Talk:Mole (unit)

What is wrong with the measurement of the mole?

Well the simple fact is nothing necessarily. This is because a mole, 6.023*10^23, is independent of mass except when it comes to weighing carbon 12 (C12) only. The same can be said for Avogadro's number, 6.022*10^23, when regarding helium 4 (He4) only.

Another thing to consider is that the rest mass of an isolated neutron (i.e. not affected by the nuclear binding energy of the nucleus of an atom) 1.67492749804*10^(-27) kg, is slightly greater than the rest mass of an isolated proton, 1.672621924*10^(-27) kg. Thus the mass of a neutron divided by the mass of a proton is 1.001378419, or about 0.138% more, and herein lies a discrepancy in mass when weighing.

One other thing to consider is that the masses of the isolated neutron and isolated proton are the rest masses. If it were possible to weigh particles travelling at relativistic speeds, the observer would need to take into account the increase in mass due to the speed the particle was travelling at if this increase in mass were of significance. This is one reason why those scientists who study the behaviour of particles in particle accelerators measure the particles in terms of energy imparted to the particle itself as it is accelerated.

Yet another thing to take into account for the sake of weighing mass both precisely and accurately is that the gravitational field strength on Earth, 9.80665 N/Kg is accurate to only 6 significant figures. Much of this fairly low degree of precision is due to the fact that the geography of the Earth varies a great deal from place to place and, for example, mountain ranges and places where weighing mass is done, like buildings have considerable and possibly significant mass, and we all know, thanks to Einstein, that the magnitude of mass affects the magnitude of the gravitational field strength.

Also worth considering is the fact that electrons have mass (at rest it is 9.109383702*10^(-31)Kg) also and are in the range of significance when it comes to weighing substance with precision. This figure makes a neutron about 1,839 times as heavy as an electron and of course this figure is only 4 significant figures.

However, charged entities such as protons or electrons exhibit a charge conserving behaviour so the possible discrepancy exhibited in an inaccurate result will rarely be encountered.

However, what is one to say about the Relative Atomic Mass Unit U? By definition this is simply one twelfth of the mass of a C12 atom. Not only does U not take into account the electron (when measuring the mass of ions), which must first be subtracted from the mass of the atom before acquiring an accurate result for U, but what about the discrepancy between the mass of a neutron and the mass of a proton? Do we just take the average between the two particles? And if so, what of differing isotopes of varying elements, and what about the rate of change in mass number versus atomic number?

Another consideration is that we don't know if the mass of the neutron varies linearly against that of the proton over the full range of atomic numbers. It's just a thought but both particles play different roles inside the nucleus. According to popular theory for example, the neutrons behave like the glue that binds the protons - the deciders of the chemical behaviour of the nucleus - together which would otherwise fly apart from each other due to electrostatic force. But this is an area which I dare say has escaped significant consideration, and the author does admit, this particular area of consideration may escape significance, or does it in fact? A possible future area of study so as to confirm whether or not.

One final thing to consider before summing up is that because there are two distinct rates of change of the curve which relates the negative nuclear enthalpy against the independent variation in atomic number (because at first the curve trends aggressively upwards towards the local maximum, corresponding to manganese (Mn) having atomic number 25, or iron (Fe) having atomic number 26 at which point the curve trends ever so slightly downward towards the heaviest elements such as plutonium and uranium) there is a significant change over the range of atomic numbers in the rate of change in nuclear binding energy and thus there is a significant change, over the range of atomic numbers, in the rate of change in the relative molecular masses of each element. Therefore one cannot straightforwardly assume that by merely taking into account the linear variation in mass number, there is a corresponding linear variation in mass.

In summing up, my point is this: there is nothing wrong with the number that is the SI unit of the mole. Let the mole, for the sake of significant figures beyond 4,5 or 6, be whatever we have found them to be or chosen them to be. However, in realistic terms one cannot expect, in light of the above argument, to gain any degree of accuracy by weighing on a mass balance, atoms beyond say 6 significant figures. In fact, as the elements you are weighing on a mass balance get heavier, the degree of accuracy diminishes until the heaviest elements where one cannot expect to get accurate beyond 3 significant figures.Laoscala27 (talk) 07:26, 23 September 2023 (UTC)

For most of chemistry, getting within 1% is close enough. Though the common centigram balance in chemistry labs often allows better than that. To get to 1%, one can ignore the fine details of atomic mass, as give for example on the chart of the nuclides. The atomic weight, that is, the isotopic abundance average of the atomic masses, or maybe just measured. In any case, they can be measured to high accuracy if desired. There was an alternate proposal to redefine the kilogram based on the mass of Si-28 atoms. (See Alternative_approaches_to_redefining_the_kilogram#Atom-counting_approaches.) That would also have redefined Avogadro's constant. In any case, atomic mass is defined for neutral atoms, including the mass of the electrons. It is easy to add/subtract when needed. Gah4 (talk) 22:24, 23 September 2023 (UTC)

I agree, but isn't it just a little cumbersome to have to refer to a chart and then add or subtract as needed. In any case your argument seems to be correct in that there are ways and means to come to a more precise result if needed. Laoscala27 (talk) 17:28, 24 September 2023 (UTC)

The ones that need isotopic values are rare. I suspect most chemists memorize the rounded values of common elements. High school chemistry classes have a giant periodic table on the wall, maybe with four digits or so. Gah4 (talk) 20:37, 24 September 2023 (UTC)

Firstly, by current (post 2019) definition one mole contains exactly 6.02214076×10^23 elementary entities.[[1]] This is by definition and never varies. Historically, the mole was empirically determined and thus prone to experimental error and systematic errors of the methods used, including assumptions about isotopic purity and mass defects etc. as discussed, but not today.

Secondly, the Avogadro constant is also currently (post 2019) defined to be an exact number, 6.02214076×10^23.[[2]] As with the definition of the mole this constant has a history of being empirically determined and thus has in the past contained errors from various sources. It is important to also understand that the definitions have also changed with time and our understanding of chemistry.

The current definitions solve many problems, including much of what is discussed here. There is no longer any ambiguity as to what a mole is or what the value of the Avogadro Constant is. There is no mass dependence on either ever. The downside is that the defined numerical equivalence between Molar Mass (g/mol) and Molecular Mass (Da) is lost, or inexact. This relationship is now to be determined empirically. This inexactness is deep in the decimal places and is not meaningful to most scientists. With respect to accurately weighing out a mole of bulk chemical, other than the accuracy of the balance is that the distribution of isotopes varies across the earth. The masses on the periodic table are averages carefully measured across the earth and the number of significant figures is intentionally limited by this variance, not the precision or accuracy of the measurements. Some elements have four sig figs because its isotopes vary in abundance more than other elements. Lithium is an excellent example of an element that exhibits great variation in isotopic distributions. Its isotopic distributions have even changed with time and varies significantly with respect to proximity to industrial processes.

Indeed, the capacity to measure masses accurately far exceeds the limitations discussed above. Weighing individual molecular masses to 9-10 significant figures is not uncommon. In this realm the resolution of isotopes and counting the number of electrons is trivial. Nick Y. (talk) 19:57, 27 September 2023 (UTC)

Yes. For much of chemistry, (except Cl) the integer atomic weights are close enough. And if not, the periodic table averages. For nuclear physics, sometimes the atomic mass of specific nuclides is needed, and use the chart of the nuclides. Otherwise, I think they should have chosen a multiple of 12. That is, that 1g of C12 should have an integer number of atoms. Gah4 (talk) 04:35, 28 September 2023 (UTC)

"Mole(unit)" listed at Redirects for discussion

The redirect Mole(unit) has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 November 9 § Mole(unit) until a consensus is reached. Steel1943 (talk) 17:24, 9 November 2023 (UTC)

For the benefit of other editors: the issue is the lack of a space between "Mole" and "(unit)" in the redirect source. Johnjbarton (talk) 17:29, 9 November 2023 (UTC)

Some common misspellings of titles are used as redirects for convenience. I don't know that there is a rule about that. In the case of the space, seems to me that either all such articles should have redirects, or none. Gah4 (talk) 01:41, 29 May 2024 (UTC)

In my opinion this is not at all a common misspelling and it should not exist. Normal users won't search for "Mole(unit)" and internal wikilinks that use Mole(unit) will be red and can be fixed. Johnjbarton (talk) 02:30, 29 May 2024 (UTC)

What is that image trying to say?

Recently this image was added

• Mass versus moles of iron vs gold.svg

It has some boxes and circles with Fe and Au labels. What is it trying to tell us? @VectorVoyager Johnjbarton (talk) 16:49, 6 March 2024 (UTC)

I actually made it for Molar mass page which I think is quite fitting there. It tells that 2 samples of 2 different elements for the same amount of mass that differ in molar mass have different number of moles in the same mass (m/M). I can take it off from this page as its not specifically a diagram to make people understand moles but that it can stay in the molar mass page if there is no errors. I am 100% open for suggestions for improvement though. VectorVoyager (talk) 22:43, 6 March 2024 (UTC)

@VectorVoyager ok thanks. the image has two cylinders and now I notice that they have different sizes. I suppose this much would be clearer to me if they were side by side with text like "same mass, different volume". but I'm not sure how to connect that to the topic. it's just to imagine a visual that works for numbers and mass without involving density. Johnjbarton (talk) 04:47, 7 March 2024 (UTC)

@Johnjbarton: hi, I made a new depiction for this page (Mole carbon-12 diagram.svg). I think something like this is more fitting for the page. Its very important that the visitors understand diagrams used on the Wiki, so I am open for suggestions to improve that previous one that is currently present on molar mass page. How can I make it more understandable in a visual way? Thanks. VectorVoyager (talk) 11:39, 7 March 2024 (UTC)

Well you picked a tough assignment ;-)

My suggestions for this version:

1. Move the 12 grams of ¹²C on to the Mole side
2. Remove the Avogadro (too much)
3. Rather than the ambiguous x602 sextillion, just write 602 sextillion Carbon atoms.

That much illustrates "Mole" but does not pinpoint "Mole (unit)".

For "Mole (unit)" maybe an image with seemingly many items and the amount in Mole? The only thing one need to get a across is that the unit is for counting items and the scale is ridiculously large.

HTH Johnjbarton (talk) 16:40, 7 March 2024 (UTC)

Thanks! I have implemented the first and third suggestions that you have written, but I think stating that the accepted exact form is Avogadro constant is intuitive for the reader to understand the connection between NA and moles. VectorVoyager (talk) 08:40, 8 March 2024 (UTC)

mol kept me from Chemistry

I found the concept of calling some arbitrary number a 'mol' of something exceedingly confusing when I was confronted with it at school. And as it is a basic concept, I got bad grades in my first test. Turns out, I was right, and there are people sharing my criticism. If anyone out there works in curriculum design: Please just leave out this nonsensical non-unit and get into the interesting stuff. Molar masses can be discussed way later, in advanced studies. Thank you. --2A01:C23:5DB9:4A00:B905:825E:E1B0:1A05 (talk) 2A01:C23:5DB9:4A00:B905:825E:E1B0:1A05 (talk) 21:15, 12 March 2024 (UTC)

This is not the place to discuss curriculum design. Pradyung (talk) 00:38, 29 May 2024 (UTC)

The missing atomic-scale unit for amount

This is not about curriculum design, but it is about the well-documented widespread confusion concerning the mole, amount of substance, the Avogadro number and the Avogadro constant. The confusion arises primarily because, unlike mass, which has a well-defined atomic-scale unit, the dalton, Da, amount (of a substance) does not have a recognised atomic-scale unit. For a substance X, the relationship between the amount of the substance, n(X), and the corresponding number of entities, N(X), is always given as: n(X) = N(X)/N_A, which can be written as n(X) = N(X)(1/N_A), implying that amount is an aggregate of N(X) "reciprocal Avogadro constants". Other than saying that amount is proportional to the number of entities, this does not help in forming a concept of the quantity "amount"—unless some physical meaning can be given to 1/N_A or to N_A itself. To say that 1/N_A is the molar number of entities, N(X)/n(X) is circular. To say that N_A is defined as 6.02214076 × 10²³/mol (where the numerical factor is the definition of the Avogadro number N₀), requires understanding what a mole is—a macroscopic unit for "amount"—which is again circular. The SI describes a mole as "containing" an Avogadro number of elementary entities. But chemists understand the mole as "being" (an aggregate of) an Avogadro number of entities.

It makes sense, therefore, to introduce an atomic-scale unit of amount equal to one entity, symbol ent—the smallest amount of any substance (retaining its chemical properties). Then a mole could be defined in an easily comprehended way as:

mol = 6.02214076 × 10²³ ent (exactly)

an aggregate of an Avogadro number of entities. Then amount is also easily comprehended as:

n(X) = N(X) ent

an aggregate of N(X) entities. So, when N(X) = 6.02214076 × 10²³, n(X) = 1 mol. The Avogadro constant is then also easily comprehended as being one per entity, N_A = 1/ent. [Although this widely misunderstood dimensional constant is not really needed!] Then molar mass has an easily understood atomic-scale unit, dalton per entity, Da/ent, as follows.

Molar mass is defined as the amount-specific mass, M(X) = m(X)/n(X) = [N(X)m_av(X)]/[N(X) ent] or M(X) = m_av(X)/ent, the (isotopic) average atomic-scale mass per entity. Writing m_av(X) = A_r(X) Da, gives the molar mass as M(X) = A_r(X) Da/ent: molar mass is the relative atomic-scale mass times the atomic-scale unit dalton per entity. Before the 2019 redefinitions, the carbon-12-based mole was (exactly) (g/Da) ent, so that Da/ent = g/mol (exactly). Unfortunately, the dalton was not redefined exactly in terms of the (fixed-h) kilogram and remains defined as m_a(¹²C)/12. But, for all practical purposes, a carbon-12-based kilogram is very nearly equal to a fixed-h kilogram, so we can write:

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

Finally, at the atomic scale, we can link number of entities, amount, and mass as follows:

N(X)/1 = n(X)/ent = m(X)/[A_r(X) Da] (exactly)

And, at the macroscopic scale:

N(X)/N₀ = n(X)/mol ≈ m(X)/[A_r(X) g]

None of this is (currently) relevant to this article on the mole. But I remain hopeful that, one day, "ent" will be recognised as the appropriate atomic-scale unit for amount (and that the dalton will be redefined exactly in terms of the kilogram) so that some of these concepts can be included. And this might help clear up some of the widespread confusion permeating this subject among beginning chemistry students (and their teachers!), as has been well documented.

Boppennoppy (talk) 15:54, 22 November 2024 (UTC)