Concentration is one of the most frequently measured quantities and, in this respect, is similar to mass, length, and temperature [i]. However, regardless of the mass character of measurements of this quantity, there is as yet no common concept of the metrological provisions for these measurements [i-7]. The basic reason for the absence of a common concept consists in that there is no common approach to the idea itself of concentration as a measured physical quantity, its units, and principles of providing for unanimity in its measurements. Recent publications on these questions [28, 29] have not only not clarified, but further made it difficult to understand the true character of concentration as a self-contained and independent quantity. An attempt is made in this article, on the one hand, to clarify prevailing contradictions on each of the positions enumerated above and, on the other, to propose solutions to eliminate some of them. Along with temperature and pressure, concentration is a basic and independent thermodynamic parameter which determines the thermodynamic properties of a specific system. Moreover, as a measured physical quantity, it belongs to the category of derived physical units in the International System of Units (SI). Analysis of Standards and Technical Documents (STD) and handbooks dealing with the SI [8-10] shows (Table i) that, unlike other physical quantities, it is necessary to establish in this case, not one, but several self-contained physical quantities which reflect the same qualitative characteristic of an object of measurement. At the same time, in accordance with [9, pp. 49 and 54], mass, molar, and volumetric fractions are not derived units of the SI and are individually distinguished as relative quantities. As per definition, the number i or its multiple fractions as percent, pro mille, or millionth fraction are units of these relative quantities. Such an interpretation of the physical quantities of concentration was naturally taken into account in educational guides and was introduced in school [Ii] and university  programs. Here, it has been especially emphasized in [Ii, p. 36] that "the fraction, a dimensionless relative quantity, cannot be termed as concentration (mass, volumetric, and molar) under any circumstances" and only two physical quantities can be placed in the category of concentration, i.e., molar and mass concentrations. This approach was presented in the form of a table as a marginal note on the cover in  (see Table 2). TABLE 1 Unit
Molar concentration Concentration of molecules, ions, neutrons (number of particles in volume unit)
Mole per i mole/m ~ per cubic centimeter i Meter raised I m-~ to power of minus three
Kilogram per cubic meter
Translated from Izmeritel'naya Tekhnika, No. 12, pp. 40-42, December, 1990.
9 1991 Plenum Publishing Corporation
TABLE 2 Expression for composition of solutions Concentration 1.~Molar concentration 2. Mass concentration 3Volumetric concentration
The contradiction in this interpretation of concentration consists, firstly, in the fact that the same qualitative characteristic of an object of analysis is expressed in the given case by, not one, but a series of physical quantities. This contradicts the definition of the concept of a "physical quantity". Secondly, if values like molar, volumetric, and mass fractions are not derived units of the SI and have nothing in common with concentration as a physical quantity (which follows from the approach established in the STD), then, how can a State Primary Standard (SPS) of the unit of molar fraction of components be created? Meanwhile, such a standard has been drawn up and adopted . Thirdly, as it follows from the very fact of adoption of the above SPS, if the molar fraction represents a self-contained physical quantity, then, the number 1 or its multiple fraction should function as its unit. And this contradicts the concept of "unit of a physical quantity." With a view to investigate these contradictions, we examine the definition of the concept "concentration" as adopted in chemistry particularly in the fields of general, physical, and analytical chemistry. The most common definition of "concentration" that can be taken as its definition as a physical quantity is in [13-15]. Thus, the following definition is given in : concentration is a quantity which expresses the relative content of a given component (component part) in a mixture or solution. Practically an identical definition is recommended by the Scientific and Technical Terminology Committee of the Academy of Sciences of the USSR . In the light of the above, the following clarification is noteworthy : "Various methods are used for expressing concentration. Here, along with methods in which amounts of a given component are expressed in identical quantities (this means selection of identical quantities both for the characteristic of the component and for that of the mixture - Yu. I. Aleksandrov), even methods in which these are expressed in different quantities are used. The most widely used methods are as follows: i) weight fraction; 2) molar fraction; 3) volumetric fraction; 4) molarity; 5) molality; 6) normality; 7) titer." As we can see, the enumerated methods of expressing concentration represent different quantities. In this context, we need to pay attention to the fact that weight, molar, and volumetric fractions are taken as equitable units of concentration along with acknowledged ones like molarity and molality. The correctness in relatig molarity, molality, titer, and also mass (weight), molar, and volumetric fractions to units of concentration is borne out by analysis of [16-21]. It can be countered that the majority of the quoted references were published when the SEV standard  was not yet in force. However, this situation can in no way affect the scientific content of the concept of concentration, i.e., on the basis of the very definition of the concept "physical quantity," concentration can be represented by only a single physical quantity. In view of the above, all physical quantities which characterize concentration, and are given in the STD as self-contained, are no more than units of this unique physical quantity. It is precisely this approach to concentration that corresponds to the basic positions, not only in chemistry, but also in metrology. In stating this, the author has no pretensions to novelty. It is sufficient to acquaint ourselves with the approach to concentration developed in the US Institute of Standards and Technologies (previously the
TABLE 3 Physical quantity name
Unit of physical ~ t i t y name
L -~ M
M-~N ,N~ M o
Molality Molar fraction Mass fraction Volumetric fraction
xi Yi X~
National Bureau of Standards, USA). I t is not by chance that, in one of the most authoritative journals on analytical chemistry [22, 23], concentration has been interpreted as an unique physical quantity of the SI which has several units. In this interpretation, molarity and molality have been unambiguously related to units of concentration. Such an approach to concentration, although with direct reference to NBS, USA, is also proposed in . Thus, there is a divergence in the approach to concentration as a physical quantity in foreign and Soviet metrology. In order to resolve this contradiction, we should proceed from the scientific content of the concept "concentration" formulated in [14, 15] and not from contradictory concepts generally accepted abroad. As the most general definition, it should simultaneously be considered as the definition itself of concentration as a physical quantity. It follows from the definition of the concept "physical quantity" adopted in metrologyy that each specific property can be represented by only one physical quantity which reflects precisely the given qualitative characteristic of the object. Hence, it must be conceded that concentration can be represented by only a single physical quantity. Moreover, in selecting units of concentration, it is necessary to account for the specific areas of its use. From this point of view, limitation of the units of concentration to only one (molar), as in the approach developed at the NBS, USA, creates only additional difficulties in practically providing for unanimity in measurements of concentration. In view of this, in practice, it is not only permissible but also advisable to use different units of the SI for these purposes . All units of concentration obtained in this case will also be units of the system of measurements. Units of concentration obtained by using units of the following three quantities for the purpose are in Table 3: mass (M); volume (L3); quantity of substances (N). The dimensionality of not only the units of concentration, but also of concentration itself is thereby determined. Mass concentration is the unit of concentration corresponding to a content of i kg of the given component in I m s of the mixture. Molar concentration is the unit of concentration corresponding to a content of i mole of the given component in I m 3 volume of the solution. Molality is the unit of concentration corresponding to a content of 1 mole of the given component in i kg of the solvent. Mass fraction of component A is the ratio of mass of component A in the mixture to mass of the mixture. Molar fraction of component A is the ratio of amount of component A in the mixture to total quantity of the components of the mixture. Volumetric fraction of component A is the ratio of volume of component A in the mixture to volume of the mixture. Mass, molar, and volumetric fractions are equal to unity when a substance is absolutely pure . Since such a state of a substance is practically unattainable, these fractions are not equal to unity but approximately close to it in the case of the main component of highly pure substances. It is a serious mistake to interpret mass, molar, and volumetric fractions of a component in a mixture as a relative quantity having nothing in common with concentration. We may encounter the affirmation that concentration itself is a relative quantity . With these approaches we allow the qualitative characteristic of the physical quantity denoted as concentration to escape from our view while keeping in mind only the method of calculating this quantity. Although concentration indicates the relative content of the component, it does not quite follow from this that it is a relative quantity. We compare specific mass with mass fraction to clarify this point.
Specific mass of a material is its mass divided by the mass of an equivalent volume of water at 4~ On the basis of its definition, it is a dimensionless quantity unconnected with any system of units which fact itself determined its extensive use in trade. Mass fraction of a component, even if defined through the ratio of masses, represents a definite property of the object, in particular, the relative content of a given component in a given mixture. The specific characteristic of concentration is the dual character of this physical quantity. On the one hand, as already pointed out concentration pertains to thermodynamic parameters which determine the properties of a specific thermodynamic system. On the other, it itself represents one of the properties of this system. In this case, there are instances when such a property, caused by the concentration of a determined component, is distinguished as a self-contained physical quantity. A classical example in this context is the so widely known property like humidity representing, besides this, nothing but simply the concentration of water (water vapor) in a specific object. Another example can be that of pH, i.e., the concentration of hydroxonium ions. In both cases, units of concentration different from those in Table 3 are used for measuring these properties. Thus, the p-function is used for measuring pH, i.e., pH = -logIHsO+] , where, hydroxonium ion concentration is represented in units of molarity while a series of units are used for measuring humidity. A discussion of this is not within the purview of our problem. Thus, concentration has characteristics distinguishing it from other physical quantities, in particular, it has, not one, but several units and it is always a concrete quantity. These characteristics of concentration themselves determine the selection of the principles of ensuring unanimity in its measurements. LITERATURE CITED i. 2. 3. 4. 5. 6. 7.
L. N. Filimonov et al., Zavod. Lab., 54, No. Ii, ii (1988). B. R. Kaplan and L. N. Filimonov, ibid, 51, No. 6, 3 (1985). N. G. Semenko, ibid, 51, No. 6, 7 (1985). L. N. Filimonov, Zh. Anal. Khim., 42, No. 4, 581 (1987). Yu. L. Pliner and I. M. Kuz'min, Zavod. Lab., 53, No. i0, 4 (1987). Yu. I. Aleksandrov~ Vysokochist. Veshch., No. i, 213 (1989). N. G. Semenko and E. G. Burykina, Creation of a System of Standard Specimens of the Soviet of Economic Mutual Assistance [in Russian], Review Information, Moscow (1987), p. 2. ST SEV 1052-78, Metrology. Units of physical quantities. RD 50--160-79, Methodical instructions. Introduction and use of ST SEV 1052-78. G. D. Burdun, Handbook on International System of Units [in Russian], Izd.-vo. Standartov, Moscow (1977), p. 29. L. R. Stotskii, Physical Quantities and Their Units, Reference Manual [in Russian], Prosveshchenie, Moscow (1984), p. 36. E. Yu. Yanson, Theoretical Principles of Analytical Chemistry: Textbook for Chemistry Faculties in Universities [in Russian], Vysshaya Shkola, Moscow (1987). Chemical Encyclopedic Dictionary [in Russian], Soy. Entsiklopediya~ Moscow (1983), p. 275. A Short Chemical Encyclopedia [in Russian], Vol. 2, Soy. Entsiklopediya, Moscow (1963), p. 707. Thermohynamics. Basic Concepts. Terminology. Nomenclature of Quantities by Letters: Collection of Definitions, Issue 103, Committee on Scientific and Technical Terminology of the Academy of Sciences of USSR [in Russian], Nauka, Moscow (1984), p. I0. N. L. Glinka, General Chemistry, Instructional Manual for Higher Educational Institutions [in Russian], Khimiya, Leningrad (1980), p. 214. W. Slabaugh and T. D. Parsons, General Chemistry [Russian translation], Mir, Moscow (1979), p. 203. H.A. Laitinen and W. E. Harris, Chemical Analysis, McGraw Hill, New York (1975). A. P. Kreshkov, Principles of Analytical Chemistry. Theoretical Principles. Quantitative Analysis [in Russian], Khimiya, Book 2, Moscow (1976), p. 60. Ya. I. Gerasimov, A Course in Physical Chemistry [in Russian], Vol. i, Khimiya, Moscow
A. I. Brodskii, Physical Chemistry [in Russian], Vol. 2, GNTIKhL, Moscow (1948), p. 499.
8. 9. i0. ii. 12. 13. 14. 15.
16. 17. 18. 19.
(1969), p. 149.
22. 23. 24. 25. 26. 27. 28. 29. 30.
"SI Units," Anal. Chem., 59, No. i, 222 (1987). "SI Units," ibid, 60, No. i, 94 (1988). G. Ewing Instrumental Methods of Chemical Analysis [Russian Translation], Mir, Moscow (1989), p. 13. P. MacGarthy, J. Chem. Educ., 6_~0, 187 (1983). G. G. Devyatykh and M. F. Churbanov, Vysokochist. Veshch., No. 2, 5 (1987). N. G. Semenko and V. A. Sapozhnikov, Izmer. Tekh., No. I0, 14 (1986). V. M. Tslaf, ibid, No. 6, Ii (1980). M. G. Kozlov and G. R. Nezhikhovskii, ibid, No. 7, 55 (1990). M. G. Kozlov et al., ibid, No. 7, 58 (1990).
MANUFACTURER'S TESTING OF DIELCOMETRIC PETROLEUM MOISTURE GAUGES S. I- Maksimov
In accordance with existing rules [i], the process of control of a dielcometric (capacitance) moisture gauge should be carried out in two stages. The first stage consists of determining the natural working characteristics of the primary capacitance transducers. The procedure here reduces to measurement of the mounting (spurious) Cm and working C O capacitances of the transducer by the method of measuring two common capacitances of these transducers in air C a = C o + Cm. In this case, the transducers are filled with liquid of known dielectric constant E (to the third place of decimals, for instance, for benzene E b = 2.340 • 0.001); C b = e0C o + Cm. A strict temperature regime of 20 • I~ has to be observed during measurements. The working capacitance C o = (C b - Ca)/(e b - i) and mounting capacitance Cm = C a - C o are determined from results of above two measurements. The second stage consists of adjustment and determination of basic metrological parameters of the moisture gauge as a whole. In accordance wieth existing standardization documents, the gauge is mounted on special stand UPVN-2 and synthetic emulsions are prepared by the method of successive additions with sample volume of not less than 8-10 liters of petroleum of one kind (up to 30 liters of total quantity of petroleums per moisture gauge) in accordance with methods in MU 331, MI 1536-86, and MI 1498-86. Difficulties come up when dielcometric petroleum moisture gauges are batch produced by the manufacturer. These difficulties are connected with the need to set up spacial testing laboratories for preparing samples of dry petroleum and certifying these for residual moisture content [i]. Difficulties are also encountered in the use of a "standard" liquid, for instance, benzene or other hydrocarbon with attested dielectric constant. These liquids are, as a rule, toxic and contaminate the environment. Thus, the use of a "standard" liquid for measuring and tuning of mounting and working self-capacitances of transducers by the existing method is a serious impediment to realizing the procedure for testing petroleum moisture gauges without real water-oil emulsions. Tests of these gauges are considerably simplified if both test stages are to be undertaken without using a "standard" liquid and oil. Mounting and working capacitances can be measured without using the liquid by means of a special design of the primary capacitance transducer (pickup). The design of an universal transducer of this sort is in Fig. i. It is a coaxial condenser containing a grounded body in the form of a pipe segment and measuring electrode mounted coaxially inside the body on two screened holders of special design.
Translated from Izmeritel'naya Tekhnika, No. 12, pp. 43-44, December, 1990.