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Mole, Mole per Liter, and Molar A Primer on SI and Related Units for Chemistry Students George Gorin Department of Chemistry, Oklahoma State University, Stillwater, OK 74078;
[email protected] The purpose of this article is to discuss the measurement units mole and mole per liter and the meaning of the adjective molar in a chemical context. Clarification of these terms is desirable because, in general, elementary chemistry textbooks do not give an adequate description of the SI system of measurement and its historical development. Students unfamiliar with these topics might reasonably wonder why the mole, used so frequently in chemistry, was not admitted into the SI until 1971. It may be surprising to some that the unit liter is not part of the SI and, consequently, they may wonder about the status of the unit mole per liter. In order to place the discussion in a proper setting, a brief overview of the pertinent historical aspects of the SI is given. Then, the relation between the concept of mole and number is considered, as well as the question of naming the quantity that is conventionally measured in mole units. The status of molar, vis-a-vis the pertinent SI units, is discussed in the final section. A Brief Historical Overview of the SI The SI is a direct descendant of the Metric System of measurements, which was devised at the behest of the French government in 1790–1799. It is based on an international treaty, the Convention du Mètre, drafted in 1875. At that time, representatives of seventeen countries provisionally ratified the Treaty. Adherence to the Treaty by the United States was formally approved by the Senate and President R. B. Hayes in 1878. At the present time, about fifty countries are members of the Convention and provide support for the International Bureau of Weights and Measures (BIPM), which is located near Paris. The BIPM operates under the authority of the General Conference of Weights and Measures (CGPM), which is made up of representatives from the member countries and is convened at regular intervals; more than twenty CGPMs have been held to date. The 11th CGPM, which met in 1960, adopted the acronym SI as the official designation for the system, which is valid in all languages. The 1960 CGPM also adopted the second as the fundamental unit of time and the abbreviation “s” for this unit. The second and five other units were classified as base units; those pertinent to this discussion are the meter (m) and the kilogram (kg). Five of these base units have been defined operationally with reference to precisely defined and reproducible experimental procedures, while kilogram is defined with reference to the International Prototype Kilogram (IPK), an artifact that was manufactured for the purpose under the supervision of the BIPM, which has custody of it. These provisions ensure that there are no ambiguities in the definition of these units beyond the uncertainty that attaches to all experimental observations. Other prototypes of the kilogram were manufactured at the same time as the IPK, examined and approved by the 1st
CGPM, and then distributed to the member countries. The United States received two prototypes of the kilogram, which are now in the custody of the National Institute for Standards and Technology (NIST). In 1896, these prototypes were declared to be “the Nation’s fundamental standards”, and all of the other units now in use in the United States have been defined with reference to these standards (1). In the SI, the units that can be defined by algebraic manipulation of the base units, without introducing any arbitrary numerical factors, are said to be “derived and coherent”. The 11th CGPM approved special names for many such units, and several have been added subsequently. A familiar example is the joule (J), defined as 1 J = 1 kg m2 s᎑2. No explicit criteria have been set down for choosing the base units, but it should be understood, in any case, that the base units are not necessarily more important than the derived units. As we have seen, the second was not formally admitted to the SI until 1960, while joule was adopted as an SI unit in 1948 by the 9th CGPM. The Concept of Mole and the Definition of Mole Unit The concept of mole developed gradually in the course of the 19th century, and its exact origin has not been identified. In any case, by the end of that century, almost all chemists had accepted a self-consistent table of atomic weights. It was generally understood that these so-called weights are unitless, inasmuch as they describe the relative masses of the element’s atoms, measured on an arbitrary scale in which the atomic weight of oxygen was set equal to 16. Subsequently, it was discovered that naturally occurring oxygen contains small amounts of nuclides with atomic weights of 17 and 18. This led many physicists to adopt a slightly different scale, in which the value of 16 was assigned to the predominant isotope of oxygen. In the 1960s, the International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics agreed to change the atomic weight scale to one in which the predominant isotope of carbon was assigned an atomic weight of 12. This agreement paved the way for the admission of mole into the SI. Formally, this action was taken by the 14th CGPM in 1971. The pertinent resolution defines mole as “the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12; its symbol is mol. The elementary entities .... may be atoms, molecules, ions ...[and] other particles or specified groups of such particles.” The resolution further states that mole is a base unit, to be added to the six base units mentioned in the previous section (2). Some aspects of this definition require further comment. First of all, what is the significance of the phrase “the amount of substance of a system”, which does not parse quite right in English? It should be noted that, in 1970, there did not exist
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a generally accepted designation for the quantity of which mole is a unit, and hence the phrase “amount of substance” was used to designate that quantity; although the chosen wording is awkward, it is not ambiguous. An early attempt to resolve this difficulty was made in 1977, when the name “psammity” was proposed for the “quantity-measured-inmoles” (3); however, that proposal did not find favor within the chemical community, and several alternative proposals have met the same fate (4). In 1993, the IUPAC Commission on Physicochemical Terminology (IUPAC/CT) recognized the term “chemical amount” as a valid synonym for amount-of-substance (5), and, based on that terminology, mole can be defined as the magnitude of chemical amount which contains as many constituent particles as 12 g of carbon-12 (6). The latter designation will be used in what follows. Since the admission of mole into the SI, numerous articles have been written, endeavoring to explicate some aspect of the subject that their respective authors regarded as unclear. In particular, several authors have argued that students would understand the concept of mole more easily if they were taught that mole is “like a number” (7). However, this is a controversial issue. With regard to the SI definition of the mole, it should be noted that the measurement of chemical amount has nothing to do with the process of counting, and that the mole must be regarded as a base unit, inasmuch as it cannot be defined in terms of the other base units; further discussion of this matter may be found in reference (6). The Status of Liter in the Metric System and the SI The original Metric System introduced liter (litre in French) for a unit of volume, or capacity, defined as the volume occupied by 1 kg of pure water at 4 ⬚C. This definition was reaffirmed by the 3rd CGPM, in 1901. However, subsequent measurements demonstrated that the cubic decimeter differs from the liter, as defined above, by about 28 parts per million. In 1964, the 12th CGPM took official note of this fact, and decided to abrogate the 1901 definition. In terms of the logical structure of the SI, as it was formulated in 1960, volume is a derived quantity, and the coherent SI unit of volume is the cubic meter. Accordingly, the 12th CGPM declared that “the word liter may be employed as a special name for the cubic decimeter ... [but that] liter should not be employed [to describe] high accuracy volume measurement” (2). The wisdom of this decision is open to question, inasmuch as it renders the status of liter somewhat ambiguous and confusing; however, a decision that has been approved by a CGPM may not be modified unilaterally. In any case, it should be clear that the issue is of no practical consequence for the vast majority of cases. NIST has declared that, within the United States, liter is an “acceptable unit”, equal to the cubic decimeter, without qualifications, and the former name will be used. The preferred abbreviation for liter is L and 1 L = 1000 mL = 0.001 m3 (8). Molar and Molarity The unit mole was introduced around 1900, and its adoption by chemists was gradual. Unquestionably, it is very convenient to use this unit in describing the composition of solutions, especially the so-called “standard solutions” that 104
are used in volumetric analysis. From about 1930 onward, most chemists have described such solutions with the adjective molar; that is, a solution that contains 0.1012 mol of HCl per liter of solution is usually said to be 0.1012 molar, and molar is represented by the symbol M. However, representing the derived SI unit (mol/L) in this way is clearly not in agreement with the recommend rules for representing SI units in general. Some textbooks use M to represent both the unit (mol/ L) and the corresponding quantity. In many textbooks, this quantity is called molarity, while a few texts call it molar concentration. This muddled symbolism and nomenclature may be confusing to students; although the intended meaning can usually be deduced from the algebraic context, using (mol/L) instead of M may be helpful in avoiding possible confusion. IUPAC/CT does not endorse the aforementioned use of molar and molarity (5). It has taken the position that the adjective molar, when modifying the name of an extensive quantity, signifies division of that quantity by chemical amount (n), as for example, in molar volume (V兾n). Although concentration is not an extensive quantity, the cited source recommends that the quantity conventionally expressed in moles per liter be called “amount (-of substance) concentration”. On the other hand, the Clinical Chemistry division of IUPAC prefers “substance concentration” to “amount concentration”. Neither designation is clearly self-explanatory, and it seems likely that the term molarity will continue to be used, at least in the near future, in preference to the recommended designations mentioned above. IUPAC/CT recommends using the symbol c for the quantity in question, and this symbol should be useful in general. In special cases, such as equilibrium expressions, alternative symbols may be preferable; confusion can be avoided by taking care to define unconventional symbols in an explicit way. A note published in this Journal in 1985 called attention to these problems (9), however no progress to date has been made toward a resolution. Consequently, the suggestion in the note still holds good at the present time. Teachers should emphasize the algebraic definition of the quantities in question, and they should not rely on approved nomenclature to make subtle distinctions between related quantities. Literature Cited 1. Treat, C. F. A History of the Metric System Controversy in the United States; NBS Special Publication 345-10; Government Printing Office: Washington, DC, 1971. 2. The International System of Units (SI); NBS Special Publication 330; Government Printing Office: Washington, DC, 1977; pp 16, 20, 26, 30. 3. Kell, S. G. Nature 1977, 267, 665. 4. Gorin, G. J. Chem. Educ. 1982, 59, 508. 5. Mills, I. M.; Cvitas, T.; Homann, K.; Kallay, N.; Kuchitsu, K. Quantities, Units and Symbols in Physical Chemistry, 2nd ed.; Blackwell Science: Oxford, 1993; pp 7, 42. 6. Gorin, G. J. Chem. Educ. 1994, 71, 114. 7. Dierks, E. Eur. J. Sci. Educ. 1981, 3, 145. 8. Taylor, B. N. Guide for the Use of the International System of Units (SI); NIST Special Publication 811; Government Printing Office: Washington, DC, 1995; p 8. 9. Gorin, G. J. Chem. Educ. 1985, 62, 741.
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