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I am currently plundering the contents of the $1969$ reprint of the 2nd edition of Data and Formulae for Engineering Students published by Pergamon International (authors J.C. Anderson, D.M. Hum, B.G. Neal, J.H. Whitelaw) which I found in my bookshelf.

In chapter 3: Physical Constants, it states:

Avogadro's number $\qquad \text N \qquad = 6.023 \times 10^{26} \ / \text {kg mole}$

It is understood that the definition of Avogadro's number (henceforth here $N_0$) was rationalised in 1971 to be the amount of substance that contains as many elementary entities as there are atoms in $12$ grams of carbon-$12$, but it is unclear (from the sources I have managed to find) what that number actually was, merely that it was known to be approximately $6.02 \times 10^{23}$.

It is also understood that the current definition of $N_0$ (as exactly $6.02214076 \times 10^{23}$) happened in 2019.

I am interested to know where the $6.023$ might have come from in the above book, or whether it's a mistake brought about by a conflation of the 2nd and 3rd decimal places (23) with the exponent of $10$. It is remarkably tempting to remember the $23$-ness of Avogadro's number and accidentally apply it to the mantissa.

The question is: what values of $N_0$ were in circulation before the 2019 redefinition? In particular, what value of $N_0$ was determined by Jean Perrin (who actually did most of the initial hard work of measuring it)?

It occurs to me that if it "suddenly" changed from $6.023$ to $6.022...$, that's a (relatively) large change to standards which in general are known to an accuracy of well under parts per million. That is to my mind something of a discrepancy.

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  • $\begingroup$ In an older publication from behind the Iron Curtain I see two values for Avogadro's number: $N_{\mathrm{A}}^{\mathrm{Ph}} = (6.02252 \pm 0.00016) \cdot 10^{26} \mathrm{kmol}^{-1}$ and $N_{\mathrm{A}}^{\mathrm{Ch}} = (6.02336 \pm 0.00020) \cdot 10^{26} \mathrm{kmol}^{-1}$, where "Ph" presumably stands for physics and "Ch" stands for chemistry? $\endgroup$
    – njuffa
    Jul 20, 2023 at 10:44
  • $\begingroup$ Perrin only contributed three of the thirteen different values (each determined by a different method) listed in his seminal publication. His values were based on measurements of Brownian motion: $(70.5, 71.5, 65) \cdot 10^{22}$. Jean Perrin, "Mouvement brownien et réalité moléculaire." Annales de chimie et de physique, 8th Series, Vol. 18, Sep. 1909, pp. 5-113 (scan at BnF Gallica) $\endgroup$
    – njuffa
    Jul 20, 2023 at 11:25
  • $\begingroup$ @njuffa sorry, thought that was clear: although it was "called" Avogadro's Number in the text, it was not A.N. that they actually did describe, but the number of particles in a kilogram-mole, which is 1000x the number in a mole, which is A.N. $\endgroup$ Jul 20, 2023 at 11:27
  • $\begingroup$ @njuffa ... and that value of $N_A = 6.225 \times 10^{23}$, I sincerely hope it was $N_A = 6.0225 \times 10^{23}$ or there's a serious mistake in that book. $\endgroup$ Jul 20, 2023 at 11:29
  • $\begingroup$ @njuffa The kilogram-mole $\text {kg mol}$ is the number of C12 atoms in 12 kg of C12, like the gram-mole is the number of C12 atoms in 12 g of C12. The latter is "almost" the same thing as a "mole", which is Avogadro's number of things. A "gram-mole" (which is what a "mole" was before 2019) is very close to a mole, but the old term "gram-mole" is used to refer specifically to the pre-2019 definition. Similarly a kilomole is "almost" the same as a kilogram-mole. $\endgroup$ Jul 20, 2023 at 11:57

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My 1975-76 CRC Handbook (56th edition) states:

Avogadro's number. -- The number of molecules in one mole or gram-molecular weight of a substance. A number of values of the Avogadro number, which is usually denoted by $N_{A}$, have been found by various methods, generally lying within a range of 1% about the value of $6.02252 \times 10^{23}$ per gram mole.

Rounding could easily make it $6.023 \times 10^{23}$ which is still within the 1% range given.

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