Accred Qual Assur (1997) 2 :354–359Q Springer-Verlag 1997 GENERAL PAPER

Wolfgang Richter Primary methods of measurement in

chemical analysis

Received: 17 April 1997Accepted: 9 August 1997

W. Richter (Y)Physikalisch-Technische Bundesanstalt,D-Braunschweig, GermanyTel.: c49-(0)531-592-3200

Abstract Primary methods ofmeasurement have a central func-tion in metrology. They are an es-sential component in the realisa-tion of the SI units and thereforeare indispensable for establishingtraceability of measurements of allkinds of physical quantities to thecorresponding SI units. This is alsotrue for chemical analysis. Gravi-metry, titrimetry, coulometry, andisotope dilution mass spectrometry(IDMS) are evaluated with regardto their potential to be primary

methods according to a generaldefinition of primary methods re-cently given by the Comité Consul-tatif pour la Quantité de Matière(CCQM). Optical absorption spec-trometry and methods based oncolligative properties are also con-sidered. A general scheme for es-tablishing traceability of chemicalmeasurements to the SI units usingprimary methods is discussed.

Key words Traceability to SI 7Primary methods 7 Comparability

Introduction

With increasing globalisation of human activities, thecomparability (more precisely: metrological equival-ence) of measurement results has become an importantissue. Comparability requires traceability to commonreferences; worldwide comparability requires traceabil-ity of measurement results to the SI units, the only gen-erally accepted reference frame available. This is alsotrue for chemical measurements (measurements for de-termining chemical composition), the more so as cross-frontier activities in environmental protection, healthcare and trade rely on credible and, hence, acceptedanalytical results.

Traceability to the SI units is ultimately accom-plished by primary methods of measurement. Primarymethods tie the realisation of an SI unit to its defini-tion, or, in other words: the value of a primary meas-urement standard of a physical quantity is determinedusing a primary method. This is the usual application ofa primary method in metrology in general, at the top ofthe traceability chain. But it can also be used to directly

tie a field measurement to the corresponding unit in theshortest way possible.

Definition and general description

The Comité Consultatif pour la Quantité de Matière(CCQM), the new metrology body under the Conven-tion du Mètre, which is responsible for all issues relat-ing to the accuracy of chemical measurements and theirtraceability to the SI units, has recently given a generaldefinition of a primary method of measurement [1].This reads:

“A primary method of measurement is a methodhaving the highest metrological qualities, whose opera-tion is completely described and understood, for whicha complete uncertainty statement can be written downin terms of SI units, and whose results are, therefore,accepted without reference to a standard of the quanti-ty being measured.”

The statement that the result of a primary method isaccepted without reference to a standard of the quanti-ty being measured is interpreted by the CCQM to mean

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that for a given quantity, X, the equation describing themeasurement method must include no unknown func-tions of X of significant magnitude. The determinationof X in terms of a reference value Xref, itself deter-mined by a primary method, does not invalidate themethod as being primary.

An example of a method which is not invalidated asa primary method by using a reference value of thesame quantity is temperature measurement with a spec-tral radiation thermometer, in which use is made of areference value determined by gas thermometry [2].The value to be measured is linked to the reference val-ue (itself determined by a primary method) via thePlanck equation, which completely describes the opera-tion of the radiation thermometer.

Obviously, such cases of complete calculability arerare in chemical analysis. Instead, empirical determina-tion of the measurement function by calibration is thecommon way. There are, however, a few analyticalmethods which have the potential for being used as pri-mary methods. These are, for example, gravimetry, ti-trimetry, coulometry and isotopic dilution mass spec-trometry (IDMS), according to a proposal of theCCQM.

The terms “definitive” or “absolute” are often usedto characterise methods in chemical analysis whichmeet the basic requirements to be fulfilled by primarymethods according to the CCQM definition. What thisdefinition adds is the requirement that the method beof highest metrological quality. This means that it mustgive results with the smallest uncertainty attainable in agiven field of measurement, also with respect to thelong-term validity of the result. Being definitive or ab-solute is, in a way, the potential of a method for being aprimary one. The advantage of the CCQM definition isthat it is more general and does not contain termswhich themselves must be defined.

In the following, existing methods are evaluatedwith respect to their potential of being primary meth-ods.

Gravimetry

A gravimetric analysis is usually carried out accordingto the following principle: The analyte to be deter-mined is separated from the sample in a weighableform (e.g., by precipitation), and its mass or amount ofsubstance is calculated from the mass of the weighedcompound whose stoichiometric composition must beexactly known. The measurement equation is very sim-ple:

ma p f mw , (1)

ma being the mass of the analyte and mw that of theweighed compound. The factor f depends only on meanrelative atomic masses (atomic weights) which are

usually known with sufficient accuracy. In most cases,the desired final result is not the mass of the analyte ina given sample but derived quantities like mass fractionor amount-of-substance concentration. Calculatingsuch quantities from the initial mass measurementusually is a straightforward process. Obviously, gravi-metry is completely described and understood (forproblems and imperfections, see below), and no stand-ard is needed of the quantity to be measured, for exam-ple a reference material of known composition.

In this connection, the mass standard necessary forcalibrating the balance is a general standard and doesnot count as a standard for solving the analytical task,even if the mass of the analyte is the final result. It isthe mass of a distinct chemical species which is to bedetermined, not a mass in general.

An important requirement for a method to be pri-mary is complete knowledge of the uncertainty [3] of itsresults. The uncertainty of gravimetric analyses is main-ly caused by imperfections of the practical realisation ofthe method. Chemical separations are never complete.In the case of a precipitation reaction, some of the sub-stance to be weighed is always lost in the filtrate due tosolubility, even if extremely low, and a small part of theprecipitate weighed does not belong to the substance inquestion but is made up of other occluded and copreci-pitated substances. Volatilisation of substance in the fi-nal step of generating the compound to be weighed isanother imperfection. These deviations from the idealbehaviour are usually small and can be corrected for byuse of one of the well-known sensitive instrumentalmethods [4].

Another possible contribution to the uncertaintymust be taken into account if there is doubt whetherthe reaction proceeds exactly stoichiometrically as ex-pected. Thorough experimental investigation can clari-fy this problem. As gravimetry as a classical method hasalready been used for a long time, a great number ofwell-characterised reactions are available.

If enough time, material and measurement equip-ment are available, the corrections can be determinedwith sufficient accuracy to make a complete uncertaintystatement at the highest metrological quality level. Theweighing steps (determination of the initial mass of thesample, determination of the mass of the reaction prod-uct) usually contribute minor uncertainty components.An important correction always necessary here is theair buoyancy correction. The inputs to the factor f inEq. 1, the atomic weights, are usually accurate enough.In a few cases, like lead, where the isotopic composi-tion varies considerably according to the origin of thematerial and increases the uncertainty of the atomicweight, f can make a discernible contribution to the un-certainty. Relative combined standard uncertainties [3]of down to below 10–4 have been achieved [5]. In gen-eral, 10–3 can be expected if the method is used in a

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metrologically correct way and at its full capability.Gravimetry can therefore be regarded as a primarymethod of measurement in chemical analysis. Becauseof its high reliability and accuracy, gravimetry is usedfor certifying SI-traceable reference materials [4] forinorganic chemistry.

It is sometimes advantageous to use gravimetry in a“reverse” mode: Instead of decomposing the sample, areference sample of similar composition is synthesisedby mixing known amounts of substance (via masses) ofthe pure components, and compared with the sampleusing an appropriate instrumental technique. In gasanalysis, for example, this approach is widely used. It isalso applicable in other fields of analysis [6] if the com-ponents of the sample are known and available in pureform and if homogeneous mixtures can be prepared.

This kind of gravimetry, i.e. the preparation of thereference sample by weighing, is also a primary methodif used at the highest metrological level.

Most kinds of instrumental analytical methods, onthe contrary, do not count among the primary methodseven if of high precision. In instrumental analysis, a sig-nal is usually produced in response to, for example, theamount-of-substance concentration of an analyte, utilis-ing a suitable measuring effect, and compared with thesignal produced by a reference material of known com-position subjected to the same procedure. Given linearresponse with equal slope in both cases, the ratio of thetwo signals can be used to calculate the analyte concen-tration. No measurement equation can, in general, bewritten down. Any attempt to formulate a mathemati-cal expression describing the signal of, for example, anatomic emission spectrometer as a function of thequantity to be measured shows that much more knowl-edge of the usually complicated processes involvedthan is available is necessary. The only way is by theempirical determination of this relation, i.e. the calibra-tion curve. In this way, the great majority of chemicalanalyses are carried out, relying on the high precision,the high speed, the high sensitivity and the versatility ofmodern instrumental techniques. Accuracy, however,can only be achieved by calibrating such secondarymethods with standards, meeting the important re-quirement that the signal due to these has the same cal-ibration curve parameters as the signal due to the ana-lyte in the sample. Very often this requirement is notfulfilled, which is well known as “matrix effect”.

Titrimetry

In titrimetry, the analyte is determined by measuringthe equivalent volume of titrant solution of known con-centration. As with gravimetry, it is an important prere-quisite for applying the method that the chemical reac-tion used for the determination must proceed com-

pletely stoichiometrially. A great number of such reac-tions are known. A characteristic feature of titrimetry isthat amounts of substance are directly obtained.

The measurement equation is:

na p vt 7 ct , (2)

where na is amount of substance of analyte, and vt andct are volume and amount-of-substance concentration,respectively, of the titrant. Titrimetry is closely relatedto gravimetry, since ct is known from gravimetric pre-paration. The method is obviously completely de-scribed and understood. The result for na is generallyused to calculate a compositional quantity of the origi-nal sample, e.g. amount-of-substance concentration ofthe analyte. A standard of this compositional quantityis not required. The standards required are those ofmass and volume. The basic requirements for a primarymethod are therefore met. It must not be overlookedthat the ultimate reference points of titrimetry are high-purity substances, namely those from which the titrantsolutions are prepared. These do not, however, inva-lidate titrimetry as a potentially primary method, be-cause they can be dealt with in the same way as thereference value in the above-mentioned example fromthermometry. As regards the uncertainty, similar con-siderations as in gravimetry apply. The main contribu-tions come from imperfections of realising the methodin practice. A typical error in titrimetry is associatedwith the determination of the equivalence point. Forthis and the other errors, corrections can be providedwith auxiliary methods whose accuracy depends on theeffort and outlay invested.

Combined relative standard uncertainties down to10–3 can be achieved if the method is used to its fullmetrological capability. Titrimetry is also used for thecertification of SI-traceable reference materials.

Coulometry

Coulometry is a particularly important primary methodof chemical analysis. Amounts of substance are directlydetermined by electrical current and time measure-ments in an electrochemical reaction. No reference tospecific pure substances is necessary; instead, referenceis made to the amount of substance of electrons. Thisholds with the same accuracy as that with which theFaraday constant is known. The current valueF p 96 485.31 (1 B 0,3 7 10–6) C mol–1 is accurateenough for any coulometric determination. The generalmeasurement equation is:

nap1

z7F# Idt , (3)

where z is number of electrons exchanged per reactionunit, I electrical current and t time. The method is com-

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pletely described and understood. Standards of electri-cal current, mass and time are required, but no stand-ard of the quantity to be determined. The result for na

is used to calculate the compositional quantity de-sired.

An important prerequisite is that the current mea-sured solely originate from the reaction under consider-ation; additional current-contributing processes mustnot occur. This restricts the application of the methodto simple systems, e.g. purity determinations of sub-stances.

Coulometry in chemical analysis is mainly carriedout in two variants: constant-current coulometry andcontrolled-potential coulometry. Titration is mostlyused as the kind of implementation, with electronsserving as titrant.

With this method also, the accuracy is limited due toimperfections of the practical realisation. One of themhas already been mentioned: unwanted side reactions.The limitations due to sample handling are similar tothose in gravimetry and titrimetry. As with the latter,the end-point detection problem is also involved incoulometric titration. Electrical potential measure-ments using auxiliary electrodes are usually applied.Again, errors can be corrected for using sensitive meth-ods which themselves need not be primary. Combinedrelative standard uncertainties as low as 2 7 10–5 can beachieved with constant-current coulometric titration[7].

The main field of application is the direct determina-tion of the purity of substances to be used as high-levelreferences [7]. Unlike the usual way of determiningpurity by summing up impurities, with coulometry theabundance of the substance itself is directly deter-mined, irrespective of the amount and kind of the im-purities. There is no doubt that coulometry is a primarymethod of chemical analysis.

Isotope dilution mass spectrometry (IDMS)

IDMS is a special version of an addition method inwhich the known amount of substance of the analyteadded, the so-called spike, is the pure analyte in a dif-ferent isotopic composition. The amount of substanceof the analyte to be determined is linked to the knownamount of substance of the spike via a measurementequation (Eq. 4) containing only isotope abundance ra-tios (isotope amount-of-substance ratios), which can bemeasured with high accuracy using a mass spectromet-er.

In detail, a known amount of substance of the spike,generally determined by weighing, is added to the sam-ple before any chemical treatment is started. Care istaken that complete equilibration is achieved, i.e. thatthe same isotopic distribution is reached in every spe-

cies of the analyte if there are more than one. Becauseof the close similarity of the isotopes, the initial isotopicratio does not change throughout the whole chemicaltreatment procedure which may be necessary, includingthe mass spectrometric process, even if substance re-covery is not complete in the intermediate steps.

In the following, an element determination in inor-ganic analysis is considered as an example. For simplic-ity of description, it is assumed that the element ismade up of two isotopes only. It is the abundance ratioof these two isotopes of the element to be determinedwhich is used as the key to the analysis. This abundanceratio (equal to the isotope amount-of-substance ratio ina given substance portion) is measured with a massspectrometer in (1) the original sample, (2) the spike,and (3) the mixture of sample and spike, after the samepretreatment in all three cases.

The measurement equation in this case is

nap(RsPRm)(1cRa)(RmPRa) (1cRs)

7ns , (4)

na and ns being the amounts of substance of analyte andspike, Ra, Rs and Rm the isotope abundance ratios ofthe two isotopes in the sample, the spike and the mix-ture of sample and spike. The extension of the consid-eration to the general case of multi-isotope elements isstraightforward. In all cases, the abundance ratio of twoselected isotopes is measured, i.e., the element musthave at least two isotopes.

The method is completely described and understoodon the basis of a measurement equation which can beexplicitly written down. The measurement is obviouslybased on another material, the spike, which is used as areference. This does not, however, invalidate IDMS asa potentially primary method, because the amount ofsubstance of the spike is itself determined using a pri-mary method, namely gravimetry, and the amount ofsubstance of the analyte can be calculated from thespike with an explicitly known equation. The situationis similar to the example in thermometry mentionedabove.

With an ideal mass spectrometer, knowledge of theR values in Eq. 4 could be taken for granted, since theisotope intensity ratios measured would be equal to theisotope abundances to a high degree of approximation,because of the highly similar chemical and physical be-haviour of the isotopes. This approximation is not val-id, of course, for different elements which have, amongother differences, different ionisation potentials andthus ionisation cross sections. The non-ideal behaviourof real mass spectrometers, which shows up, for exam-ple, in a mass bias (dependence of the signal on themass), even if the isotopes are close together on themass scale, can, in general, be corrected for using auxil-iary methods. This does not devaluate the method butlimits its accuracy.

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The accuracy achieved in the analytical result de-pends on the kind of mass spectrometer – more precise-ly, on the kind of ionisation and mass separation used.The properties of the mass spectrometer must be stableand exactly known so that the appropriate correctionscan be applied. The accuracy of the total analytical pro-cedure is usually limited by uncertainty components as-sociated with the sample pretreatment – in particular, ifmany steps are involved. In general, IDMS yields moreaccurate results than other methods, given the same de-gree of analytical difficulty. Because of its insensitivityto substance losses in the sample pretreatment stage,IDMS particularly shows its superiority in analyticaltasks where complex matrices are involved. This iswhat makes IDMS so versatile, at the same time retain-ing high accuracy comparable to that of gravimetry andtitrimetry.

After these considerations it can finally be statedthat IDMS has all properties of a primary method inchemical analysis. This statement is not invalidated bythe fact that IDMS can be used in variants in which itsprimary capability is not fully used. This can be advan-tageous if, for example, the spike is not completelycharacterised, but a high-purity substance which can beused as a laboratory standard is available instead. Insuch a case, the spike is essentially used as an indicator,and the analyte is determined iteratively [8]. In organicanalysis, application of IDMS mostly relies on deuter-ated or 13C-labelled compounds as spikes. Because ofthe higher relative mass separation of 13C and 12C and,in particular, D and H compared with, for example,206Pb and 208Pb, differences in behaviour of the isotopicsubstances are more likely to occur, thus requiringlarger corrections associated with higher uncertainties.

A special version of IDMS in organic analysis, whichincludes a combustion step converting analyte andspike into a mixture of 12CO2 and 13CO2 which is thenanalysed using a dedicated mass spectrometer, can beexpected to yield optimum results [9].

Other methods

Methods using colligative properties like freezing-pointdepression or boiling-point elevation for amount-of-substance determinations have, in principle, also thepotential of being primary methods. The basic require-ments at least are fulfilled. Whether highest metrologi-cal quality can be reached depends on the results of in-vestigations currently underway.

Optical absorption spectrometry is also a candidatefor a primary method. The measurement equation:

t(l) p exp [Pk (l) c l], (5)

often called Lambert-Beer’s law, is valid under certainconditions. The lower the concentration of the absorb-

ing centres (e.g. molecules) in the light path and thenarrower the observation band width compared withthe width of the absorption feature (e.g. spectral line orband) of the substance to be determined, the better thecompliance with these conditions. In Eq. 5, t(l) is thetransmittance of the (homogeneous) optical mediumcontaining the analyte, k(l) the concentration-relatedabsorption coefficient, c the concentration of the ana-lyte to be determined and l the optical absorption pathlength. If k(l) is known from independent primarymeasurements with known (small) uncertainty, optical-absorption spectrometry meets the essential require-ments of a primary method. The overall uncertainty at-tainable depends on the perfection in which Eq. 5 canbe realised in practice. Important requirements are: ac-curate knowledge of the effective path length l andcomplete symmetry between the two radiative powermeasurements constituting t(l), namely the one withabsorbing sample and the one without absorbing sam-ple in the light path. The symmetry requirement meanshere that it must be possible to exchange the sample forthe non-absorbing medium keeping everything elseconstant. This is a very demanding requirement.

An important application of optical absorption spec-trometry is ozone determination in ground-level air andin the stratosphere using optical absorption in the UVspectral range. Eq. 5 can be regarded as being applica-ble here (very low concentrations, between 1 and10 mmol/m3, narrow observation band width due to us-ing the 254-nm Hg emission line, broad UV absorptionband of ozone with maximum at 255 nm), and the ab-sorption coefficient is known, at least as a conventionaltrue value [10]. The measurement instrumentation forozone determination has reached a high degree of so-phistication. Because of its high reactivity, ozone pres-ents special handling problems even in this low concen-tration range, so that it is difficult to use optical absorp-tion spectrometry, being a primary method in principle,to its full capability in this special case.

Establishment of traceability of chemical

measurements to the SI units using primary methods

As mentioned already in the introduction, primarymethods of measurement serve the important purposeof establishing traceability of measurement results ofall kinds of physical quantities to the corresponding SIunits. Chemical measurement results, in particular, canbe made traceable to the corresponding SI units usingthe primary methods described above to link up inter-mediate reference points with the SI units. With respectto such reference points instrumental analytical tech-niques are calibrated which are nowadays mostly usedfor carrying out chemical analyses at the working level,because of their high sensitivity, speed, versatility and

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Fig. 1 Possible ways of realising traceability of chemical measure-ments to the SI units using primary methods and intermediate ref-erence points

precision and hence cost-advantage, but which arethemselves usually not primary methods. In this way, atraceability system can be built up, at least for the mostimportant analytical measurement tasks. Figure 1shows how this goal can be achieved.

Four routes are distinguished in Fig. 1. Starting onthe left side, reference materials of chemical composi-tion are shown as intermediate reference points. Refer-ence materials are most frequently used as measure-ment standards in chemical analysis. If these are linkedup with the SI units of the corresponding compositionalquantities by means of primary methods and, at thesame time, sufficiently match the sample matrix, thetraceability chain is complete. For many analyticalmeasurement tasks, local or sectorial comparability issufficient. In such cases, of course, traceability to the SIis not required, and reference materials based on con-sensus values, for example, can be used as referencepoints. But even in such cases, reference materials can-not solve every analytical problem. Besides matrix mis-match, mentioned already, limits due to substance in-stabilities are set, in which case reference materials can-not be prepared.

Other measurement standards, for example in theform of measurement devices (including procedures)which can provide or reproduce chemical compositionswith high accuracy, can be used as intermediate refer-ence points in such cases. The ozone spectrometermentioned above is given as an example in the secondroute of Fig. 1. Dynamic calibration gas-generating de-vices based on primary flow measurement methods areanother example. Reference laboratories specialisedfor distinct measurement tasks and themselves tracea-ble to the SI units via primary methods serve as inter-mediate reference points in the third traceability route.Because of the high complexity of many chemical

measurement tasks, specialised laboratories will play anincreasingly important role as reference points. In clini-cal chemistry, for example, reference laboratories formany analytical measurands have been established fora long time. Traceability to the SI units, at least for thewell-defined analytes, is of particular importance and isincreasingly sought by these laboratories.

The fourth route, finally, exemplifies cases in whicha chemical laboratory (in the field) is able to establish adirect link to the SI units using a primary method for aparticular chemical measurement problem. Of course,this is not the usual application of a primary method.Primary methods will mainly be reserved for linking upreference points to the SI units (e.g. reference materi-als), thus providing access to the SI units for the work-ing level in a convenient and economical way, accord-ing to the principle of division of labour. Direct appli-cation of primary methods is open, however, to everywell-equipped and experienced laboratory.

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