ferro-vanadium 3.57 12 0.06 1.7Spiegeleisen 19.93 11 0.06 0.30Manganese ore 58.35 3 0.06 0.10Ferro-manganese 80.67 11 0.11 0.14

W. F. Hellebrand and G.E.F. Lundell, Applied Inorganic Analysis, (New York: Wiley, 1929), p. 880. Reprinted by permission of the Lundell Estate.

taBle 35-3Determination of Phosphorus in Various Materials*

Material

Phosphorus, %

Number of Analysts

Average Absolute Error

Average Relative Error, %

Ferro-tungsten 0.015 9 0.003 20Iron ore 0.014 31 0.001 2.5Refractory 0.069 (P2O5) 5 0.011 16Ferro-vanadium 0.243 11 0.013 5.4Refractory 0.45 4 0.10 22Cast iron 0.88 7 0.01 1.1Phosphate rock 43.77 (P2O5) 11 0.5 1.1Synthetic mixtures 52.18 (P2O5) 11 0.14 0.27Phosphate rock 77.56 (Ca3(PO4)2) 30 0.85 1.1

W. F. Hellebrand and G.E.F. Lundell, Applied Inorganic Analysis, (New York: Wiley, 1929), p. 882. Reprinted by permission of the Lundell Estate.

taBle 35-4Determination of Potassium in Various Materials*

Material

Potassium Oxide, %

Number of Analysts

Average Absolute Error

Average Relative Error, %

Soda-lime glass 0.04 8 0.02 50Limestone 1.15 15 0.11 9.6Refractory 1.37 6 0.09 6.6

2.11 6 0.04 1.92.83 6 0.10 3.5

Lead-barium glass 8.38 6 0.16 1.9

W. F. Hellebrand and G.E.F. Lundell, Applied Inorganic Analysis, (New York: Wiley, 1929), p. 883. Reprinted by permission of the Lundell Estate.

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35C Accuracy in the Analysis of Complex Materials   969

data from the best value (second column), and averaging these deviations. The fifth column was obtained by dividing the data in the fourth column by the best value (second column) and multiplying by 100%.

The results shown in these tables are typical of the data for 26 elements reported in the original publication. We conclude that analyses reliable to a few tenths of a percent relative are the exception rather than the rule in the analysis of complex mix-tures by ordinary methods and that, unless we are willing to invest a huge amount of time in the analysis, errors on the order of 1 or 2% must be accepted. If the sample contains less than 1% of the analyte, we must expect even larger relative errors.

These data show that the accuracy obtainable in the determination of an element depends strongly on the nature and complexity of the substrate. Thus, the relative error in the determination of phosphorus in two phosphate rocks was 1.1%. In a synthetic mixture, the error was only 0.27%. The relative error in an iron determina-tion in a refractory was 7.8%. In a manganese bronze having about the same iron content, the relative error was only 1.8%. In this example, the limiting factor in the accuracy is not in the completion step but rather in the dissolution of the samples and the elimination of interferences.

The data in these four tables are more than 80 years old, and it is tempting to think that analyses carried out with more modern tools and additional experience are likely to have significantly better accuracy and precision. A study by S. Abbey suggests that is simply not the case however.3 For example, the data, which were taken from Abbey’s paper, reveal no significant improvement in silicate analyses of standard reference glass and rock samples in the 43-year period from 1931 to 1974. Indeed, the standard deviation among participating laboratories appears to be larger in later years.

The data in Tables 35-1 through 35-5 show that we must be skeptical of the accuracy of analytical results on real samples, even if we perform the analysis ourselves.

Fundamental sources of systematic and random error that plagued us 80 years ago still haunt us today.

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taBle 35-5Standard Deviation of Silica Results*

Year Reported

Sample Type

Number of Results

Standard Deviation (% absolute)

1931 Glass 5 0.28†

1951 Granite 34 0.371963 Tonalite 14 0.261970 Feldspar 9 0.101972 Granite 30 0.181972 Syenite 36 1.061974 Granodiorite 35 0.46

Reprinted (adapted) with permission from S. Abbey, Anal. Chem., 1981, 53, 529A. Copyright 1981 American Chemical Society.

3S. Abbey, Anal. Chem., 1981, 53, 529A, DOI: 10.1021/ac00227a718.

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