The author replies to Karol.

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 N_A 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 N_A 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 N_A is still valid along with the “integer” definition, then the statement is nonsense; one cannot logically have two, possibly incompatible, definitions of 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 = N_A Da, 1 kg = 1000 N_A 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.

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 N_A monons (3).

Literature Cited

1. Mills, I.; Cvitas, 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 x 10²³; 1.6n27 = 1.6 x 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.
   

See Letter re: this letter.

See Karol's subsequent Letter re: this letter.