Vol.
32 No. 1
JanuaryFebruary 2010
What is a Mole?: Old Concepts and New continued
Closing Comments from Ian M. Mills
This discussion is really about choosing between two alternative definitions for the unit mole:
 The mole is that amount of substance that contains the same number of entities as 12 grams of carbon 12.
This is the current definition. It has the effect of fixing the molar mass of carbon 12 as exactly 12 g/mol.
 The mole is that amount of substance that contains exactly 6.022 141 79 x 10^{23} entities.
This is the proposed new definition. It has the effect of fixing the value of the Avogadro constant to be exactly 6.022 141 79 x 10^{23} mol^{1}.
The choice 1 is connected with the history of the development of the quantity amount of substance and the unit mole. The choice 2 is thought to be simpler, and removes the dependence on the kilogram; this is thought to be desirable, in order to clarify the distinction between the quantities amount of substance and mass (which are often confused). Although I can see advantages in choice 1, most people prefer choice 2 because of its simplicity.
Jeannin also believes that the Avogadro constant is a “fundamental constant of a lesser breed,” in contrast—for example—to the Planck constant, or the speed of light, which he thinks of as true fundamental constants. He argues that the Avogadro constant is free for us to choose; we could choose to have a different number of entities in a mole; it is at our choice. Many people express that view. However, I believe that is a misunderstanding. It is the numerical value of the Avogadro constant that is free for us to choose, but the value of the Avogadro constant, N_{A}, is a true constant of nature just like c and h.
Consider the effect of choosing 12.044 in place of 6.022. We would then have twice as many entities in a mole, so that we would in effect be defining a new mole that would be twice as large. It should then be given a new name, such as newmole. We would have 1 newmole = 2 mole. For the value of the Avogadro constant we would have N_{A} = 12.044 x 10^{23} newmol^{1},
but this is equal to 6.022 x 1023 mol^{1} because we have doubled both the number and the unit, and the value of N_{A} is the number divided by the unit mol. That is perhaps my strongest criticism of Jeannin’s
presentation.
The impact of redefinition of the mole is significant for practical metrology. The following excerpt from section 4.1.4 of ref. 4 (vide supra, Metrologia, 43 (2006) 227–246) summarizes the idea: “One of the most signiﬁcant beneﬁts of redeﬁning the mole so that it is linked to an exactly known value of the Avogadro constant N_{A} (assuming h, e, and k also have exactly known values) is that other constants will become exactly known, namely, the Faraday constant F, molar gas constant R, Stefan–Boltzmann constant σ, and molar volume of an ideal gas V_{m} (at a speciﬁed reference temperature and pressure), all of which have practical importance in a number of ﬁelds of chemistry and physics.”
The actual values are presented and compared in tables 1 and 2 below. Overall, the uncertainties across the new SI will decrease significantly, and this is
desirable.
Even though not exactly zero by definition, the molar mass uncertainty in the new SI is sufﬁciently small that it can be considered negligible in calculating molar mass for use in the determination of amount of substance. Consequently, the new deﬁnition of the mole will require no change in current metrological practice in any ﬁeld.
Table 1. Comparison of constant uncertainties in the current SI versus and new SI. 

Table 2: Relative standard uncertainties for a selection of fundamental constants multiplied by 10^{8}
(i.e., in parts per hundred million). 

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