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The terms "gram-atom / gram-molecule" are obsolete nowadays in chemistry and got replaced by the concept of "mole/ Avogadro Number". But recently, I encountered a question that can have two different answers depending on how "gram-atom" was defined early in Chemistry.

Q: A new atomic mass scale, called UM, was introduced as 1/24th part of the mass of a single C-12 atom. Find the gram-atomic weight of Hydrogen (H) as per the new scale ?

The above question can have two answers if I use two available definitions of "gram-atom" from the web :

gram-atomic weight: the amount of an atomic substance whose weight, in grams, is numerically equal to the atomic weight of that substance.

According to this definition, as the new scale will show the atomic weight of Hydrogen as 2 UMs, its gram-atomic weight should be 2 grams. And thus there would be $ 2N_A$ atoms of Hydrogen in one gram-atom of Hydrogen (as per new scale).

But, if I just use the definition of 1 gram-atom as nothing but 1 mole ($1 N_A$) of atoms i.e. Gram-atom = Mole.

Then the answer would be 1 gram-atom of Hydrogen = 1 mole of Hydrogen = $1N_A$ X $2UMs$ (No of UMs in 1 Hydrogen atom) = 1 gram

So, which approach is correct (historically) ?

Was the definition of "gram-atom" pre-required the proper definition (w.r.t. kg/gm) of **amu ** as in the second approach?

Or ppl just took any relative microscopic unit like amu (in real life) or UM (in our hypothetical question) and just replaced the relative atomic weight w.r.t. that unit with gram and called it gram-atomic weight?

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The first one is the correct approach. As you may note now, most the "weighing" at atomic scale is defined circularly. Atomic weights have more than two hundred years old history. We need an arbitrary reference atom. Historically H was numerically set exact 1, and every atomic weight was measured with respect to that. Then came oxygen which was set to 16 exactly. Finally, in the 1960s, carbon-12 was set exact 12. Let us look at the definition.

gram-atom n. the quantity of an element having a mass in grams numerically equal to its atomic weight.

As per your exercise, if 1 amu were 1/24 the mass of carbon-12 (12 exact), then all atomic weights double.

Coming to the mole, The symbol mol is due to Ostwald who was a very influential and respected physical chemist more than a century ago. In German, "mole" is "Mol". It is a shortform of Molekül.

I believe the Internet Archive has an English translation of his historically famous book of 19th century. This is where I recall reading this. The original reference is W. Ostwald Hand- und Hilfsbuch zur Ausführung physikochemischer Messungen. This book is available on Google Books (pg 278). A footnote appears there:

"Um nicht stets den schleppenden Ausdruck Gramm -Molekulargewicht brauchen zu müssen, werde ich diese Größe in der Folge kurzweg Mol nennen, und erlaube mir, diesen Vorschlag zur allgemeinen Annahme zu empfehlen. Man schreibt ohnedies diese Größe häufig Mol., und braucht daher nur den Punkt fortzulassen."

"In order not to always have to use the sluggish expression gram-molecular weight, I will simply call this quantity Mol in the following, and allow me to recommend this proposal for general acceptance. Anyway, this quantity is often written as Mol., so you only have to omit the point."

Translated via (www.deepl.com) with some manual changes.

So the number $N_A$ is experimentally determined with respect to the accepted definition of atomic weights.

Your second definition is then dimensionally inconsistent. 1 gram-atom is not a number, it is a weight in grams. It is not equal to $N_A$. 1 gram-atom, as per accepted definition, will consist of $N_A$ atoms.

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