Avogadro’s constant

In science, Avogadro’s constant or number, symbol N or NA, is the number of atoms, molecules, or chemical entities in one mol of substance. [1] The modern definition of Avogadro’s number is defined as the number of atoms in a twelve gram sample of carbon twelve, which is:

N_{\rm A}=6.022 \times 10^{23} \left (  \frac{entities}{mol} \right ) \,

History
In 1811, Italian chemist Amedeo Avogadro, the eponym of the constant, advanced the hypothesis that all gases under the same conditions of temperature and pressure, in unit volume, have the same number of molecules.

In 1895, the term gram-molecule began to be truncated as ‘mol’ by Walther Nernst, a term introduced two years earlier by Wilhelm Ostwald. [2]

In 1909, French chemist Jean Perrin, in his “Brownian Motion and Molecular Reality”, building on Albert Einstein's 1905 Brownian motion work, stated that Avogadro's hypothesis is equivalent to saying that 'any two gram-molecules contain the same number of molecules', and commented further by stated:

“The invariable number N is a universal constant, which may appropriately be designated Avogadro’s constant.”

Perrin gave the following value: [3]

N = 70.5 \times 10^{22} \,

which, it seems, to the number of molecules in 32-grams of oxygen.

In 1911, Irish chemist Edmund d’Albe was defining the ‘gram-molecule’ as the number of hydrogen atoms in one gram of hydrogen to be: [6]

0.91 \times 10^{24} \,

In 1913, American chemist Robert Mulliken gave the following value: [4]

N = 60.62 \times 10^{22} \,

In 1914, American physicist Harvey Fletcher calculated the following value of Avogadro’s constant for the number of molecules in a gram molecule of air: [5]

N = 60.3 (\pm 1.2) \times 10^{22} \,

(add)

Sociological Avogadro's number
See main: Social Avogadro number
The first to make an attempt at representative particle unit number equivalent for sociological thermodynamics calculations was Hungarian sociologist Babics Laszlo who in 2003 calculated what he called a "sociological Avogadro's number" of A = 60. On the high end, Laszlo also notes that the mean population number (6.01E7 in 1992) for each of the top 87 of the world's countries could serve as a representative A, although he considers this value to be too high for meaningful calculations. [7]

American chemical engineer Libb Thims had discussed this same issue with Russian physical chemist Georgi Gladyshev during a meeting in Chicago in 2006, during which Thims alluded to the idea that the value should be around 1,000 and possibly be called the Gladyshev number (or Gladyshev constant), being that Gladyshev was the first to do some of the pioneering work in sociological thermodynamics calculations of Gibbs free energy, which has units of J/mol. In this sense, in order to make calculations of quantities such as Gibbs free energy, entropy, internal energy, or enthalpy, for social processes, one first has to redefine the idea of the 'gram-molecule' for systems, groups, or masses of humans.

The central issue here is that humans aren't typically measured in groups by mass. In short, the standard SI base unit for 'amount of substance' is not applicable to calculations of reactions involved in larger systems of interacting humans. One could say, for instance, that in a 1,000-kg sample of average humans (70-kg) that there are about 14 human molecules on average. Using an alternative methodology, for instance, one could use the figure of 477, being the average number of students in a typical US elementary school in the 2001-2001 school year, as a representative Avogadro number for humans. Noting there various alternatives, the issue seems to require more thought.

References
1. Daintith, John. (2005). Oxford Dictionary of Science. Oxford University Press.
2. (a) Nernst, Walther. (1895). Theoretical Chemistry: from the Standpoint of Avogadro’s Rule & Thermodynamics. MacMillan and Co.
(b) Ostwald, Wilhelm. (1893). Hand- und Hilfsbuch zur ausführung physiko-chemischer Messungen (Handbook and Support for Making Physico-Chemical Measurements). Leipzig. p.119.
3. (a) Perrin, Jean. (1909). “Brownian Motion and Molecular Reality” ("Mouvement brownien et réalité moléculaire"), Annales de Chimie et de Physique, 18: 1–114.
(b) Engl. Trans. by Frederick Soddy (London: Taylor and Francis, 1910) [Excerpt: sections 1-6 complete (from: David M. Knight, ed., Classical Scientific Papers: Chemistry (New York: American Elsevier, 1968) and the abridgment reprinted in Henry A. Boorse & Lloyd Motz, The World of the Atom, Vol. 1 (New York: Basic Books, 1966)].
4. Mulliken, Robert. (1913). “Article”, Ann. d. Phys. 41: 759-.
5. Fletcher, Harvey. (1914). “Determination of Avogadro’s Constant N From Measurements of the Brownian Movements of Small Oil Drops Suspended in Air”, Physical Review, 4: 440-53.
6. D’Albe, Edmund. (1911). Contemporary Chemistry (gram-molecule, pgs. 69-70). D. Van Nostrand Co.
7. (a) Laszlo, Babics. (2003). “A Tomegtarsadalmak Mechanikajaes Termodinamikaja”, 92-page manuscript. Feb 10.
(b) Laszlo, Babics. (2010). “The Mechanics and Thermodynamics of Mass Societies”, Journal of Human Thermodynamics, Vol. 6, pgs. 39-46, Aug.

External links
Avogadro constant – Wikipedia.

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