Module 0503

The Avogadro constant: Why is it that number?

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What a strange (and enormous) number is the Avogadro constant!

6.02214076 × 10^23 (or 602 214 076 000 000 000 000 000)

A number decided by scientists, and not a universal constant (like the speed of light)

Why have scientists decided on this number? The reasons are entirely historical.

Well, since you are interested in learning chemistry for understanding .....

Prof Bob presents the historical reasons leading to the decision to define the Avogadro constant as a particular, fixed number.

KEY IDEAS - The Avogadro constant: Why this number?

I used to think that the number 602214076000000000000000 is infinite. Until somebody told me to add 1 to it ......

In 2019 ....

As recently as 2019, the Avogadro constant was defined as:

"The number of atoms in a sample of the carbon isotope C-12 whose mass is exactly 12 g".

And so, it is the number of (defined) particles in a 1 mol sample of any substance (See Module 0501 Chemical amount and its unit of measurement, mole).

This follows an earlier decision to use 12 g (exactly) of the isotope C-12 as the standard of molar masses. The molar mass of every substance was determined in comparison to this standard.

There are historical reasons for this arbitrary decision (See Prof Bob's video presentation, above).

Arbitrary (judgemental) decision made by scientists

The value of the Avogadro constant is not an immutable universal constant like the speed of light, or Planck’s constant.

Its value depends on certain human decisions that have been made in the past. For example, it may have been decided, for whatever reason, that the Avogadro constant is the number of atoms in exactly 12 kg of the C-12 isotope, or in 17.00 tonnes of the O-18 isotope, or ….. any other chosen standard.

Any of these decision would have given rise to a self-consistent set of data and relationships that give us the same answers as we deduce using the current definition.

Or IUPAC (the International Union of Pure and Applied Chemistry) could decide to define the Avogadro constant as a particular, fixed number. It could choose (randomly) the number 1 456 091, for example, but if it did, 1 mol of a substance would be too small to weigh out. Not very convenient! And there is no logical reason to choose such a number.

So how many atoms are in exactly 12 g of C-12?

In 2019, the best estimate of the number of atoms in 12 g of carbon isotope C-12 was 6.02214076 × 10^23.

Like all measurements or estimates, this number has a level of uncertainty – although in this case, very small since the uncertainty is in the tenth significant figure. But over time, technology is allowing measurements of higher and higher precision.

The accepted value of the Avogadro constant has been continually changing over the years as more, and more precise, measurements have become available.

Whenever the accepted value is changed, there are repercussions for other chemical values.

That's a bit inconvenient, so .........

To today's definition: a fixed number

IUPAC recently re-defined the Avogadro constant as a fixed number, regardless of any further changes of the estimate.

The number decided upon (6.02214076 × 10^23) is, for very logical reasons, the best estimate of the number of carbon atoms in exactly 12 g of C-12 isotope.

This re-defined one mole of any substance as that amount of it that contains 6.02214076 × 10^23 defined particles. No more changes!

This decision to decide on a forever-fixed number removes the level of uncertainty of the estimate, or revisions of the value as technology improves the ability to measure, as well as repercussions to the values of other quantities in chemistry and physics.

A review of decisions related to the Avogadro constant

The reasons are generally due to increasingly precise measurement techniques:

First, hydrogen atoms were assigned a value of exactly 1 on the scale of relative molar masses. Since hydrogen atoms are the lightest of all elements, the values for atoms of every other element were greater than one. Makes sense? By the way, on this scale, the relative molar mass of oxygen atoms was 15.879.
But, from place to place the relative proportions of the hydrogen isotopes C-1, C-2 (deuterium), and C-3 (tritium) are a little different. We couldn’t have a standard that is not fixed!
Chemist decided to use as the standard the average mass of naturally occurring oxygen (a mixture of isotopes O-16, O-17, and O-18) with a value of exactly 16. Fortunately (or by decision), this left hydrogen with a molar mass on the new scale greater than 1.
It had not been appreciated how different are the relative amounts of the O isotopes in compounds from different natural sources (air, plants, minerals). So once again, it was realised that the standard was not exactly fixed.
The masses of isotopes of elements are immutable, so a new standard was assigned: the carbon -12 isotope was defined to have a mass on the relative scale of exactly 12. And this is how it stayed until 1919.
As measurement techniques became even more precise, different research laboratories reported different estimates of the number of C-12 atoms in 12 g of the pure isotope (that is, the Avogadro constant). We are talking about difference in the ninth significant figure of the value measured – nonetheless, different. IUPAC was forced to continually revise the best estimate – which meant corresponding (small) small changes in other dependent parameters.
How to avoid continual revision of the value of the Avogadro constant? Simple …. define it to be forever the value that is the currently accepted value: 6.022140857 × 10^23. No more uncertainty! But there are repercussions, including conceptualization by those learning chemistry – even if with Prof Bob.

Over all of these changes, the relative values for the masses of each element have remained “in the same ball park”: On today’s scale, hydrogen has a relative mass of 1.008, and oxygen 15.999.

Other resources

To see the definition of the Avogadro constant in the IUPAC Gold Book, click here and to read broader discussions in Wikipedia, click here.

You will find links related to chemical amount and mole in these sources in module 0501 Chemical amount and its unit of measurement, mole.

Do you sometimes feel that there is a never-ending interdependent relationship among the concepts of chemical amount, mole, the Avogadro number and molar mass? And that none of them has meaning without the others?

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