Primary methods of measurement in chemical analysis

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  • Accred Qual Assur (1997) 2 :354359Q Springer-Verlag 1997 GENERAL PAPER

    Wolfgang Richter Primary methods of measurement inchemical 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 Comit Consul-tatif pour la Quantit de Matire(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


    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 Comit Consultatif pour la Quantit de Matire(CCQM), the new metrology body under the Conven-tion du Mtre, 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.


    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 104 have been achieved [5]. In gen-eral, 103 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 areverse 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.


    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 to103 can be achieved if the method is used to its fullmetrological capability. Titrimetry is also used for thecertification of SI-traceable reference materials.


    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 7 106) C mol1 is accurateenough for any coulometric determination. The generalmeasurement equation is:


    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 nais 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 se...