Talk:Avogadro constant

Plans for setting the Avogadro constant to a fixed, exact value

Copied from Good Article? above: The Avogadro constant is likely to be given a fixed value in the relatively near future, and we should mention the discussions that are going on in that direction. It's quite a big job to cover the whole plans for remodelling SI but, as there's editor interest here, I'll try to get the refs together quickly.

I would be interested to help document the proposed changes in the SI system and update the article as they get implemented. The mole (unit) article talks about the redefinition of the kilogram, but the implications for the mole are not spelled out, so the motivation to include it was not clear to everyone. I personally am looking forward to a better word for the quantity "amount-of-substance", which is a mouthful ("chemical amount" is being discussed, and is already used in some textbooks - an improvement, but still not as compact as Stoffmenge).Theislikerice (talk) 19:56, 18 August 2010 (UTC)

You can propose to call this physical property stuff then. Other than that we should be careful to not do original research WP:OR by interpreting what is going to come and go. Kbrose (talk) 21:10, 18 August 2010 (UTC)

It doesn't really matter what it's called (and it would be a bit WP:FORUM to discuss it here). Nevertheless, the debate seems notable, and kilogram shows that a lot could be said about it. For this article, the Avogadro constant seems likely to get a defined value in the near future, although the "near future" might be 2015 rather than 2011: 2011 is the earliest possible date, but the debate has been going on for several years now and so seems worthy of a neutral mention. As far as understand it, we can't talk about "consequences" yet, because there are still too many options open. Physchim62 (talk) 22:40, 18 August 2010 (UTC)

The redefinition of "mole" as a fixed exact number of particles has happened. The article has been partly updated accordingly. --Jorge Stolfi (talk) 02:23, 1 June 2019 (UTC)

New value determined for the Avogadro constant (2011-01-27)

To the main editors of this article:

Please follow this link from Physikalisch-Technische Bundesanstalt (PTB), 2011-01-27:

The "new" kilogram is approaching

Here is the abstract and citation:

A milestone in the international Avogadro project coordinated by the Physikalisch-Technische Bundesanstalt (PTB) has been reached: With the aid of a single crystal of highly enriched 28Si, the Avogadro constant has now been measured as exactly as never before with a relative overall uncertainty of 3 · 10-8. Within the scope of the redefinition of the kilogram, the value NA = 6.02214078(18) · 1023 mol-1 permits the currently most exact realization of this unit. The results have been published in the most recent edition of the journal "Physical Review Letters".

Andreas, B.; Azuma, Y.; Bartl, G.; Becker, P.; Bettin, H.; Borys, M.; Busch, I.; Gray, M. et al. (2011), "An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal", Phys. Rev. Lett. 106 (3): 030801 (4 pages), doi:10.1103/PhysRevLett.106.030801.

Pmronchi (talk) 01:31, 10 February 2011 (UTC)

Interesting. I haven't read the article, but just noticed that the accuracy was improved only by a factor of 18/30. Materialscientist (talk) 01:38, 10 February 2011 (UTC)

Another interesting comment. Materialscientist (talk) 03:34, 10 February 2011 (UTC)

Materialscientist, please post your reasons for the deletion from the article. SpinningSpark 07:10, 10 February 2011 (UTC)

No hard feelings, potentially interesting material, but: (i) copy/paste from the quoted source; (ii) claims of an extraordinary achievement, whereas the accuracy was improved by less than 50% only, and at least another 50% is needed to reach the goal of "better kilogram standard" (i.e. work in progress); (iii) even though this was published in a respectable journal (Phys. Rev. Lett.), such strong-claim results are to be evaluated by international committees. Materialscientist (talk) 07:23, 10 February 2011 (UTC)

I've read through the article and it is odd, i.e. I don't understand the novelty claim: same accuracy was reported by NIST in 2007, but the difference in the N_A values is beyond that accuracy. Materialscientist (talk) 08:16, 10 February 2011 (UTC)

With the 2019 redefinition of mole and Avogadro number, these measurements now become measurements of the value of the dalton in relation to the kilogram. The section on experimental measurements should perhaps be moved to atomic mass unit. --Jorge Stolfi (talk) 02:26, 1 June 2019 (UTC)

Referencing, in Wikipedia, the value of constants whose precise value is still being determined

To the main editors of this article (and other articles regarding constants)

Even though I´m not sure that this is the right place to raise this topic, I believe that constants whose precise value is still being determined, should not have too many digits of precision represented in articles different from the main article that deals with the constant. For instance, in the case of th Avogadro constant, as of today, it is represented in Amedeo Avogadro as being 6.02214179(30)×10²³, which is not so anymore. If it were quoted as "being approximately 6.02214×10²³", for instance, that article would be correct no matter future, more precise definitions. The full precision value would be modified and found only in Avogadro constant, this article.

Pmronchi (talk) 01:36, 10 February 2011 (UTC)

The correct way forward is to raise it on the talk page of the article(s) concerned, or else to edit the article directly yourself. There is nothing that can be done on this article to influence other articles. SpinningSpark 18:09, 10 February 2011 (UTC)

With the 2019 redefinition of mole, this point is now moot. But the observation may stil apply to atomic mass unit. --Jorge Stolfi (talk) 02:28, 1 June 2019 (UTC)

Pity the poor reader!

Pity the poor reader who comes to this article with the hope of understanding what is "Avogadro's number"! Instead of the plain old definition, he is given half a page of hair-splitting hiper-ultra-meta-talmudic discussions and convoluted definitions, with detailed pseudo-explanations that are of no interest whatsoever to 99.999+% of the people who use the concept, including 99.999+% of all chemists and physicists.
Indeed, if we are to believe this article, "Avogadro's number" and the "Avogadro constant" are utterly distinct concepts. Well then, in that case each should have its own article, no?
Seriously, this article should be renamed "Avogadro's number", since that is the primary concept: namely the number N_A of atoms in 12 grams of ¹²C. The mole is clearly a secondary concept, namely "the amount of a substance that contains as many elementary entities as there are atoms in 12 g of the isotope carbon-12" --- that is, "N_A elementary entities of that substance". (It is a more complicated concept than N_A, because for many substances the concept of "elementary entity" is ambiguous or meaningless.) And the Avogadro constant is a tertiary, rather convoluted concept: according to the article, it is the (number of constituent particles in a given sample of a subtance) divided by ((the mass of that sample) divided by (the mass of (a sample of the substance that contains as many elementary entities as there are atoms in 12 g of the isotope carbon-12))). Which, we are told, is not Avogadro's number, but an entirely distinct constant with precisely the same value. Sure. And William Shakespeare's plays were not written by him but by another person with the same name... Jorge Stolfi (talk) 06:31, 10 June 2011 (UTC)

Almost ten years later, and the reader is still to be pitied. Why is this article written for the college physics student, who already knows all the first paragraphs' material, instead of for the lay reader or high-school student trying to understand what is a confusing but not really complicated concept?37.99.86.5 (talk) 13:34, 2 May 2021 (UTC)

I agree wholeheartedly. I'm already familiar with Avogadro's number/constant but anyone who wasn't would find the opening two sentences baffling. Terms like "amount of substance" are highly technical - indeed it's hard to understand "amount of substance" without already having understood Avogadro's constant/number.

There's a key concept here that needs to be mentioned right at the beginning: that atoms/molecules of different elements/compounds do not all have the same mass, so that the same mass of two different substances contains different amounts of particles; Avogadro's constant provides (loosely speaking for now) the connection between the mass of the particles, the number of particles, and the mass of the sample.

I might have a go at this because it's badly needed. Macboff (talk) 08:59, 6 August 2021 (UTC)

The article has been considerably rewritten, and the complaints above hopefully have been addressed.--Jorge Stolfi (talk) 16:41, 9 August 2023 (UTC)

New value

Following the link in the article, I get the new value 6.022 141 29(27) x 10²³ mol^-1. Perhaps an update is needed. -- 202.124.75.11 (talk) 13:41, 10 October 2011 (UTC)

Updated. Thanks. Materialscientist (talk) 06:25, 11 October 2011 (UTC)

The article would be much clearer if all the other values are better identified as 'non-official' or estimates or calculated values or whatever they are that makes them not official. It is confusing to see these multiple values, especially when it is not clear why one is 'right.' Also, I expect most people do not understand the notation being used in expressing the number. What does the digits in parenthases mean? Where can a reader go to find out? 69.174.87.100 (talk) 22:33, 23 May 2012 (UTC)

Since "amount of substance" now means effectively "number of particles", and "mole" is now just a fixed number of particles, the "Avogadro constant" is now a pure number.
One could write "rad" or "deg" after a number as if they were "units of angle", but "1.57 rad" or "60 deg" are pure numbers for dimensional analysis; and the conversion factor can be written as "180/π deg/rad", but it is also a pure number.
--Jorge Stolfi (talk) 02:37, 1 June 2019 (UTC)

Even though mole is now effectively a dimensionless number, like the number of degrees per turn, the 9th BIPM retains the old dimensional analysis where "amount of substance" is considered a physical quantity while number or particles is a dimensionless number. Thus, bureaucratically, the Avogadro constant still has dimension mol^-1 while the Avogadro number is dimesnionless. Oh well.--Jorge Stolfi (talk) 16:39, 9 August 2023 (UTC)

Units in Article: Error?

The last paragraph of the history section has me skeptical:

While it is rare to use units of amount of substance other than the mole, the Avogadro constant can also be defined in units such as the pound mole (lb-mol) and the ounce mole (oz-mol).

N_A = 2.73159757(14)×10²⁶ lb-mol⁻¹ = 1.707248479(85)×10²⁵ oz-mol⁻¹

Based on what is written, the article appears to be defining the Avogadro constant in terms of pounds per mole and ounce per mole. I'm not a chemist, but I think someone should take a look at that and consider editing.

Thelema418 (talk) 06:09, 16 June 2012 (UTC)

Also noted that the article contains both lb-mol⁻¹ and (lb-mol)⁻¹. This might be the main issue I am having. Thelema418 (talk) 19:56, 4 July 2012 (UTC)

Agreed. The unit for the Avogadro constant is mol⁻¹. It is independent of mass, hence using units lb-mol⁻¹ and oz-mol⁻¹ (or kg-mol⁻¹) is nonsense. — Preceding unsigned comment added by 92.13.20.6 (talk) 16:58, 19 July 2012 (UTC)

(lb-mol) is not a pound times a mole, but rather an amount of substance containing the same number of entities as 12 lbs of carbon atoms. It's an obscure unit, but has the same dimensions as mole. So the article is correct, but confusing because it mentions a unit that is hardly ever used. --Theislikerice (talk) 03:59, 3 August 2012 (UTC)

Seems resolved now. --Jorge Stolfi (talk) 02:59, 1 June 2019 (UTC)

Avogadro's constant is the number of entities contained in a mole, equal to the number of atoms contained in 12 grams of carbon-12, obviously the number of atoms remains unchanged if we adopt a unit of weight other than the gram, but still equivalent to 12 grams of carbon-12.--Starace Aniello (talk) 02:59, 22 April 2021 (UTC) This article of mine clarifies the matter, in practice the Avogadro constant is wrong https://www.academia.edu/49021635/Costante_di_Starace_Articolo_revisionata --Starace Aniello (talk) 08:56, 2 May 2021 (UTC)

No, the defiinition of mole has changed radically in 2019. Now one mole means exactly 6.022'140'76 × 10²³ particles; which is close, but not equal, to the number of atoms in 12 grams of ¹²C.--Jorge Stolfi (talk) 16:47, 9 August 2023 (UTC)

Units of Avagadro's constant/number

In the current(1971) definition of a mole, Avagadro's number is the number of atoms in 12 grams of carbon ( C₁₂ ). Thus in this definition, the number has units of g^-1. The inverse of Avagadro's number is approximately the mass of a neutron in grams. If Avagadro's number were dimensionless there would be no need for lb-mol, and oz-mol. If this number were fixed by definition AND the existing definition were retained, then Avagadros number would effectively define the kilogram in terms of the mass of an atom of carbon-12.

But this is not the proposal, the proposal is to give a fixed value to Avagadro's number and change the definition of a mole such that the mass of an atom of carbon-12 is to be determined by experiment. If this definition is adopted then Avagadro's number becomes dimensionless and so does a mole. As follows:

• Proposal

The mole is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.02214X ×10²³ when it is expressed in the unit mol^-1. (where X is a digit yet to be agreed upon).

Martin Milton(NPL)-A new definition for the mole based on the Avogadro constant; a journey from physics to chemistry, 7 April 2014
http://www.ucl.ac.uk/~ucahhwi/LTCC/section3-dimensional.pdf

In other words, under the new definition a mole, becomes 6.022 14X ×10²³ particles and is not linked to any particular mass.

Davidcroquet (talk) 11:08, 7 April 2014 (UTC)

I thought it was called Avogadro's Number not 'Constant'. As I understand it, the units are grams per mole [g/mol]. — Preceding unsigned comment added by 81.99.111.179 (talk) 16:13, 21 May 2014 (UTC)

The unit of the Avogadro constant is not g⁻¹.
If the defintion of N_A was "the number of atoms in 12 grams of carbon", then N_A would be an adimensional number.
However most people seem to understand it as "the constant that, multiplied by the amount of substance in a sample, gives the number of particles of that substance in that sample". Thus one must consider how "amount of substance" is defined. Here is what I understand from the IBPM deliberations:
Between 1971 and 2019, in the SI, "amount of substance" was a separate dimension of measurement, like length or time, and the mole was a unit of that quantity. Thus the Avogadro constant had the dimension of reciprocal of amount of substance, and it was about 6.02×10²³ mol⁻¹, which was to be determined experimentally.
After 2019-05-20, in the SI, "amount of substance" is essentially "number of particles", and "2.5 moles of X" means "exactly 2.5 × 6.02214076×10²³ particles of X". Thus the amount of substance in a sample is a pure number (of particles), and the Avogadro constant too is now the pure number 6.02214076×10²³ ("the number of particles in 6.02214076×10²³ particles"); even though it can still be written as 6.02214076×10²³ mol⁻¹ or 6.02214076×10²³ particles/mol.
--Jorge Stolfi (talk) 03:23, 1 June 2019 (UTC)

Error in Value of constant?

According to my Oxford Dictionary of Science 6th Edition, the value of the Avogadro constant is 6.02214179(30) x 10²³ mol^-1.

Can someone verify this? --Nishantrvps (contribs) 10:21, 7 April 2013 (UTC)

This is, in fact an incorrect value. The most recent CODATA 2010 value (http://physics.nist.gov/cgi-bin/cuu/Value?na%7Csearch_for=avogadro) is 6.022 141 29(27) x 10²³ mol^-1. --j.meija 14:03, 7 April 2013 (UTC) — Preceding unsigned comment added by J.meija (talk • contribs)

J.meija and contribs, understand that that value still has the uncertainty of 0.0000000027

Since May 2019, the Avogadro constant is defined to be 6.022'140'76 × 10²³ particles per mole, exactly. That is, one mole is now 6.022'140'76 × 10²³ particles, by definition. --Jorge Stolfi (talk) 16:51, 9 August 2023 (UTC)

Wrong unit?

The units for this constant (or "number") for some is kg/kmol, not just g/mol, as specifically mentioned in many physics textbooks. In chemistry due to small laboratory measurements it is g/mol. I changed it to kg * mol^-1 to clarify this. Dandtiks69 (talk) 02:11, 20 May 2015 (UTC).

No, the unit of the Avogadro constant is "particles per mol", not "g/mol" or "kg/mol". Before 2019 "mol" whas the unit of "amount of substance" which was a separate measurement dimension like length or time. Now it is just a number of particles, so the constant is a pure number. --Jorge Stolfi (talk) 03:28, 1 June 2019 (UTC)

Significance needs to be better explained

Why do scientists care about this number? That's unclear. I get that it's part of (most of, really) the definition of how many atoms in a mole, but what is unclear is why they didn't simply set one mole to equal 10^24 and be done with it — Preceding unsigned comment added by 64.121.6.113 (talk) 16:16, 10 November 2015 (UTC)

Explained now, hopefully. Makes "mass of one mole in grams" equal to "mass of one molecule in daltons". --Jorge Stolfi (talk) 03:32, 1 June 2019 (UTC)

Daltons per Gram

It needs to be more clearly explained that Avogadro's Number is also the number of daltons (atomic mass units) in a gram. Without that piece of information the mole seems like an absurd arbitrary unit.

Done already --Jorge Stolfi (talk) 03:33, 1 June 2019 (UTC)

External links modified

Hello fellow Wikipedians,

I have just modified 2 external links on Avogadro constant. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Corrected formatting/usage for http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html
• Added archive https://web.archive.org/web/20050404003919/http://gemini.tntech.edu:80/~tfurtsch/scihist/loschmid.html to http://gemini.tntech.edu/~tfurtsch/scihist/loschmid.html

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{Sourcecheck}}).

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 15:10, 22 October 2016 (UTC)

External links modified

Hello fellow Wikipedians,

I have just modified 2 external links on Avogadro constant. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Corrected formatting/usage for http://gemini.tntech.edu/~tfurtsch/scihist/loschmid.html
• Added archive https://web.archive.org/web/20110717124427/http://www.inrim.it/Nah/Web_Nah/home.htm to http://www.inrim.it/Nah/Web_Nah/home.htm

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 15:11, 12 July 2017 (UTC)

(6.03676081927e+23 Avogadro) , (Gas Constant 8.33464489072)

((((376.730313/299792458) (m^2)) / (pi s)) / (6.03676081927e+23 * ((mol / 1000)^(-1)))) / Planck's constant = 1 mol / kg

1.38064852e-23 * 6.03676081927e+23 = 8.33464489072

((2.176470e-8 kg) * ((1.616229e-35 m)^2)) / ((1.416808e+32 K) * ((5.39116e-44 s)^2) * (1 gram)) = 1.38064821e-23 Boltzmann

((2.176470e-8 kg) * ((1.616229e-35 m)^2)) / ((1.416808e+32 K) * ((5.39116e-44 s)^2)) = 1.38064821e-26 Boltzmann / 1000

Mol is per Gram = (Mol * 1000) per kilogram

Mol should be Adjusted to units of Kilograms for Clarity

(6.03676081927e+23 Avogadro) , (Gas Constant 8.33464489072) , (Boltzmann's Constant) , (Mole)

((((376.730313/299792458) (m^2)) / (pi s)) / (6.03676081927e+23 * ((mol / 1000)^(-1)))) / Planck's constant = 1 mol / kg

1.38064852e-23 * 6.03676081927e+23 = 8.33464489072

((2.176470e-8 kg) * ((1.616229e-35 m)^2)) / ((1.416808e+32 K) * ((5.39116e-44 s)^2) * (1 gram)) = 1.38064821e-23 Boltzmann

((2.176470e-8 kg) * ((1.616229e-35 m)^2)) / ((1.416808e+32 K) * ((5.39116e-44 s)^2)) = 1.38064821e-23 = Boltzmann per kilogram

Mol is per Gram = (Mol * 1000) per kilogram

(Moles, Gas Constant & Avogadro Constant) should be Adjusted to (Units of Kilograms & Boltzmann's Constant) for Clarity

1.38064821e-23 * 6.03676081927e+26 = 8334.64301932

0.25 / 0.0000299792458 = 8339.10237995

1 / (4.00e-13 * 3e+8) = 8333.33333333

https://en.wikipedia.org/wiki/Mole_(unit)

The number of molecules per mole is known as Avogadro's constant, and is defined such that the mass of one mole of a substance, ((expressed in grams)), is equal to the mean relative molecular mass of the substance.

((2.176470e-8 kg *(1.616229e-35 m)^2/(1.416808e+32 K *((5.39116e-44 s)^2) =(1.38064852e-23 m^2 kg s^-2 K^-1)

https://en.wikipedia.org/wiki/Boltzmann_constant

(1 / ((c^3) * ((1.616229e-35 meters) / (pi / (((1 / (2 * pi)) + 1)^0.5))) * ((5.39116e-44 seconds) / (pi / (((1 / (2 * pi)) + 1)^0.5)))))^0.5 = 6.02220471e+26

https://en.wikipedia.org/wiki/Avogadro_constant

((1 / ((c^3) * ((1.616229e-35 meters) / (pi / (((1 / (2 * pi)) + 1)^0.5))) * ((5.39116e-44 seconds) / (pi / (((1 / (2 * pi)) + 1)^0.5)))))^0.5) * 1.38064852e-23 = 8314.54802

https://en.wikipedia.org/wiki/Gas_constant

pi / (1 / (2pi) + 1) = 2.71024393443899972

Fuller.david (talk) 16:34, 25 September 2017 (UTC)

Article head is now incorrect?

It seems that now the SI definition of mole is "an amount of substance that contains N_A particles", where N_A is the Avogadro constant. Therefore N_A is a fixed pure number 6.02...×10²³, not a "number of particles per mole", (since the latter would make the definition of mole circular). No? --Jorge Stolfi (talk) 06:41, 18 May 2019 (UTC)

No, otherwise formulas like $n=N/N_{A}$ wouldn't work. But see the IUPAC press release[1]: "The mole [...]. This number is the fixed numerical value of the Avogadro constant, $N_{A}$, when expressed in mol⁻¹, and is called the Avogadro number." Christian75 (talk) 09:29, 18 May 2019 (UTC)

The thing is confusing since the number of moles is itself dimensionally a pure number. "One mole" is totally like "one dozen" or "one million". Think of "two moles of H2" as "two dozen H2s" Amounts in moles or in number of molecules are like angles in degrees or in radians. The formula n = N/N_A is similar to ang_degrees = (180/π) × ang_radians. The constant 180/π can be said to have units of "degrees per radian", but since both are adimensional, it is a pure number too. Or the conversion between inches and mm by the formula "length_mm = 25.4 × length_inches". The constant "25.4" can be said to have units "mm/inch", but that is at best a mnemonic, because dimensionally it is a pure number too.
There seems to be a popular perception that "amount of substance" is a physical quantity like "mass", and thus "mole" has a physical dimension like "kg". That is not what I read in the IUPAC, although their language is rather convoluted -- perhaps to bow to this popular feeling?
--Jorge Stolfi (talk) 04:01, 20 May 2019 (UTC)

OK, now I see that, in the SI, "amount of substance" was an independent dimension of measurement between 1971 and 2019. Then N_A had the dimension "reciprocal of amount of substance" and (non-trivial) unit mol⁻¹. But since 2019, "amount of substance" is just "number of particles", the mole is a fixed number N_A of particles, and N_A is therefore a pure number ("particles per 6.02214076×10²³ particles") even though one may still write "N_A = 6.02214076×10²³ mol⁻¹" or "N_A = 6.02214076×10²³ particles/mol". --Jorge Stolfi (talk) 03:42, 1 June 2019 (UTC)

Move section "Measurement' to atomic mass unit

Now that the value of N_A is defined to be a fixed integer, the section "Measurements" is no longer about determining N_A, but instead about determining the value of the dalton in grams; that is, the number of atoms in 12 g (exactly) of carbon-12 (which is no longer equal to 1 mol of carbon-12).
Therefore I propose moving that section to atomic mass unit, with the appropriate changes.
--Jorge Stolfi (talk) 03:53, 1 June 2019 (UTC)

Why is Einstein not mentioned?

Einstein used Brownian motion to estimate Avagadro's number in 1905? If my history is correct, and it might not off a little, he obtained it as the ratio of the ideal gas constant, usually denoted by "R", to Boltzmann's constant which is usually denoted by k or k_B: N_A = R/k_B. I saw the Scientific American piece (by Bodin, I think) who wrote as if Perrin was the first modern estimate of N_A and was puzzled by his neglect of Einstein on this issue. I guess I can add something but I'd have to dig up the original reference. Ok. I found the original reference to Einstein's Brownian motion paper. The final equation in the 1905 "miracle year" paper gives Avagadro's number in terms off the time and displacement of spherical random walkers: N = t/lambda_x^2 RT/(3 pi kP). Here lambda_x^2 is the mean (square) displacement of the random walkers, t is the time they walked for, R and T and the ideal gas constant and absolute temperature, k is the coefficient of friction of the liquid, and P is the radius of the spherical walkers. To my mind this ought to appear pretty high in the article. Smoluchowski also solved the Brownian motion problem in 1906 and my understanding is that his work was independent of Einstein's. I haven't read Smoluchowski though, so I don't know whether he too derived an experimental formula for Avagadro's number. Further my understanding is that in these years you couldn't shake a stick without running into Avagadro's number and it was its appearance in so many places all giving similar experimental values that ultimately vanquished the anti-atomists. I think something along these lines is in Pais' Einstein biography "Subtle is the Lord."

Additionally, his doctoral thesis, "A New Determination of Molecular Dimensions” contains an estimate of Avagadro's number which came in at about 2 x 10^23.

— Preceding unsigned comment added by 76.113.29.12 (talk) 13:49, 3 June 2019 (UTC)
Einstein doctoral thesis pag. 65 report N=2.1 x 10^23 and pag. 69 report Avogadro constant=3.3 x 10^23 http://www.zhenzhubay.com/zzw/upload/up/2/378598b.pdf --Starace Aniello (talk) 13:45, 22 May 2021 (UTC) This article of mine clarifies the matter, in practice the Avogadro constant is wrong https://www.academia.edu/49021635/Costante_di_Starace_Articolo_revisionata --Starace Aniello (talk) 08:59, 2 May 2021 (UTC)

Confusion of Avogadro constant with Avogadro number

Jorge Stolfi, this edit creates the impression that the Avogadro constant N_A and the Avogadro number N_N are the same quantity. This is incorrect. I am tempted to revert the edit, but will allow time for you to correct it if you wish to retain the valid changes. —Quondum 01:47, 6 June 2019 (UTC)

• @Quondum: They were distinct until last month. Now that "amount of substance" in the SI is just a number of particles, the distinction is only "talmudic". That is explained in the History section. For most readers, the difference is immaterial--Jorge Stolfi (talk) 07:08, 6 June 2019 (UTC)

Jorge Stolfi, this is a rather poor (indeed, invalid) argument. You have not taken the trouble to explain how your understanding of the SI position justifies such a conclusion, so I will not take the time to rebut it. I will simply state that the SI nowhere equates the base quantity "amount of substance" with any dimensionless quantity such as "number of particles". It is clear that you have a poor conception of the people to whom the distinction will make a difference, including school age young scientists who could do with as little confusion on the topic as possible. I am reverting your edit since the longer it stays up the more people may be infected by this confusion (there are over 1000 pageviews per day); if you wish to re-instate any conflation of N_A and the N_N, seek consensus first. The history section (specifically, "The mole was redefined as being exactly 6.02214076×10²³ elementary entities"), incidentally, is worded incorrectly. —Quondum 12:22, 6 June 2019 (UTC)

@Quondum: Well, you have not taken the trouble to explain why my understanding of the new SI definitions are invalid. Unfortunately the references in the head paragraph are all prior to last month's change; I apologize for not updating them.
The restored edits still reflect the old view that "amount of substance" was an independent physical quantity (N) on par with mass (M), length (L), time (T), and temperature (Θ); and "mole" was one of the "base SI units", on par with kilogram, meter, second, and kelvin. In that old framework, the Avogadro constant indeed had metric dimesionality N⁻¹ and SI unit of "mol⁻¹". Note that it was not "particle/mol", since a number of particles is considered adimensional and hence is not part of the unit.
Well, these definitions were changed in the 106th meeting of the BIPM and took effect last month. Here is the relevant quote from the Proceedings of that meeting:

The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76[mistyped as 8Y?] × 10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, N_A, when expressed in the unit mol⁻¹ and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

So, in the first two sentences, the BIPM seems to imply that the "Avogadro constant" still has a metric dimension, while the "Avogadro number" is adimensional. But the third sentence says that "amount of substance" is no longer considered a separate physical quantity in the SI system, but is synonymous with "number of elementary entities". Substituting this definition into the first sentence gives

The mole, symbol mol, is the SI unit of number of elementary entities. One mole contains exactly 6.022 140 76 × 10²³ elementary entities.

So the SI "mole" now is just an explicit number of particles, and therefore is metrically adimensional. While one can still say that the Avogadro "constant" is "6.022 140 76 × 10²³ particles per mole", that is like saying that the constant for converting radians to degrees is "180/π degrees per radian" -- which may be a useful mnemonic, and is not wrong, but dimensionally that constant is just a pure number, like "180/π". And saying that the constant is "180/π rad⁻¹" is not wrong either, but is rather weird.
It may help to imagine that BIPM had also defined a "bole" (symbol "bol") as being one billion particles, exactly. Then "2 bol of water" would be synonymous of "2,000,000,000 molecules of water", and it would have the same dimensionality as "1 molecule of water" -- that is, a pure number.
My edits were in fact intended to reduce the confusion, especially among school age young scientists. The obsolete (currently restored) version of the article, that seems to imply that "amount of substance" is a property of a sample that is neither mass nor quite the number of particles, is very confusing. You may want to check this article.
It does not help that the words "amount of substance" also have a common meaning in the English language, that is different from the jargon one. If you say "take equal amounts of water and sulfuric acid" to someone who is not a zealous Third-Level Master in Chemical Freemasonry, he is more likely to understand "equal masses" or "equal volumes" than "equal number of moles" or "equal number of molecules".
Thankfully the 2019 revision of the SI has done away with that confusing concept, and now students and scientists alike may think of "1 mole of CO2" as being just a convenient way of saying "6.022 140 76 × 10²³ molecules of CO2".
If you want to be helpful to your students (and to the wikipedia readers), from now on replace the term "amount of substance" by "number of {molecules|atoms|particles}" everywhere. The resulting text will be perfectly correct (as per the above BIPM definition), but infinitely more clear.
Even before the change, the distinction between "Avogadro constant" and "Avogadro number" was irrelevant for practical work. After the change, the distinction became quite artificial, like the difference between "180/π deg/rad" and "180/π".
While the 2019 redefintion has no consequences whatsoever for practical work, it requires radical changes in many other definitions (like "molar mass", which now is just a mass) and explanations. For example, all the experiments that were meant to measure the Avogadro constant/number are still relevant, but must now be described as experimental measurements of the atomic mass unit (still defined as 1/12 of the mass of a ¹²C atom) in kilograms.
And, in particular, all explanations of the (non-)difference between "Avogadro constant" and "Avogadro number" must be re-thought and rewritten.
All the best, --Jorge Stolfi (talk) 22:12, 7 June 2019 (UTC)

I appreciate the care in your reply. While the CGPM minutes do reflect decisions of the CGPM, consider the "enactment" thereof, in the form of the 9th edition of the SI Brochure (2019), which gives a good deal more detail and explicit interpretation. I'll refer to the English-only PDF. You should notice that N_A = 6.02214076×10²³ mol⁻¹ (§2.2, p. 127 and again with explicit unit in Table 1, p. 128), which does not imply that mol = 1. From §2.2.1: "The Avogadro constant N_A is a proportionality constant between the quantity amount of substance (with unit mole) and the quantity for counting entities (with unit one, symbol 1)." [underlining by me] – a 'proportionality constant' does not imply 'equality'. "Thus it has the character of a constant of proportionality similar to the Boltzmann constant k." We would have to interpret from this that the Boltzmann constant is adimensional (and hence that temperature is now simply an energy, thus dispensing with another base quantity). From §2.3.1 (Table 2, p. 130), it is clear that there are still seven base quantities, and seven corresponding coherent base units. See also the equation on p. 134, 1 mol = ⁠6.02214076×10²³/N_A⁠, which would have been the ideal place to finish off with a final "= 1" if the numerator and denominator were to be considered equal ... but they didn't. Then in §2.3.3, Table 3, p. 136, we still have the symbol N for the dimension of the base quantity "amount of substance", further emphasized by the equation dim Q = T^αL^βM^γI^δΘ^εN^ζJ^η. I think it should be abundantly clear that the New SI has not eliminated the base dimension N by considering it adimensional. Had they chosen to do so, wouldn't you expect them to at least mention such a fundamental revision of the underpinnings of the system? I'll also mention that adimensional quantities are treated explicitly on pp. 136–137, e.g. where the units rad and sr are formally treated as such: but not so the mol. Anyhow, you might want to read through it and form your own interpretation. Metrology jargon is tricky. —Quondum 00:22, 8 June 2019 (UTC)

@Quondum:I will not try to re-revert the edits, but I am still very unhappy with the current text. I still believe that it is unnecessarily confusing, by trying to stay close to the old way of thinking (in which "amount of substance" is technically neither mass nor number of particles), instead of the logical consequences of the new definitions (where "amount of substance" is explicitly defined as "number of particles"). While the passages that you cite are consistent with the view that "mole" has a non-trivial dimension, they are also consistent with the view that it is just a count of particles, hence adimensional. Moreover, all those passages cannot negate the explicit definition of "amount of substance" as a count of particles.
Being a huge international committee, the BIPM naturally has tremendous inertia, and generally avoids changes that are too extensive or may upset many members, even if the changes are logically necessary and have no practical consequences whatsoever (other than making the system easier to understand). Carrying out the new definitions of mole and amount of substance to its logical conclusion would require extensive changes to the text, including removing "amount of substance" from the list of fundamental quantities, "N" from the dimensionalities, and changing "mole" from a base unit to an adimensional unit like "radian".
Here are some other quotes from that Brochure that would support such a rewrite:

• From the 8th Brochure. p.114: Amount of substance is defined to be proportional to the number of specified elementary entities in a sample, the proportionality constant being a universal constant which is the same for all samples. [emphasis mine].
• From the 9th Brochure (as above), p.134: The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. [ditto]
• From the 9th Brochure, p.136: There are quantities Q for which the defining equation is such that all of the dimensional exponents in the equation for the dimension of Q are zero. [...] Such quantities are simply numbers. The associated unit is the unit one, symbol 1, although this is rarely explicitly written (see 5.4.7). There are also some quantities that cannot be described in terms of the seven base quantities of the SI, but have the nature of a count. Examples are a number of molecules, a number of cellular or biomolecular entities (for example copies of a particular nucleic acid sequence), or degeneracy in quantum mechanics. Counting quantities are also quantities with the associated unit one. [ditto]
• From the 9th Brochure, p.137: Plane and solid angles, when expressed in radians and steradians respectively, are in effect also treated within the SI as quantities with the unit one (see section 5.4.8). The symbols rad and sr are written explicitly where appropriate, in order to emphasize that, for radians or steradians, the quantity being considered is, or involves the plane angle or solid angle respectively. [...] However, it is a long-established practice in mathematics and across all areas of science to make use of rad = 1 and sr = 1. For historical reasons the radian and steradian are treated as derived units, as described in section 2.3.4. It is especially important to have a clear description of any quantity with unit one (see section 5.4.7) that is expressed as a ratio of quantities of the same kind (for example length ratios or amount fractions) or as a count (for example number of photons or decays). [ditto]
• From the 9th Brochure, p.140: The SI unit of frequency is hertz, the SI unit of angular velocity and angular frequency is radian per second, and the SI unit of activity is becquerel, implying counts per second. Although it is formally correct to write all three of these units as the reciprocal second, the use of the different names emphasizes the different nature of the quantities concerned. It is especially important to carefully distinguish frequencies from angular frequencies, because by definition their numerical values differ by a factor1 of 2π. Ignoring this fact may cause an error of 2π. [ditto].

Even though these quotes from the 9th Brochure were not intentionally written with "amount of substance" in mind, for consistency they should apply to that quantity too after its redefinition. That is, writing "mol" in measurements of amount of substance, like writing "rad" or "counts", is still necessary to clarify the value and nature of the measurement (just as "2 billion pairs", "2 billion", and "2" are not the same thing). Dimensionally, however, a mole it is now a pure number (like radians and decay counts).
It is sad that the BIPM has missed the opportunity to de-obfuscate this issue. I still think that the Wikipedia article should follow logic rather than slavishly copy the text of the Brochure. In particular, I believe that it would be totally correct, but much better for everybody, to write

The Avogadro constant or Avogadro number is the number of constituent particles, usually molecules, atoms or ions that are contained in one mole, the international (SI) unit of particle count: by definition, exactly 6.02214076×10²³. The constant is named after the scientist Amedeo Avogadro, and is usually designated with the symbol N_A or L.

and then note, further down, that the two terms historically were quite distinct, but now they are essentially the same (or the distinction is only "bureaucratic"). But, again, I will not try to do it myself.
By the way, I cannot avoid observing that the BIPM Brochures are terribly obfuscating also in the definition of other concepts, such as:

• Brochure: [The second] is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s⁻¹.
• Meaning: The second is 9,192,631,770 periods of the the radiation emitted in the unperturbed ground-state hyperfine transition of caesium-133.
   
• Brochure: [The metre] is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s⁻¹, where the second is defined in terms of the caesium frequency ∆νCs.
• Meaning: The metre is 1/299,792,458 of the distance traveled by light in vacuum in one second.
   
• Brochure: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10⁻¹⁹ when expressed in the unit C, which is equal to A s, where the second is defined in terms of ∆νCs.
• Meaning: The ampere is the electric current of 1/1.602,176,634 × 10¹⁹ electron charges per second.
  

All the best, --Jorge Stolfi (talk) 03:36, 8 June 2019 (UTC)

Let's see whether I can understand your position (for now entirely ignoring my perspective). Quoting you above: 'Now that "amount of substance" in the SI is just a number of particles [...]'. Let's say we have a droplet of water with 10²⁰ water molecules in it. Since this is an adimensional number, namely number (of particles), you'd say that the amount of substance (the substance being water, being composed of particles, each of which is an H₂O molecule) is what number? Since amount of substance is "just the number of particles", do I have this right that the amount of substance is n_H2O = 10²⁰? And from your example of 'bol' above, that if n = 1 mol, then n = 6.02214076×10²³, or equivalently, that 1 mol = 6.02214076×10²³? And further, do you claim that in the New SI, the Avogadro constant N_A and the Avogadro number N_N are the same thing, with N_A = N_N = 6.02214076×10²³? —Quondum 02:01, 9 June 2019 (UTC)

Jorge Stolfi, I don't know whether you have looked at the implication behind my question. However, at this point I may as well clarify what I am driving at. We have several claims:

• 'The BIPM **DID** decide that, starting last month, "amount of substance" is just "number of particles"' This implies 1 mol = N_N (since SI regards 'number' as adimensional with 1 entity = 1).
• 'They [N_A and N_N] were distinct until last month' – your first comment above in this thread. Which is to say, the implication is that N_A = N_N.

The BIPM documentation, which states that 1 mol = N_N/N_A, where N_N = 6.02214076×10²³. These equations collectively constitute a contradiction. Something in your interpretation has to change. —Quondum 19:19, 10 June 2019 (UTC)

@Quondum:Yes, I see clear "philosophical" contradictions in the 9th brochure between the definitions of amount of substance and mole, and the accompanying discussions, including the description of the "Avogadro constant" and "Avogadro number". Fortunately, the contradiction creates needless confusion, but has no concrete implications. It only affects names and ways of writing measurements, but not the actual concepts or the intrpretation of written measurements.
The amount of substance in that example droplet is not just "10²⁰", but "10²⁰ particles" or "1/6.02214076 × 10⁻³ moles". Just as the measure of a right angle is "90 degrees" or "π/2 radians"; not just "90" or "π/2".
As the 9th brochure explains for herz, bequerel, angular speed, and radians, even when the quantity being measured is adimensional one must be careful to indicate the unit of measurement, as well as what specifically is being measured. Thus, when specifying an "amount of substance", one must still specify whether one is counting particles in units of particles or moles (or "boles"), and whether one is counting molecules, atoms, or nucleons.
Likewise, if you write "n = 1 mol", then you are saying "n is 1 mole", which exactly the same as "n is 6.02214076×10²³ particles" (not just "n is 6.02214076×10²³"; and it had better be clear from the context which "particles" (molecules, atoms, or nucleons) you are referring to.
The discussions in the 9th brochure are inconsistent, because they still include "amount of substance" as a fundamental quantity, and mole as a base unit, even though the new definitions of those concepts says that they are mere counts. According to the discussions and definitions of hertz, radians, etc., "amount of substance" (like "number of cycles"), being just a count, should have been excluded from the fundamental quantities, and the "mole" should be an adimensional unit like "radian".
Note that those choices that the BIPM made in the discussions have no concrete implications whatsoever, whereas their decision to define the mole as a a fixed number of particle has concrete (if numerically very small) implications: for instance, one mole of carbon-12 is not exactly 12 grams of carbon-12, as it was two months ago, but now may be off from that mass by almost 10 nanograms.
Thus, in spite of what the discussions in the 9th brochure say, the unit of the Avogadro constant N_A is, according to its definitions, "particles per mole"; which should be written out for clarity, but dimensionally is a pure number -- that is, the Avogadro constant is the same as the Avogadro number. Said another way, "6.02214076×10²³ particles/mol" and "6.02214076×10²³" are just two equally correct ways to write the same thing -- one more menmonic than the other.
Just as the "Anguladro constant" (that relates measurements of an angle in degrees and radians) is best written as "180/π deg/rad" for clarity, but it is a pure number too, hence the same thing as the number "180/π".
For yet another example, one could define the unit of area "round meter" (symbol m^•) as the area of a circle whose radius is 1 meter. That unit would be handy every time one needs to consider areas of circles and ellipses: for instance, the area of an ellipse whose semidiameters are 2 m and 3 m is 2 × 3 = 6 m^•. Measurements of the same area in round meters and square meters are related by the "Archimedes constant" which is "π m²/m^•". It is a good idea to write the constant that way, to make it clear whether it should be multiplied or divided into the measurement; however, since both m² and m^• are units for the same physical quantity, the "Archimedes constant" is a pure number, and it is formally correct to write it just as "π".
Again, it is a pity that, having made the bold and humongous simplification of defining the mole as a fixed count of particles, the BIPM chose to retain the now superfluous and confusing concept of "amount of substance" as a fundamental physical quantity in the accompanying discussions -- thus ensuring that students, teachers, and chemists (and wikipedia editors!) will continue to waste time and neurons on those pointless issues for another decade or two. Sigh.
All the best, --Jorge Stolfi (talk) 19:32, 10 June 2019 (UTC)

Jorge Stolfi, we may yet get to the root of this. I agree 100% with you up to but not including "... that is, the Avogadro constant is the same as the Avogadro number". Let us focus on the glaring algebraic error, and leave the nuances of (a)dimensionality for now. Let me give you a few blunt clues:

• "Anguladro constant" (one example of a unit conversion factor to yield the same quantity in different units):
  • 1° = π rad / 180 (true: self-evident)
  • 180/π °/rad = 1 (true: algebraic reformulation of the previous equation)
  • 180/π °/rad = 180/π (false, but you claim this above)
• Avogadro constant (another example of a unit conversion factor to yield the same quantity in different units):
  • 6.02214076×10²³ particles = 1 mol (true; claimed by you above)
  • 6.02214076×10²³ particles/mol = 1 (true: reformulation of the previous equation)
  • 6.02214076×10²³ particles/mol = 6.02214076×10²³ (false, but you claim this)

You are making the glaring mistake of simply dropping the (adimensional) units that are unequal to 1, thus introducing an algebraic error. Conclusion: N_A = N_N particles/mol = 1 ≠ N_N = 6.02214076×10²³. —Quondum 22:52, 10 June 2019 (UTC)

@Quondum: Sorry, but I can't folow your derivations. The deg/rad "unit" in the Anguladro constant "180/π deg/rad" is only a mnemonic that helps get the units right; it has no value by itself.
I don't think there is any error in what I wrote. To convert a measurement in moles to a measurement in particles, you multiply it by the Avogadro constant:

• (2 mol) x (6.02214076×10²³ particles/mol) = 12.04428152 × 10²³ particles.

According to the discussion in the 9th brochure, that same conversion is

• (2 mol) x (6.02214076×10²³ mol⁻¹) = 12.04428152 × 10²³

which is exactly the same thing, except that they decided that the unit "particle" is not to be written. Similary, to convert a measurement in radians to a measurement in degrees, you multiply it by my "Anguladro constant":

• (5 rad) x (180/π deg/rad) = 900/π deg.

Or, to convert a measurement in inches to a measurement in millimeters, you multiply by the "Thumbadro constant" 25.4 mm/in:

• (12 in) × (25.4 mm/in) = 304.8 mm.

The unit algebra checks in all cases. No? --Jorge Stolfi (talk) 05:35, 11 June 2019 (UTC)

@Quondum: PPS. Let me try again. The basic concepts of metrology are

• A physical quantity, like "the mass of my dog";
• A measurement of such a quantity, that is the formal product of a numeric value (a pure number) by a unit (a physical quantity of the same nature but with a fixed magnitude).

Then "5 kg" and "5000 g" are two different measurementts of the same physical quantity.
In order to convert a measurement (like "5 kg") from some unit (kg) to some other unit (g) of the same nature, one may do either:

• Multiply the numeric value by an appropriate factor (another pure number), in this case "1000"; and replace the old unit by the new unit; or
• Multiply the measurement by the formal product of that same factor by the formal quotient of the new unit by the old unit -- in this case, "1000 g/kg". That is, the conversion is done by the formal algebra "(5 kg) × (1000 g/kg) = 5000 g".

Note that, in the second case, the quotient "kg/kg" cancels out; but the quotient "g/kg" must not be interpreted in any way. The only logical interpretation of "g/kg" would be the pure number 0.001; but then the algebra would become "(5 kg) × (1000 g/kg) = (5 kg) × (1000 x 0.001) = 5 kg" -- that is, the formal trick would not work.
That is the only difference between the Avogadro constant "6.02214076 × 10²³ particles/mol" and the Avogadro number "6.02214076 × 10²³". The "particles/mol" (or "mol⁻¹", per the 9th brochure) in the constant is not a unit of measurement, but only a formal trick to get the correct unit when doing the unit algebra.
Makes sense? --Jorge Stolfi (talk) 06:51, 11 June 2019 (UTC)

"Unit symbols are mathematical entities" (§5.2 of the 9th SI brochure). There is nothing mnemonic about them: we use them entirely algebraically. As soon as you start using the word "formal" you are showing the gaps between your approach and what I understand to be the standard approach.

Uh-oh: 'then the algebra would become "(5 kg) × (1000 g/kg) = (5 kg) × (1000 × 0.001) = 5 kg" -- that is, the formal trick would not work' – no,

this does work: 5 kg = (5 kg) × (1000 g/kg) = (5 kg/kg) × (1000 g) = 5 × (1000 g) = 5000 g.

I can't believe that you're being serious. —Quondum 12:41, 11 June 2019 (UTC)

• @Quondum: Sorry if I did not explain myself cleary. What I meant above is that the trick does work as long as you only cancel "kg/kg", but do not try to compute or interpret "g/kg". If you try to compute "g/kg" before combining it with the other "kg", the result can only be "0.001" (pure number) so you just get back "5 kg". Correct, but pointless...
  --Jorge Stolfi (talk) 18:56, 11 June 2019 (UTC)
• @Quondum: PS. By "formal product" I mean that the product "5 kg" cannot be evaluated further.
  The term "formal" contrasts with ordinary "numeric" product of numbers: the product "5 × 4" can be evaluated and replaced by the number "20". Whereas the product of the number "5" by the mass represented by "kg" would be a mass, but one cannot glue that mass to the paper; one must leave the formula "5 kg" --which is a measurement, not a physical quantity -- unevaluated. One can still combine measurements with algebra (distributive, associative, commutative, etc), but a measurement never gets fully evaluated to a single thing unless it is a pure number.
  Formal products are an established tool in mathematics. E. g. one can manipulate the sequence $S=\langle 1!,2!,3!,\ldots \rangle$ as a formal series $\textstyle P(z)=\sum _{k=0}^{\infty }k!z^{k}$; where z does not represent a number, but is only a dummy variable that is used to hold the terms together. Then one can manipulate $P$ algebraically, e.g. by differentiation, and eventually get some meaningful results about the sequence S -- even though the series itself cannot be computed, because it diverges for any z.
  I hope that you agree that what we are discussing is not physics, but only an algebra -- a formalism -- that is supposed to help us get the right units and powers of ten when evaluating formulas of physics and converting between different units of the same nature.
  All the best, --Jorge Stolfi (talk) 21:13, 11 June 2019 (UTC)

You have been using an argument about formalism to argue towards an invalid conclusion, namely that under the New SI, N_A = N_N. You seem to have missed the principle enshrined in SI that units are simply examples of physical quantities, subject to exactly the same algebraic rules. I am not here to teach you fundamental principles in SI: your position and interpretation with regard including this in the article is contested, and that is sufficient to decide the issue until you obtain consensus for your perspective. —Quondum 12:07, 12 June 2019 (UTC)

Again, I am not going to fight against the view that N_A ≠ N_N; even though I still believe that the definitions of mole and amount of substance in the 9th brochure contradict the commentary in that brochure, which is inconsistent with itself.
However, I still intend to rewrite the head section of this article, that is currently very bad for many other reasons. Later today I will try to post a propiosal that incorporates the changes I made that do not seem to be controversial, while retaining the N_A ≠ N_N position.
All the best, --Jorge Stolfi (talk) 17:15, 12 June 2019 (UTC)

@Quondum: PS. And, again, I don't think that we disagree about anything of substance, or that I don't understand the "fundamental priciples" of SI. I even hope that you agree with me that the commentaries in the 9th brochure are inconsistent in the way they handle quantities that are just counts of things. Our disagreement seems to be only on how to handle that inconsistency.
All the best, --Jorge Stolfi (talk) 17:54, 12 June 2019 (UTC)

I do not see the inconsistency that you refer to. —Quondum 19:46, 12 June 2019 (UTC)

Perhaps I can preempt your response. When the definition says "One mole [of substance] contains exactly 6.022 140 76 × 10²³ elementary entities", the word contains should not be construed to mean is defined as. When I say "18 grams of water contains approximately 6 × 10²³ molecules", I do not mean that 18 g ≈ 6 × 10²³ molecules. —Quondum 21:19, 12 June 2019 (UTC)

Avogadro number in the New SI

"[...] replaces the earlier concept of an experimentally-determined, dimensionless, Avogadro number." Not really accurate: it has not been replaced, and it is no longer experimentally determined, even though it was previously. The 2019 redefinition provides a definition of the Avogadro number, and the lead should IMO reflect the modern position, with history in an appropriate section. The New SI defines both the Avogadro constant (N_A) and the Avogadro number (with no symbol being provided by the definition, but here I'll use N_N) in such a way that N_A = N_N ⋅ 1 mol⁻¹. —Quondum 16:32, 6 June 2019 (UTC)

Ad I tried to explain in the previous section, the definitions in the 9th brochure now say that the "mole" is a specific count of particles (like "dozen particles" or "billion particles"), that the units "mol" and "mol⁻¹" are adimensional (like "rad" and "rad⁻¹"; and therefore the "Avogadro constant" is now adimensional, and the same as the Avogadro number — in spite of what the accompanying discussions in the brochure suggest. --Jorge Stolfi (talk) 19:42, 10 June 2019 (UTC)

I've simplified the intro to skate over this technical distinction for the time being, until we have consensus about what position the article should take on this. -- The Anome (talk) 18:56, 12 June 2019 (UTC)

My original point in this thread was unrelated to the technicalities being discussed in the thread above. My point was that there is a new definition of the Avogadro number that is not experimentally determined, and that we should state this in the lead. This is not replaced by the Avogadro constant; the new definition of the Avogadro constant uses this definition of the Avogadro number. —Quondum 20:14, 12 June 2019 (UTC)

I propose "The Avogadro number is defined to be the dimensionless value 6.02214076×10²³. The Avogadro constant is defined in terms of the Avogadro number." to replace "The exactly defined Avogadro constant replaces the earlier concept of an experimentally-determined Avogadro number that emerges from some other definition of the mole." in the lead. This is a reasonably accurate reflection of the definition in the recent 9th SI brochure: "The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076×10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, N_A, when expressed in the unit mol⁻¹ and is called the Avogadro number." —Quondum 23:02, 14 June 2019 (UTC)

Proposed rewrite of the head section

The current head section seems to be written for metrologists rather than the intended Wikipedia readership -- students, chemists, physicists, and interested lay people. Please consider the following proposed rewrite:

Amedeo Avogadro

Avogadro's number or the Avogadro number, sometimes denoted N or N₀, is the number of constituent particles (usually molecules, atoms or ions) that are contained in one mole, the international (SI) unit of amount of substance: by definition, exactly 6.02214076×10²³. It is named after the scientist Amedeo Avogadro.

Avogadro's constant or the Avogadro constant, usually denoted by N_A, is the factor that, multiplied by the amount of substance in a sample, measured in moles, gives the number of constituent particles in that sample. Its numerical value is the Avogadro number, and its unit is the reciprocal of mole; that is, N_A = 6.02214076×10²³ mol⁻¹.

The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the average mass of one molecule of the compound, in atomic mass units (daltons); one dalton being approximately the mass of one hydrogen atom. So, for example, the average mass of one molecule of water is about 18.0153 daltons, and one mole of water (N molecules) is about 18.0153 grams. Thus, N_A is the proportionality factor that relates the molar mass of a substance to the mass of one molecule. The Avogadro number is also the approximate number of nucleons (protons and neutrons) in one gram of ordinary matter.

The Avogadro constant also relates the molar volume of a substance to the average volume nominally occupied by one of its particle, when both are expressed in the same units of volume. For example, since the molar volume of water in ordinary conditions is about 18 mL/mol, the volume occupied by one molecule of water is about 18/6.022 × 10⁻²³ mL, or about 30 ų (cubic angstroms).

The Avogadro number (or constant) has been defined in many different ways through its long history. Its approximate value was first determined, indirectly, by Johann Josef Loschmidt in 1865. (Avogadro's number is closely related to the Loschmidt constant, and the two concepts are sometimes confused.) It was initially defined by Jean Baptiste Perrin as the number of atoms in 16 grams of oxygen. It was later redefined as the number of atoms in 12 grams of the isotope carbon-12 (¹²C). In each case, the mole was defined as the quantity of a substance that contained the same number of atoms as those reference samples. In particular, when carbon-12 was the reference, one mole of carbon-12 was exactly 12 grams of the element.

These definitions meant that the value of the Avogadro number depended on the experimentally determined value of the mass (in grams) of one atom of those elements, and therefore it was known only to a limited number of decimal digits. Recently, however, the International Bureau of Weights and Measures changed its approach: effective May 20, 2019, it defined Avogadro's number as the exact integer N = 6.02214076×10²³, and redefined the mole as N constituent particles of the substance in consideration. Under the new definition, the mass (in grams) of one mole of any substance (including hydrogen, carbon-12, and oxygen-16) is N times the average mass (in grams) of one of its constituent particles—a physical quantity whose precise value has to be determined experimentally for each substance.

Justification:

1. Avogadro's number is a simpler concept than the Avogadro's constant, and the term is much more common (Google hit ratio 7 to 1). Thus it should be defined first, and in fact the article should be renamed after it.
2. The names with apostrophe ("Avogadro's number") are both significantly more common than the names without ("the Avogadro number"). Note that the latter requires an article, while the forrmer should be used without it.
3. The number of particles in a mole is (obviously) Avogadro's number. Avogadro's constant is not a number; it is the conversion factor defined above. This distinction is clearly made in the 9th BIPM brochure.
4. However, some authors and textbooks seem to use the two terms (number and constant) interchangeably. Perhaps readers should be warned about that.
5. The current version of the head paragrah states that "The Avogadro number, and its definition, was deprecated in favor of the Avogadro constant and its definition." That claim may refer to previous definitions (e.g. Perrin's), or to the way the mole is defined in the 9th BIPM brochure. However, these historical or textual details cannot justify the claim that "Avogadro number" is deprecated; as a distinct concept, it deserves a distinct name. If anything, the name now makes sense, since it is now an exact number and no longer a value to be determined experimentally.
6. The notation N (or N₀) for the Avogadro number is not used by the 9th BIPM brochure, but seems to have been used by several respectable authors.
7. The third paragraph is very important, since it explains the essential idea behind the number. The fourth paragraph is only an obvious consequence of the third one. The first four paragraphs are all that 99.99% of the readers (including almost all chemists and physicists) need to know about the concept. The rest of the article is of interests only to metrologists and historians of technology.
8. The last sentence of the third paragraph corrects the similar claim in the present version of the article: "It is the proportionality factor that relates the molar mass of a substance to the mass of a sample". This statement does not make sense: the molar mass of water is ≈18 g/mol, the mass of a sample can be 0.001 kg or 3.14 kg, and obviously the relation between the two has nothing to do with Avogadro's constant.
9. The last two paragraphs are intended for those readers who are familiar with the previous definitions of the concept, and need to be informed that the definitions have changed in a fundamental way on 2019-05-20 (even though the change has no practical consequences whatsoever, except to metrologists working in the topic).
10. The relationship between Avogadro's number/constant and the Loschmidt constant is too complicated for the head section; it is better discussed in its specific article.
11. The references in the current version of the article are inadequate and have several typos. For one thing, the 9th brochure is not even cited directly (only the minutes of the 2018 meeting are).

I also propose to replace the current History section by this previous version, which I believe is more complete, better organized, and more readable than the current one. I will try to merge into it any recent changes to that section.
All the best, --Jorge Stolfi (talk) 01:42, 2 July 2019 (UTC)

---

Your list under "Justification" is helpful; I'll respond to each. Please don't be put off by the negative responses to the initial points.

1. Google hit rates are not useful for determining relative notability. You would need to find notable modern references to substantiate modern usage (as would be appropriate for an encyclopaedia). Chemistry and physics has little use for the Avogadro number other than to define the Avogadro constant and the mole, and pedagogically. The Avogadro constant finds many uses: in defining the molar gas constant, the Faraday constant, molar mass and the like. Scientists rarely count large numbers of particles, so the Avogadro number should never appear in a formula other than as the numerical part of the Avogadro constant. I see that the last paragraph of molar mass needs correction. Also keep in mind that what an encyclopaedia should be trying to capture is modern notable scientific usage (which is trending towards more exact terminology and algebraically precise notation), not everyday usage, or scientific usage from yesteryear.
2. Same comment about apostrophe versus non and Google.
3. Sure.
4. Agreed.
5. Agreed.
6. Sure.
7. No problem. Here I would say "12 daltons being the mass of one carbon-12 atom" in place of "one dalton being approximately the mass of one hydrogen atom". My inclination would be to omit the fourth paragraph from the lead; this is getting unnecessarily esoteric, but further explanation in the body of the article could accommodate it.
8. Yep, such errors should be corrected.
9. Sure.
10. No objection.
11. Yes, updating of referencing has lagged.

Other than disagreeing with the naming, the aims of clarity and correctness (considering the readership) are good, and seem fairly well achieved in this. —Quondum 01:50, 3 July 2019 (UTC)

Thanks for the comments!
You say Also keep in mind that what an encyclopaedia should be trying to capture is modern notable scientific usage (which is trending towards more exact terminology and algebraically precise notation), not everyday usage, or scientific usage from yesteryear. Well, I disagree somewhat. While it does not harm to make Wikipedia useful also to scientists, these have much better sources -- more accurate, authoritative, precise, detailed, etc., and written specifically for them, using their language. The target public for a Wikipedia article is the general public that may need information about the topic in question -- from "what does this word mean" to specific historic and technical details. That's why the head section must be written in the simplest possible language, avoiding expert's jargon and undue assumptions about prior knowledge (but naturally without sacrificing accuracy).
As a consequence, the article must also take into account the current nomenclature, not just the official nomenclature used by some standards body.
(Moreover, one should not give undue weight to those standard bodies. The BIPM "owns" the second, the meter, and the gram, so the BIPM definitons of those units are the definitions, period. But they do not quite "own" the concept of mole, nor Avogadro's number. They provide one definition each for those concepts, that all scientists hopefully will use and should be taught to students; but those concepts were not conceived by them. So, strictly speaking, one should say "the SI mole" or "the SI value of Avogadro's number" for the concepts defined above. But I digress...)
Anyway, I would still keep the order above, because the "number" is a simpler concept to explain and unedrstand than the "constant".
On the other hand, I don't care much about the apostrophed versions, or their order. I thought that both versions should be mentioned, since both are correct and common usages; but maybe we can assume that the reader is smart enough to infer either version, if given the other...
As for your other comment, Here I would say "12 daltons being the mass of one carbon-12 atom" in place of "one dalton being approximately the mass of one hydrogen atom" I am fine with adding the first sentence, but the purpose of the second one was to explain to the reader the "spirit" of the concept of "atomic mass unit"; that is, why did the BIPM define the mas of a C-12 atom is as 12 amu, rather than 1 amu or 1000 amu.
What do you think of replacing that sentence with "the approximate mass of one proton or neutron" (still after the SI C-12 definition)? The error in both approximations seems to be about the same, 0.0007–0.0008 amu (which is kind of surprising, since the mass of the electron is 0.0005 amu, and the C-12 atom has 12 nucleons and 6 electrons).
Finally, as for the "utility" of the concept: I learned about Avogadro's number ("6.02 × 10²²") in high school, almost surely even before the concept of "mole". I don't remember exactly how it was defined, but probably it was like "the number of atoms in one gram of hydrogen". Its main "utility" at the time was to give us an idea of how ridiculously small and numerous atoms are, and also to tell us that Science does know how big they are.
All the best, --Jorge Stolfi (talk) 22:30, 3 July 2019 (UTC)

I carefully used "scientific usage", not "concepts as defined by standards bodies". I also used the word "modern", just as you used the word "current". What I was saying is that it is for us to determine what the current scientific usage is, and to avoid skewing factors such a Google searches. We need to describe all this in simple language, as you say. I do feel that listing of competing/alternative terminology has little place in the lead, though.

Why would the BIPM "own" any base unit more or less than another? I would say that by your criteria the BIPM has far less claim on "ownership" of the second than they do of the mole, considering its much, much longer history. Would you say that they have not at last taken ownership of the Avogadro number when they dictated its exact value? And I seem to have anticipated your "learned about ... in high school" with my "... and pedagogically".

I did not object to the order of presentation: it is easier to follow when the Avogadro number is introduced before the Avogadro constant. This is not an argument for renaming the article though, and I was arguing that the Avogadro constant is the concept that the article centres on.

The phrase "the approximate mass of one proton or neutron" is (to me at least) an intuitively more natural way to consider the dalton than in terms of the mass of any given atom. It alludes more directly to the composition of atoms and the basis of the definition than does a "hydrogen atom", especially considering that some readers are not automatically familiar with the typical composition of hydrogen (besides, hydrogen occurs naturally in three relatively stable isotopes). The carbon-12 example had two things going for it though: it is the (current) real definition (and it does sound a bit like we are defining the dalton), and the juxtapositions of the two 12s is difficult to miss and natural to draw inferences from. This is a really minor point, though. —Quondum 01:00, 4 July 2019 (UTC)

Why would the BIPM "own" any base unit more or less than another? AFAIK, the BIPM is the direct male-line descendant of the French/International committee that invented the metre and the gram (and the litre, and the power of ten prefixes, and a few other things).
That committe did not invent the second, but it had no clear owner before, so its appropriation was normal by the mores of the time. It used to be 1/(3600×24) of a solar day, but it had long been known that the later was not constant, and advances in clock technology had already made that definition obsolete. So, even the Greenwich Observatory relinquished their claims over that territory to the BIPM, very early on. Thus it seems reasonable to say that the BIPM "owns" those units by traditional Western inheritance law.
I mean, there are no accurate definitions of those units that are worth mentioning, except those promulgated by the BIPM - just as there are no meaningful definitions of "Nobel Prize in Physics" other than the one given by the Nobel Foundation. It would be silly to write "the SI meter" or "the SI gram", because there never were any other metres and grams.
The BIPM, on the other hand, had no role in the conception of the mole. AFAIK it was invented by Perrin in 1909, as a hack to simplify the life of chemists: namely, the mole was meant to be an amount of a substance whose mass in grams was equal to the mass of the molecule relative to the mass of an atom of hydrogen (the lightest atom, and so a natural unit of molecular mass). This relative molecular mass was known, with sufficient accuracy, from chemical reactions and the atomic/molecular theory of matter. AFAIK, for some time the mole was standardized by the IUPAC, not the BIPM. Only much later did the BIPM, as a service to chemists, included the mole in the SI, so that it could be more firmly tied to its definition of the dalton. (Was that in the 8th brochure?)
Anyway, for many decades (almost a century?) the authoritative definitions of the mole were not promulgated by the BIPM. So, I feel that it is still too early to consider it "BIPM property". I would say that it is at best a "protectorate" of the BIPM, like Palau is to the US. And it seems still necessary (especially after 2019-05-20) to say "the SI mole" in some contexts, like this article...
All the best, --Jorge Stolfi (talk) 02:58, 4 July 2019 (UTC)

PS. As for nomenclature: it is a long-standing standard practice in Wikipedia to mention in boldface all sufficiently common alternate names in the head section -- even informal, incorrect, or obsolete ones. The justification is that many readers will arrive at this article by looking up one of those alternate names, and would get confused if the head section does not mention it.
On the other hand, again, I do not feel strongly about having both apostrophed and unapostrophed versions. Is it reasonable to assume that "the Xxx constant" can always be called also "Xxx's constant", for any person Xxx? If so, only one version (the one most appropriate grammatically) needs to be given.--Jorge Stolfi (talk) 03:14, 4 July 2019 (UTC)

---

I have edited the article as discussed above. I followed my choice the disputed points, but I am not fanatic about them. All the best,--Jorge Stolfi (talk) 03:19, 4 July 2019 (UTC)

Do you seriously think someone might be confused if they follow a link from "Avogadro's constant" and arrive at page with a bold "Avogadro constant" that they will be confused at not finding the linked term? And do you not think that by giving equal prominence to an archaic term we are creating the confusion that this is an equally prominent modern term? (I'm not saying it is archaic, just that the argument is spurious.) —Quondum 12:56, 4 July 2019 (UTC)

No, no, sorry!
The reason why I left both the apostrophed and unapostrophed versions is that I wasn't sure about the grammatical issue. As I asked above: Is it reasonable to assume that "the Xxx constant" can always be called also "Xxx's constant", for any person Xxx? Are "Newton's equation" and "the Newton equation" both "correct" English? If the two forms are always both correct, for any person name, then only one version (the one most appropriate grammatically at that point) needs to be defined in bold in the article, and the other can be used in the text when appropriate. On the other hand, if, for some constants, only one of the forms is correct English, then it may make sense to point that out where appropriate.
And by "correct" I mean "commonly used", which is the modern approach of linguists and dictionary editors. To be really pedantic, since it was not defined by Avogadro, it should always be called "the Avogadro constant/number", never "Avogadro's constant/number". And, for gold-medal pedantism, one should say "Perrin's Avogadro constant". (Check the story of "Stoke's equation", by the way.) However, both forms are widely used, so they are both correct English.
Sorry but I didn't get your second point. Just to clarify my view: the two concepts are clearly distinct (at least in the mainstream reading of the 9th brochure) and very relevant. If one wants to be formally correct, one must always be careful to say "Avogadro number" when referring to the number of particles in one mole, and "Avogadro constant" when referring to the units conversion factor. I anything, the 9th brochure, by defining the number to have a precise and immutable value, made the "number" even more important than before.
And, again, everybody who has gone through high school knows about the Avogadro "number". Only some chemists and physicists know that the Avogadro "constant" is not the same thing as the "number" — and only they really need to know the difference. So, I agree that the article must carefully define the two terms and clearly explain the difference; but I definitely do not agree that the "number" should be presented in a way that implies it is "archaic", or less important than the constant.
In fact, the number should be defined before the constant, simply because the text is much easier to understand that way.
All the best, --Jorge Stolfi (talk) 19:57, 5 July 2019 (UTC)

We seem to be unsure of each other's subtleties – we seem to be agreeing, nevertheless. I was admittedly being hyperbolic in my use of the term "archaic", but was meaning in relation to the "'s", definitely not the "number". With regard to modern usage, while all four terms occur (see ngrams), compare relative hits rate for "avogadro number": 74,800, "avogadro's number": 42,200, "avogadro constant": 26,900, "avogadro's constant": 5,120. This should make the hypothesis that in scholarly circles the popularity of the apostrophe version of each is not dominant look reasonable. Proper diligence would demand that the actually check notable papers. —Quondum 22:32, 5 July 2019 (UTC)

Thanks for the numbers. I am satisfied that both versions (with apostrophe and with article) are correct. My scruples were about whether this is true in general, or hold only for some constants. (I am not a native English speaker.)
I have now ran your test on a few other constants; you may want to look at the results. It seems that, yes, both forms are common enough for all those constants to be considered both correct. So it is indeed unnecessary to mention both forms in this article. I will fix that.
All the best, --Jorge Stolfi (talk) 02:20, 6 July 2019 (UTC)

To answer your implied question directly, from my understanding as a native English speaker but not having formally studied the language, the two constructions (with and without apostrophe) are not equivalent (or interchangeable) as a general statement. With, it has an element of "ownership" (the "'s" is called the possessive), and might be used automatically in an informal context where something is attributed to someone. Without, it is a more formal modifier or tag used in forming a name of something. For example, the Paris Cathedral is unambiguous, but Paris's cathedral is a bad construction, since there is at least one other. Actual usage overrides this (usage creates phrases that often behave atomically), but this varies between groups and over time, often influenced by the preferences of the group. My perception is that in the academic world, especially more recently, there is a strong tendency towards constructions that imply that a constant is named in honour of someone, rather than that it "belonged" to them. In most cases, unique and direct attribution is problematic, but using someone's name to distinguish something while honouring them is not so. Such a widespread preference becomes a strong determiner of usage. As with any fashion, there are the trendsetters who ignore the "rabble" but set the future norm, in this case the "educated elite".

A caution that bears repeating: Google's statistics are to be used highly advisedly. Useful in guiding hypotheses and discussions, but far too easily thrown out of whack, even for its primary function of counting occurrences (explained here). I have found Google ngrams persuasive in one instance only: when a term in a recent book could not be found at all, I decided that this was sufficient to consider it non-notable. If I want to find usage or interpretation, I access a fair number of references (usually via Google), rate each for quality, and look at their take. Scientific journalism is unfortunately often abysmal. I usually have to discard over 90% as irrelevant or unusable: selection for quality on the internet is crucial, else the data is just garbage. But a historical account by someone versed in the field can be a pleasure to read, and is often well-researched. —Quondum 13:49, 6 July 2019 (UTC)

Proposal to move the "Measurement" section to atomic mass unit/atomic mass constant

I propose to move the whole "Measurements" section to the atomic mass unit article, with the appropriate adaptations and ordering. (Note that there is already a separate proposal to merge atomic mass constant into that article as well.)
The justification for this move is that, given the new SI definitions of the mole and of the Avogadro constant, those experiments have become irrelevant to these concepts. The Avogadro number no longer needs (or can) be measured experimentally.
On the other hand, those experiment now can and must be viewed as being aimed to determine the mass (in grams) of whatever reference particle was/is used to define the dalton; and, as such, they continue to have the same current or historical interest that they had until the redefinition.
Thoughts? --Jorge Stolfi (talk) 03:58, 4 July 2019 (UTC)

There is quite a bit in this article that needs this sort of rewrite. Keep in mind, though, that some version of this might still belong in the 'History' section. —Quondum 22:35, 5 July 2019 (UTC)

@Quondum: I moved the section as announced above. I agree that some of that material should be restored to the history section, but probably in an abridged form; the reader who needs more information should be directed to atomic mass unit. Makes sense?
I will try to do that later this week (drained my batteries for today...)
All the best, --Jorge Stolfi (talk) 05:10, 9 July 2019 (UTC)

Definitely. —Quondum 12:06, 9 July 2019 (UTC)

misprints

"universal atomic mass unit" appears instead of "unified atomic mass unit" at least two times.

18/6.021 appears instead of 18/6.022

pietro151.29.1.146 (talk) 18:52, 9 February 2020 (UTC)

Practical usage?

I think an interesting + useful addition to this article would be a discussion of when students/researchers are likely to encounter the constant in any practical setting. I.e., aside from the definitional value and knowing the concept, is the Avogadro constant ever frequently used in any context during calculations, experiments, or other purposes? Supernova87a (talk) 20:42, 13 March 2021 (UTC)

Same Mass But Different Number Of Moles

Number of moles = Mass Given/(Atomic Mass) or Molecular Mass

Number of moles = Volume Given at STP/ 22.4 L (22.4 dm^3)

Number of moles = Molecule Given or Atoms Given/ Avogadro’s number

WATER: One liter is defined as the volume of one kilogram of pure water at maximum density (+4 °C) and standard pressure

Number of moles = Volume Given at STP/ 22.4 L

Number of moles = 1 L/ 22.4 L

Number of moles = 0.04464286

Atomic mass of H2O = 16 + 2 = 18g/moles

Number of moles = Mass Given/(Atomic Mass) or Molecular Mass

Number of moles = 1000g/18

Number of moles = 55.556

PLATINUM: Of which the standard Kilogram is made of (https://en.wikipedia.org/wiki/Kilogram)

Atomic mass of platinum = 195.084

Mass of 1 Kg of Platinum = 1000 g

Number of moles = Mass Given/(Atomic Mass) or Molecular Mass

Number of moles = 1000/195.084

Number of moles = 5.125

One liter of platinum weighs 21.45 kg (source internet)

Therefore volume of one liter (1L) of platinum = 1/21.45 L=0.04662005

Number of moles = (1/21.45) L/ 22.4 L

Number of moles = 0.00208125

ANY MISTAKE OR REASONS — Preceding unsigned comment added by 39.32.85.182 (talk • contribs)

Methods of determining the Avogadro constant

I think there should be a section outlining some of the methods that have been used to determine the Avogadro constant, particularly the early ones. The article mentions Perrin and Loschmidt as having done it (or something equivalent) but the articles on those people don't describe how they did it either.

I emphasised the historical methods above, because discovering how much atoms/molecules weigh is a monumental step in our understanding of matter, so it would be good to see how that step was achieved.

As I came to the article in search of information on this topic, I am, necessarily, unqualified to write on it myself! Macboff (talk) 09:08, 6 August 2021 (UTC)

Chemistry

Avogadro's number 2400:ADCC:10C:8800:C844:27EE:7DFF:B9B2 (talk) 05:03, 17 May 2022 (UTC)

Two to the power of 79

I often wonder why it is not more well known that Avogadro's number is close to 2^79 (it's off by less than 0.4 %). It means that if you take an amount of a substance equal to 1 mole, you can in principle halve it 79 times; then you are left with just one molecule. (Also, if you have an amount of matter somewhere between a grain of sand and a bus, you can halve it between roughly 70 and 100 times - except neither is of course made up of one kind of molecule only.)

I think it is a brilliant way to illustrate the scale of Avogadro's number, and the graininess of the material world. But ... of course, to add it here, we'd need a source. Does anyone know of a valid source for this? Nø (talk) 14:04, 26 September 2022 (UTC)

PS. It is also fairly close to 24!, but here the error is nearly 3%, and unlike the power-of-two, there is no obvious popular interpretation. I have found a few internet pages discussing one or the other of these two spurious facts, including posts claming that there is a movement to replace the official value of the Avogadro constant with 2^79. But I have found no pages that are valid sources - not even close! Nø (talk) 10:33, 23 February 2023 (UTC)

I don't know whodunnit, but as of right now, y Article on Avagadro's number constant contains sheer nonsense, substituting y word approximate for y word exact, and y word nucleons for y words particles or molecules. It is now '023 Feb 21 Tues 07:06EST. I am RA Fritz Skees, of NC State University school of Electrical Engineering, A1FritzYeCat@Yahoo.com, 8282796535 cel'phone. This nonsens must be fixed.

Fix this Nonsense. 2600:1004:B172:5DC5:5208:62FE:A94:3994 (talk) 12:15, 21 February 2023 (UTC)

Visiting the article 15 minutes after this post, I don't see the problem. The article hasn't been revised for a copuple of weeks (unless the edit & reverse has been hidden). If you still se a problem, please explain more carefully. Nø (talk) 12:32, 21 February 2023 (UTC)

A load of nonsense

It is now 2023-05-21. I agree with RA Fritz Skees who pointed this out on 23rd Feb 2021. The definition is a messy contradiction, and it needs rewritten. Someone knowledgeable please rewrite, and distinctly separate history from definition. EdwinaTS (talk) 06:02, 21 May 2023 (UTC)

First Measurements

The article currently notes The electric charge per mole of electrons is a constant called the Faraday constant and has been known since 1834, when Michael Faraday published his works on electrolysis. The work of Faraday was based on mass of a substance having no relation to Na, i.e. the notion of a specific number of particles per mole. The Faraday Constant as related to the mole was named in his honor some time later after Avogadro's number was established. The fundamental origin of the value associated with Avogadros number was the Boltzmann constant Kb which was originally assigned by Max Plank. Na = R/Kb Zxooom (talk) 22:29, 31 May 2023 (UTC)

"Avogadro number" vs. "Avogadro's number"

Since @Quondum reverted my edit, I'd like to bring "Avogadro" vs "Avogadro's" number to discussion.

Firstly, "Avogadro's" seems to be in much higher use, as even when you restrict the search to be "Avogadro number", the vast majority of sources use the possessive form, and a wide array of reliable sources spell it as such.

Quondum's main point was citing: Bureau International des Poids et Mesures (2019): The International System of Units (SI), 9th edition, English version. And they do call it the "Avogadro number". But does it really outweigh all the others? I know it is kind of the one authoritative source on this, but at least both should be listed in my opinion. BhamBoi (talk) 21:57, 11 June 2023 (UTC)

Google hit counts are pretty meaningless, Google's algorithm clearly does not use the "restriction" the way you intend it, and you seem to think that majority occurrence across the web carries weight on WP for technical terminology. The term "Avogadro's number" also is often used to mean the Avogadro constant, so you'd have to figure out how to filter by meaning. Ideally, we need reliable sources that discuss the terminology. You have unfortunately not provided anything that can be worked from. —Quondum 23:34, 11 June 2023 (UTC)

Different values 6.02252 vs 6.02214076?

Would someone talk about why some places on the web show the Avogadro constant or number is: 6.02252×10^23

but Wikipedia cites it as: 6.02214076×10^23

Those two are not the same number.

Confer #1 & #2 below, with #3 Wikipedia.

(#1): https://www.infoplease.com/encyclopedia/science/chemistry/concepts/avogadros-number

Avogadro's number ... is equal to ... 6.02252×10^23.

(#2): https://www.encyclopedia.com/science-and-technology/chemistry/chemistry-general/avogadros-number

Avogadro constant (Avogadro number) The number of molecules, atoms, or ions in one mole of a substance: 6.02252 × 10^23 per mol. 

(#3): Wikipedia

The Avogadro constant ... with an exact value of  6.02214076×1023 Jrodor (talk) 09:04, 31 May 2024 (UTC)

Those are probably old values with larger uncertainty than what the last experimentally determined value had. See the table of old values at https://chemistry.stackexchange.com/a/144406 Jähmefyysikko (talk) 15:21, 31 May 2024 (UTC)

Thank-you for the URL to that table of historical values! That is exactly what I was looking for, but couldn't find on my own. Perfect response! Jrodor (talk) 05:44, 1 June 2024 (UTC)

Clearly distinguishing between the Avogadro constant and the Avogadro number.

One of the most confusing things to students (and, judging by modern chemistry textbooks, to many of their teachers) is the difference between the Avogadro constant (the subject of this article) and the Avogadro number. And then there's the "apostrophe" problem: Avogadro's constant or Avogadro's number. First, it is important to point out that Perrin used the term "constant d'Avogadro" (Avogadro's constant in English) to mean what is now called the Avogadro number: the (dimensionless) number of entities in one mole. This number is not some universal constant of Nature. Until recently, this number was always simply the ratio of two man-made mass units, the gram and the atomic-scale mass unit in use at any given time. So, for example, in terms of oxygen or carbon: the Avogadro number = (0.016 kg)/m_a(¹⁶O) or (0.012 kg)/m_a(¹²C), the latter being the gram-to-dalton mass-unit ratio. By trying to "find" the value of "Avogadro's constant", Perrin was, in effect, trying to measure the mass of an oxygen atom in grams.

Since the redefinitions of SI base units in 2019, the (dimensionless) Avogadro number is now defined as exactly 6.022 140 76 × 10²³. [But this is not g/Da, which is still not defined exactly.] Whereas, the Avogadro constant, N_A , is defined as an Avogadro number per mole: N_A = 6.022 140 76 × 10²³/mol.

Since a mole is an aggregate of an Avogadro number of entities:

mol = 6.022 140 76 × 10²³ ent

a more comprehensible definition of the Avogadro constant is one per entity: N_A = 1/ent. Unfortunately, one entity (symbol ent, dimension N) is not recognised by the SI or other standards bodies—although it is an obvious (and easily comprehended) choice as an atomic-scale unit for amount, paralleling the dalton for mass. Then the relationship between the amount (of a given substance X), n(X), and the corresponding number of entities in the sample, N(X), would be written:

n(X) = NX) ent

i.e. amount is an aggregate of N(X) entities. So if N(X) = 6.022 140 76 × 10²³, the corresponding amount is (exactly) one mole. The SI formula relating amount and the number of entities is:

n(X) = NX)/N_A = N(X)(1/N_A)

—an aggregate of N(X) "reciprocal Avogadro constants". From which we see that a reciprocal Avogadro constant is (exactly) one entity.

Molar mass, M(X) = m(X)/n(X) = [N(X)m_av(X)]/[N(X) ent], where m_av(X) is the (isotopic) average entity mass. Cancelling N(X), we see: M(X) = m_av(X)/ent, the entity mass per entity, a straightforward concept. However, this is usually written as M(X) = m_av(X)N_A , which is not as easy to conceptualise. Since m_av(X) = A_r(X) Da, the molar mass can be written as: M(X) = A_r(X) Da/ent, the relative atomic-scale mass times dalton per entity. For all practical purposes (although not exactly), we then have the easily conceptualised relationships:

M(X) = A_r(X) Da/ent ≈ A_r(X) g/mol = A_r(X) kg/kmol

Boppennoppy (talk) 20:31, 15 November 2024 (UTC)