# How it was found that 12 g of carbon-12 has Avogadro's number of atoms? [duplicate]

I just want to know the history of finding Avogadro's number of atoms in 12 gm of C-12 and why C-12 only? Like I was asking how scientists came to conclusion that there is exactly 6.023*10^23 atoms in 12g of C2 . what was the methodology scientist opt to find this at that time and what made them believe this number can be used as a unit for atomic substances ?

• Tiny tweezers and a lot of patience. Nov 24, 2022 at 20:13

This Chemistry.SE answer captures most of the argument, but I'll paraphrase here. (Oh, who am I kidding. The history of units and conventions is never short. "Paraphrase" should be taken loosely!)

The idea of working with some exchange ratio between number of atoms and our SI units of mass (i.e. grams) predates our use of C-12. The first, and potentially the most natural approach was that of John Dalton. He built his atomic table with a mass number for each element relative to that of Hydrogen -- thus Hydrogen always had the mass of 1. (In 1993, it was suggested that we give the unit his name in his honor, so the mass of the average hydrogen atom is now known as 1 Dalton).

However, we ran into a problem. It turns out that Hydrogen has multiple isotopes. All of them have one proton, but they vary in the number of neutrons, so some have much more mass than others! Adjustments would need to be made to deal with this discovery.

Jean Perrin suggested a solution: use oxygen. He suggested that we define one oxygen atom to weigh 16, and to solve the isotope issue, he pegged it to be an oxygen-16 atom, specifically. Oxygen has a nice advantage of bonding simply with many compounds, making measurements via reactions easy. So this encouraged a large camp to campaign to shift the atomic scale from being built around $$1\;H = 1$$ to $$1\;^{16}O = 16$$.

However, these scales differ by more than the simple tables might expect. Due to effects that would be understood later (due to binding energy and relativity) shifting from $$1\;H = 1$$ to $$1\;^{16}O = 16$$ changed measurements by a factor of 275ppm, which was quite a lot by the standards of those days. Not everybody was happy with the suggestion.

In 1957, Alfred Neir suggested an alternative. In mass spectroscopy, Carbon-12 had found a niche as a second mass standard (the primary being Oxygen-16). As it turns out, if you shift the scale from $$1\;H = 1$$ to $$1\;^{12}C = 12$$, it only involves changing the old numbers by 43ppm. Decreasing the amount that the new scale would shift the old scale was a considerable advantage, so in 1971, there was enough agreement on the $$1\;^{12}C = 12$$ that BIPM was able to make it the standard.

Of course, we don't use this scale anymore. In 2019, it was decided to define the kilogram differently. Up to this point, it was defined based on a physical block of platinum iridium known as the IPK, sitting in a vault in France under several vacuum bells. It was noted that its siblings (several other clones of the IPK which were used, avoiding damage and wear to the IPK itself) were differing in mass from the IPK. This was unsettling for physicists. So in 2019, they defined the kilogram based on Plank's constant, and defined Avagadro's constant to be exactly $$6.02214076\cdot10^{23}\;\text{mol}^{-1}$$, which was the best measurement at that date. The relative difference between this value and the molar mass factor of $$1\;^{12}C = 12$$ was $$4.5\cdot10^{-10}$$, which was deemed insignificant enough compared to the value of finally fixing $$N_0$$.

So that's the story. We started with a hydrogen based scale, before discovering that isotopic ratios plagued its accuracy. For a while we switched to Oxygen-16, which had some great properties, but was different enough from the original Hydrogen scale to cause problems. Carbon-12 was a stable alternative that was in use for mass spectroscopy already, and had numbers very similar to that of the Hydrogen scale, so it won out. And now, we don't even reference Carbon in the definition of $$N_0$$ at all. It is simply a number.

• To your credit, "paraphrasing" is not a promise of "summarizing" :D Nov 24, 2022 at 6:28

In 1971, the International Bureau of Weights and Measures (BIPM) decided to regard the amount of substance as an independent dimension of measurement, with the mole as its base unit in the International System of Units (SI). Specifically, the mole was defined as an amount of a substance that contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12.

• That's how it was defined prior to the massive 2019 redefinition. The new definition means that a mole of carbon-12 might no longer have a mass of exactly 12 grams. Nonetheless, plus one. Nov 23, 2022 at 16:00
• @DavidHammen Yes, indeed, this is the information that one readily finds by following the link in this answer. Nov 23, 2022 at 16:03

Loosely speaking, you can think of the mole as number of nucleons (protons or neutrons) you need to collect together to have 1 gram of mass. That's why you get statements like "12 grams of carbon 12 is 1 mole of carbon 12 atoms" -- a single carbon-12 atom has 12 nucleons, so gathering one mole of carbon 12 atoms means gathering 12 moles of nucleons, which then by construction are 12 grams.

However, real life is messy in several ways. First, the masses of nucleons don't quite add up in a naive way due to binding energy (and electrons do have some mass even if it is tiny), so the above math will break down if you include enough decimal points. Second, for many materials it's difficult or impossible to get a large enough sample to weigh that contains only only one kind of isotope. There may be other considerations that turn up as well; I am not a chemist. So, to give a rigorous and reproducible definition, we pick a reference material that is relatively easy to get pure samples of and weigh. That kind of though process leads to the definition in Roger Vadim's answer.

As it turns out, most atoms have masses that are approximately convenient integer multiples of 1/12th the mass of a C-12 atom.

So, if we use "1/12th the mass of a C-12 atom" to define a unit of mass (let's call it $$1amu$$), then the masses of other atoms are convenient integers like $$3amu$$, $$10amu$$, $$50amu$$ etc.

But in chemistry labs, we don't deal with a few atoms of some element. We deal with a few grams of them. One of our interests is to figure out how many atoms of an element do $$x$$ grams of the element contain. The number of atoms will be:

$$\frac{x \text { grams}}{\text{mass of one atom}}$$

$$=\frac{x \text { grams}}{k \text{ amu}}$$

$$=\frac{x}{k} \frac{1 \text { gram}}{1 \text { amu}}$$

$$=\frac{x}{k} N_A$$

$$N_A$$ is defined as the ratio $$\frac{1 \text { gram}}{1 \text { amu}}$$. To measure it, we measured the mass of one C-12 atom in grams, i.e. $$\text {1 amu}$$ in grams, and we calculated the ratio $$\frac{1 \text { gram}}{\text {mass of one C-12 atom in grams}}$$. This came out to be $$6.022 \times 10^{23}$$.

Note that when $$x=k$$, then number of atoms $$=N_A$$. For example, if atomic mass of an element is $$5 \text{ amu}$$, then $$\text{5 grams}$$ of that element contain $$N_A$$ atoms.

• Approximately would be a useful addition to the first sentence "convenient integer multiples". For two reasons: binding mass in other nuclei and the fact that periodic tables give the atomic mass as the average over isotopic composition (though this only applies to bulk elements not individual atoms). Nov 23, 2022 at 16:55
• @matt_black I was keeping it simple, but yeah Nov 23, 2022 at 17:12