How did the early chemists make a connection between gram formula weight with 1 mole and Avogadro's number?

According to one historian Mustafa Sarikaya's article in Foundations of Chemistry DOI 10.1007/s10698-011-9128-7, the mole concept was introduced to chemistry earlier than Avogadro’s number. The mole concept was introduced by the German chemist August Horstmann. How did the early chemists determine that if we weigh an amount of a pure compound in grams (solid/liquid/gas) equal to its gram formula weight, it will contain an Avogadro's number of "particles." The second question is related to the arbitrary definition of atomic mass scale of C-12 as 12 (as an exact number). This was a scaling choice made to make physicists and chemistry agree without changing much of their old tabulated values of atomic weights (c.f. chemical scale and physical scale of atomic masses). Does 12.00000000 g exactly contain Avogadro's number of C-12 atoms or the value of Avogadro's number was also adjusted when C-12 was chosen as a standard by the IUPAC? Thanks.

Edit: The key query here is how the gram formulae of any solid, liquid or gas were connected with Avogadro's number in the early 19th century? What experimental evidence led them to conclude that the gram formula weight of any pure substance has Avogadro's number of particles?

• This is covered pretty well in the Wikipedia history sections on the Avogadro constant and Mole. The equivalent weight concept that was in use in the 19-th century in place of the mole did not even require one to believe in particles. Dec 30 '18 at 3:44
• Thanks, the Wikipedia history pages just state the facts and definitions. The still do not answer the how this connection was made among Avogadro's number, mole and the gram formula weight. See this one link.springer.com/article/10.1007/s10698-011-9128-7 Dec 30 '18 at 5:37
• According to your reference, Loschmidt calculated the number of molecules in a cubic centimeter of a gas under normal conditions as 1.83x10^18 in 1865, and Than first determined the molar volume of gases as 22.33 L in 1889. Horstmann introduced the gram-molecular weight in 1881, so by 1889 the Avogadro number could be calculated by multiplying Loschmidt’s and Than's numbers. Dalton, Avogadro, et al., left the number unspecified, and equivalent weights sufficed for most practical purposes anyway. Are you looking for confirmation (to complement the Wikipedia article, maybe)? Jan 1 '19 at 1:18
• Hopefully, we can improve the Wikipedia page (history section). I am specifically looking for the particular experiments (or thought process) in which was shown that weight in grams corresponding to a gram formula weight of any pure compound (solid, liquid or gas) corresponds to Avogadro's number of particles. Jan 1 '19 at 2:41

(Question: "How did the early chemists make a connection between gram formula weight with 1 mole and Avogadro's number?")

The article cited in the question has unfortunately led to a misconception, because that cited article starts out from a fundamental mistake about Avogadro's work. Avogadro did not discuss anything like what is now (honorifically) called Avogadro's number, he did not deal in absolute numbers or quantities. His important advance was concerned with relative combining proportions and not with absolute measures. Even the title of his original work already makes that quite clear, thus:

"Essai d'une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons; par A. Avogadro"; Journal de Physique 73, 58-78 (1811): (emphasis added) (https://gallica.bnf.fr/ark:/12148/bpt6k9608503q/f64.image).

This title becomes in English:

"Essay on a manner of determining the relative masses of the elementary molecules of bodies, and the proportions in which they enter into these compounds" (again, emphasis added).

This title comes from a very useful English translation, of which the main parts are given here, of Avogadro's original paper, made in about 1890 by the Alembic Club (Edinburgh). Their translation is also provided with a large number of helpful notes which should assist in the avoidance of misunderstanding .

The notes to the Alembic Club translation also mention the honorific origin of the expression 'Avogadro number', which was named a century after the time of Avogadro himself, after breakthrough experiments by Millikan to measure the charge on single electrons, thus enabling determination of scale factors between macroscopic and atomic-scale measures. Previous to that experimental achievement, the idea of this number had remained an indeterminate concept that there was a definite number of particles in a standard gram-atomic weight quantity (or a different definite number for any other adopted macroscopic scale-unit), but no way to measure any of these supposed numbers or even to verify that the concept was justified in reality.

This is well-expressed in the wikipedia article on Avogadro's constant, thus:

"Accurate determinations of the Avogadro constant require the measurement of a single quantity on both the atomic and macroscopic scales using the same unit of measurement. This became possible for the first time when American physicist Robert Millikan measured the charge on an electron in 1910."

In other words, the Avogadro number is hardly a constant, but rather a calibration factor, and it's also important that the above statement in Wikipedia doesn't specify which quantity is measured nor on which macroscopic scale. Clearly, different values for the calibration factor result from different choices of atomic-weight scale and macroscopic mass-scale, although in practice until recently the uncertainties of measurement practically swamped any differences due to variants in the chosen atomic-weight scale.

So, the answer to the question as put is that the early chemists did not make a connection between gram formula weight with 1 mole and Avogadro's number, @conifold's comment is correct, the concepts named in the question were altogether later concepts, and the earlier chemists dealt with relative measures not absolute numbers or quantities.

The Avogadro number, thus named much later 'after Avogadro', as an honorific not as something he actually dealt with himself, is thus not a fundamental constant of nature, it provides a scale factor to relate two chosen standardized scales, one on an atomic level and the other on a macroscopic level but both of them essentially arbitrary. The present-day value of the Avogadro number is effectively the calibration factor between the current relative standard scale of atomic weights, and the current standard scale that includes the gram, i.e. the number of atoms or molecules in the quantity of a pure compound which is its atomic or molecular weight taken to be expressed in grams.

It may be helpful to add mention of the main historical 'ingredients', so to speak, of the modern concept, they should really include all of the elements of the history of relative atomic-weight determinations:

-- Dalton's (chemical) atomic theory;

-- Gay-Lussac's law of combining volumes;

-- Avogadro's law (initially hypothesis) about the equality of molecular numbers in the same volumes of different gaseous compounds and elements under standardized temperature and pressure -- to begin with.

Then these principles had to be augmented, by further experimental facts that led to the concepts of

-- valency and

-- alternative oxidation states for many chemical elements, and thus to the need for a distinction between (gram-)atomic weight and

-- equivalent weight. (One and the same element, with a single (gram-)atomic weight, would have a different equivalent weight for each of any different oxidation-states or valencies with which it enters into its different compounds: its equivalent weights are related by small-whole-number ratios or fractions with its (gram-)atomic weight.)

The modern value(s) of Avogadro's number thus rests on two kinds of arbitrary decision:

(1) to fix the relative scale of atomic weights, based thus far on ratios, by adopting a convention-based number for the weight of one of the elements in the network of ratios: and then this determines the scale weights of the others upon the adopted convention.

(Among the convention-based numbers (scales) that have been historically used are H=1 (Dalton and more general use until near the end of the 19th century); (chemical) O=100 (Berzelius, used for a time in the earlier 19th-century, thanks to @m-farooq for his reminder of this one); and a (chemical) O=16 scale adopted near the end of the nineteenth century. There were slight adjustments made to the atomic weight scale and its basis during the course of the 20th century which have only very slightly altered the numbers, much less than the change from H=1 to O=16, but the value of the Avogadro number depends on these alterations too.) (For a reference-source, see IUPAC's "History of the recommended atomic-weight values from 1882 to 1997", from 'Pure & Applied Chemistry', Vol. 70, No. 1, pp.237-257 (1998), which also discusses the differences between current and older values and the uncertainties of earlier ones).

(2) A second arbitrary element in the definition of the present-day Avogadro number and mole is to assign to each arbitrary unit of the relative atomic weight scale an arbitrary unit of macroscopic weight or mass. For the purposes of chemical science, that unit has been traditionally and arbitrarily the standard gram, the definition of which has experienced slight alterations too. The practical value of such an assignment is to bring the abstracted relative atomic weights back into the concrete world by matching them up with actual measurable weights.

The chemical terminology used to include expressions such as 'gram-atomic weight', 'gram-molecular weight', and 'gram-equivalent weight' or even 'gram-formula weight', mostly superseded now by the expression 'mole' which means the same as 'gram-molecular weight' i.e. molecular weight on the arbitrary standard scale, but taken to be expressed in grams.

Only after these two steps have been definitely taken and standardised can it make sense to speak of a specific number as the Avogadro number. The Avogadro number can thus be seen to depend on two standardized arbitraries: the scale-unit assigned for the relative atomic weight scale, and the standard mass-measure to be associated with that scale-unit.

• Thanks for the details. This discussion renewed my interest in Perrin's (1909) Brownian Motion and Molecular Reality. This 70-80 paged book is available as an English translation. This should have the thought process which led to Avogadro's number. Feb 3 '19 at 4:19

In 1806, John Dalton published a table of the relative weights of elements. Since elements are very light, he decided to publish the weights of "one pack of X elements, with X chosen such as the weight of the pack for Hydrogen is one gram". This is called the atomic mass unit.

Since writing "one pack of X elements, with X chosen such as the weight of the pack for Hydrogen is one" is a bit long, in 1893, Wilhelm Ostwald invented the word "mole" to simplify things.

To make experiments easier, the definition of the mole has been changed to "one pack of X elements, with X chosen such as the weight of the pack for Carbon-12 is twelve grams" around 1960. It turns out that it basically represents the same thing.

However, this definition is only as precise as the measurement of twelve grams of Carbon-12. To overcome this difficulty, the mole has been defined in 2019 as exactly $$6.02214076×10^{23}$$, and not related to an actual element in any way.

TL,DR:

A man named Dalton decided that $$N_a$$ (Avogadro constant) elements of Hydrogen would weight one gram.

It stuck.

• I feel several historical concepts are mixed up here. What Dalton calculated were relative atomic weights (hydrogen taken as unity). However, it switched back and forth between O and H, and by the early 19th century, they found out that the atomic weight of H would be 1.006 g with O as 16 (exact). The atomic mass unit was instead an invention of the physicists. Still, the question that remains is how the gram formulae (or Ostwald's mol) were connected with Avogadro. Dec 31 '18 at 19:33
• Einstein's analysis of Brownian motion gave a different way and confirmed Loschmidt's estimate. Jan 1 '19 at 19:32
• I agree with most of what @m-farooq writes here, Dalton did no such thing as this answer states in the "TL,DR" -- see his book at (archive.org/details/newsystemofchemi01daltuoft). But it was only at the end of the 19th-c. that the switch was made from H=1 to O=16 implying H= about 1.007 (see the IUPAC reference in the answer I just posted). Feb 3 '19 at 2:01