# [Physics] What would happen if we changed Avagadro’s Number

physical-chemistry

What would happen if we changed Avagardro's number to be smaller, say, $10^6$?

As part of this change, the definition of one mole would change, but the amount of moles in a substance would remain the same. Think as if we are making the number of atoms in an object larger, but keeping the object's volume the same, this making the number of atoms decrease.

Edit: to clarify, this question is in regard to if we changed the structure of a theoretical universe so that Avagardro's number was experimentally determined to be exactly one million. I'm asking of what changes would be necessary to make this universe function, and how it would be different from our current universe.

Let's look at the definition of Avogadro's number:

Avogadro's number is the number of carbon-12 atoms found in 12g of carbon-12.

So let's say this number changes. This can occur in one of two ways. The first is the exciting but impossible one you are looking at: the mass of carbon-12 atoms changes. Our current physics assumes the conservation of mass. If "the class of things we call carbon-12" decreases in mass-per-atom, that mass has to go somewhere. Where does it go? The answer to that is 100% dependent on how these carbon 12 atoms change mass. If the mass is "converted" to gamma rays, the result will be very different from if a deity turns a knob on the universe (in which case, I would ask the deity this question).

The more interesting and reasonable answer to this is that our definition of a kilogram changes. This is interesting because... well... our definition of a kilogram is a bit embarrassing. As it turns out, we currently define the kilogram with respect to an internationally recognized mass, known as the International Kilogram Prototype (IKP). This is literally a block of platinum-iridium alloy that everyone in the world has agreed is "the definition of what 1kg of mass is." That's it. That's all a kilogram is. End of story.

So that suggests that, the mystical and non-existent effect which changed Avogadro's number would change the mass of the IKP at the same time. If this happened, we would find the two effects cancel each other out, and we'd find that Avogadro's number didn't change at all! Hilarious!

Interestingly enough, there is an effort to change Avogadro's number. There's an effort to set it to be equal to $6.02214X×10^{23}mol^{-1}$ (where X is one digit that has not yet been agreed upon). This would be done by setting the definition of the kilogram to be with respect to a certain number of atoms. This is being done to try to free ourselves from the joy of having our entire unit system built around a single physical block of metal locked in a vault. If the new definition took place, we could create a kilogram reference out of a polished sphere of silicon like this:

These spheres are carefully polished to have a very exacting diameter, and thus a very exacting number of atoms within the sphere. If this change takes place, anyone with sufficient skill could construct a kilogram directly, rather than having to attempt to copy an existing physical kilogram mass! These spheres are currently undergoing long term stability study to make sure they don't gain or lose mass over time at an unacceptable rate. Metals pick up an oxide layer over time, and those extra oxygen atoms can add up when you care about parts per million! If it works, we can replace the IKP, which technically is losing mass slowly because they have to clean it every time it is used, and that cleaning pulls metal off!