Avogadro's Number Is Up ...

"The Number" is up for discussion in New Orleans at a special symposium that is of fundamental interest to chemists. In conjunction with the kilogram and the mole, Avogadro's number is facing another round of definition changes. Quantitatively, these definition changes amount to tweaks, improving uncertainties by at least a factor of 10. Qualitatively, they involve serious shifts in ease of understanding. Pending alterations were previously highlighted in C&EN (C&EN, July 18, 2005, page 29).

The International System of Units (SI) has seven fundamental base units: the meter, second, ampere, kelvin, mole, candela, and kilogram. As of 1983, the speed of light in a vacuum was exactly defined as 299,792,458 meters per second. The second is exactly defined as the ground-state hyperfine splitting transition frequency of the ¹³³Cs atom, which is 9,192,631,770 Hz. On the basis of these two measurements, the meter can be exactly defined.

In distinct contrast to the second and the meter, the kilogram is defined on the basis of a physical artifact: a cylinder of platinum-iridium alloy secured under lock and key in a suburb of Paris by the International Bureau of Weights & Measures.

Last September, ABC News reported on an article titled "Shrinking Kilogram Bewilders Physicists," concluding that a kilogram just isn't what it used to be. The international metric mass standard, now well over a century old, is mysteriously losing weight, a fact known for some time. The kilogram standard poses a dilemma because three other SI base units—the ampere, the mole, and the candela—rely on its definition.

Back in 2005, the International Committee for Weights & Measures (CIPM) proposed to redefine the kilogram to improve precision and restore stability. In order to do this, a reference quantity, either Planck's constant, h, or Avogadro's number, N_A— would be used. At about the same time, the ACS Committee on Nomenclature, Terminology & Symbols (NOM) proposed an alternative based solely on Avogadro's number. Both choices are somewhat problematic.

In 2006, a proposal to implement the CIPM recommendation was put forth in the journal Metrologia, advocating a choice that chemists arguably would regard as, by far, the poorest of the options. NOM has promoted the upcoming public forum at the ACS meeting in New Orleans to resolve, or at least clarify, these competing proposals prior to implementation.

One of the leading alternatives for a 21st-century kilogram standard is an almost perfectly round sphere made of an ultrapure single silicon crystal that would have a fixed mass. The silicon option, though, is still a physical artifact and involves making an X-ray crystal density measurement.

Alternatively, the link between quantum-based electrical measurements and mechanical properties, including mass, is being strongly advocated for definition purposes by CIPM. Part of the rationale is that Planck's constant "from the point of view of fundamental physics ... plays a more important role than N_A," because it is the central constant of quantum mechanics, just as the speed of light is central to relativity.

Noted are the beneficial metrological consequences to both the Josephson constant, K_J = 2e/h, and the von Klitzing constant, R_K = h/e², where e is the elementary charge, and the consequent definition of the kilogram as the unit of mass "such that the Planck constant is exactly 6.6260693 ?? 10^-34 joule seconds." But the basis of measurement systems is taught in schools and universities, and it is preferable, as all seem to agree, that definitions be comprehensible to students in all disciplines. The physics-based revisions seem not to fit that bill.

Avogadro's constant, as of 2006, was defined as 6.0221415(10) × 10²³ mol^-1, where the number in parentheses is the precision of the last digits. The fundamental base unit mole is easily understood as the number of atoms in exactly 12 g of ¹²C and inherently involves a definition of the gram or kilogram. The chemistry proposal under discussion is to combine these two statements as follows: Avogadro's number of ¹²C atoms has a mass of exactly 12 g and contains 6.02214180 × 10²³ atoms. Note the absolute lack of uncertainty, implying that Avogadro's number, analogous to what has been accepted for the speed of light and the second, is an integer (with lots of trailing zeros). The particular value chosen is consistent with the best determination to date and purposely divisible by exactly 12 for the ancillary part of the proposal that follows.

The mole is Avogadro's number of anything—substances or even photons. It intrinsically follows from the above definition that the kilogram is exactly the mass of 5.0184515 × 10^{25 12}C atoms. Both the mole and the kilogram would consequently be invariant in nature, an objective of all redefinition proposals.

The symposium "Past, Present & Future of the Kilogram" is cosponsored by the Division of Chemical Information and the Division of the History of Chemistry. Participants will present historical developments and the rationale behind the competing options for redefining the kilogram on Sunday afternoon, April 6, starting at 3:30 PM in the Marriott Convention Center Hotel, Blaine Kern Ballroom, Room C. Composed of four talks, the program may be the only chance to air this debate on behalf of the extensive user community.