Chemical Education Today
Letters SI for Chemists: Persistent Problems, Solid Solutions
SI Basic Units: The Kilogram and the Mole1 I was stirred by two recent articles in the January 2003 issue of this Journal (1, 2). The persistent perceived problem with the base units kilogram and mole addressed in those articles is resolvable once it is finally recognized that we have been using a double standard: the international platinum– iridium kilogram prototype and 12C. I believe this practice is unnecessary. It has led arguably to bewilderment and a plethora of commentary in this Journal and elsewhere (see citations in 1, 2 ), some of which has just compounded the confusion. Among the seven SI base units, the second has been defined since 1967 as (3): the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
Also the meter has been defined since 1983 as (3): the length of path traveled by light in vacuum during a time interval of 1/299,792,458 of a second
(the reciprocal of the integral speed of light, defined exactly). Both of these base unit definitions involve integers and are not subject to experimental uncertainty. I propose, following the lead of what the physicists did for time and distance, that we consider the SI base unit, the mole, to be an integer, which logically it should be. Avogadro’s number is exactly the integer 602,214,180,000,000,000,000,000 and the mole is equal to Avogadro’s number.2 The US National Institute of Standards and Technology (NIST) for several years has been addressing the unsatisfactory situation of the standard kilogram ingot by designing a highly sophisticated watt balance from which the “electronic kilogram” could be standardized (4). This yeoman’s achievement would lead to a more precise and stable standard, but one still a step shy of reaching the fundamental status shared by other base units. Avogadro’s number is also the number of atoms of 12C in 12 grams of 12C. It leads to an exact definition of the kilogram, the mass of (1000/12) moles 12C atoms, or the mass of 50,184,515,000,000,000,000,000,000 atoms of 12C. The unified atomic mass unit is then defined exactly (in grams) as the reciprocal of Avogadro’s number (or as the reciprocal of 1000 times Avogadro’s number for kg). Only integers are involved in the definitions. The (platinum–iridium) international prototype of the kilogram, established in 1901 (which should tell you something) is currently the only SI base unit entrenched in an artifact rather than in a fundamental natural property. With the proposed re-definition, that relationship is relegated to being of secondary importance.
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The mole is a number. I regard “amount of substance”, used in the mole’s existing controversial definition, as an unacceptable alternative. Contributing to my bias in this regard is the fact that spectroscopists have a unit, the einstein. which is defined as a mole of radiation quanta, the latter definitely not being a substance under accepted terminology. Notes 1. The proposal herein received unanimous endorsement by the ACS Committee on Nomenclature, Terminology, and Symbols by those attending its March 24, 2003, meeting in New Orleans, LA. 2. This is in the same sense as a dozen is equal to the number 12.
Literature Cited 1. Freeman, R. D. J. Chem. Educ. 2003, 80, 16–21. 2. Gorin, G. J. Chem. Educ. 2003, 80, 103–104. 3. Mills, I.; Cvita`s, T.; Homann, K.; Kallay N.; Kuchitsu, K. Quantities, Units and Symbols in Physical Chemistry; Blackwell Scientific: Oxford, 1988. 4. Schwarz, J. P.; Liu, R. M.; Newell, D. B.; Steiner, R. L.; Williams, E. R.; Smith, D.; Erdemir, A.; Woodford, J. J. Res. NIST 2001, 106, 627–640. Paul J. Karol Department of Chemistry Carnegie Mellon University Pittsburgh, PA 15213
[email protected] The author replies: Karol’s letter is a prime example of the type of article about which he complains in his first paragraph. There are four major flaws in Karol’s suggestions. First, Karol suggests defining Avogadro’s number NA and then defining the kilogram in terms thereof. The only way to do that—and avoid circular reasoning—is to count individual atoms/molecules, that is, to use the definition directly in the experimental observations. One can quickly show that one million chemists, each counting water molecules at the rate of two per second, or one chemist counting two million per second, would require about ten billion years—roughly the age of the universe—to count one mole of molecules. Unless Karol can point to specific technology which can do much faster counting, his suggestion deserves no consideration. Second, a few lines after he defines NA as an integer, Karol writes “Avogadro’s number is also the number of atoms of 12C in 12 grams of 12C.” It is not clear how this statement is to be interpreted. If it is meant to be an assertion that this present definition of NA is still valid along with the “integer” definition, then the statement is nonsense; one cannot logically have two, possibly incompatible, definitions of
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a given quantity. On the other hand, if Karol’s statement is meant to be a new definition of the “gram”, that should have been stated explicitly and the procedure for realizing the “new gram” in terms of a counted number of atoms should have been described and/or referenced. Third, Karol emphasizes the desirability of defining a base unit in terms of an integer. We already have an integer unit for mass —unfortunately, not (yet?) the base unit. The “unified atomic mass unit”, or better, the dalton, is defined: 1 Da = m(12C)/12, or equivalently, m(12C) = 12 Da, exact. For the kilogram, since 1 g = NA Da, 1 kg = 1000 NA Da. The problem with redefinition of the kilogram is not the absence of “an integer”; rather it is the difficulty in comparing macroscopic masses with microscopic masses and in determining the mass of large (1 kg) masses with adequate precision. For example, in ref 1 masses of many nuclides are given, in u or Da, with an uncertainty of a few parts in 1p9 (2), and some a few parts in 1p10; in contrast, masses of the electron, proton, and neutron are given, in kg, with an uncertainty of a few parts in 1p6. The relation between u/Da and kg is given with an uncertainty of 1 in 1p6. Fourth, Karol’s insistence that “The mole is a number” is a restatement of an illusion that has plagued chemical logic for many years. To illustrate, consider a certain quantity of liquid in a flask. How do we tell someone what is in the flask? We could say: The flask contains (1) 18 grams of water, or (2) 18 milliliters of water, or (3) one mole of water.
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By Karol’s logic, item (3) translates to “The flask contains 6.022p23 of water”, a statement neither clear nor logical. Alternatively, we could describe what is in the flask this way: The flask contains some liquid, water, (A) which has a mass of 18 grams; (B) which has a volume of 18 milliliters; or (C) which is composed of one mole of H2O.
Items 1, 2, 3 are the usual, everyday statements—shortcuts for items A, B, C that emphasize that in each case we are talking about the same quantity of matter, but are describing it in three different ways. It makes no sense that this quantity of matter would be described in terms of a physical quantity—a number with a unit—in 1, 2, A, and B, but by a number only in 3 and C. The proper interpretation of “mole” is: the quantity of matter (and energy) in NA monons (3). Literature Cited 1. Mills, I.; Cvita`s, T.; Homann, K.; Kallay N.; Kuchitsu, K. IUPAC Quantities, Units, and Symbols in Physical Chemistry, 2nd ed.; Blackwell Scientific: Oxford, 1993. 2. In this notation, 6.0p23 = 6.0 ⫻ 1023; 1.6n27 = 1.6 ⫻ 10᎑27. See the articles Freeman, R. D. J. Chem. Educ. 1978, 55, 103 and Peckham, G. D. J. Chem. Educ. 1997, 74, 64. 3. Freeman, R. D. J. Chem. Educ. 2003, 80, 16–21. Robert D. Freeman Enody Unlimited 116 S. Kings St. Stillwater, OK 74074-2513
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