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I know that the relation between atomic mass unit and Avogadro's number is a reciprocal relation.

My question is if the definition of atomic mass unit is changed, suppose instead of 1/12th mass of carbon-12 isotope, we consider 1/24th mass of carbon-12 isotope, will the Avogadro's number change?

And if Avogadro's number changes will that change the mass of a mole of atoms of any element?

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  • $\begingroup$ No , it will not. Avogadro number is related to mole as 12 is to dozen. $\endgroup$
    – Vedant Chhapariya
    May 20, 2021 at 14:56
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    $\begingroup$ The Avogadro constant is defined exactly as $N_\mathrm{A} = \pu{6.02214076E23 mol−1}$ $\endgroup$
    – Poutnik
    May 20, 2021 at 14:57
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    $\begingroup$ See the wikipedia article Avogadro constant which gives an interesting oversight on the constant. The gist is that IUAPC has defined some fundamental constants, including the Avogadro number, as having exact values which are not expected to change ever again. $\endgroup$
    – MaxW
    May 21, 2021 at 20:07

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Simple and actual answer:

The current definition of Avogadro's number doesn't depend on the unit of mass. They are completely independent quantities. The Avogadro's number is currently simply defined as $\pu{6.02214076e23}$. It's just a number which is important enough to get a special name.

The answer you are probably looking for:

Historically the Avogadro's number was defined in such a manner that it did depend on the unit of mass.

At that time the Avogadro's number was defined as the number of atoms present in $\pu{12 g}$ of $\ce{^{12}C}$ isotope of carbon.

Now as you can see even if we defined an atomic mass unit as $1/24$ of the mass of an $\ce{^{12}C}$ atom instead of $1/12$, it won't make any difference to the Avogadro's number as it was defined on the basis of grams of carbon and not atomic mass units of carbon.

Now coming to your second question of whether this would have changed the mass of a mole of a substance. Yes it would have changed that, all the molar masses would have been double of as known currently.

Note:

All this discussion is just about how someone wrote a definition and the loopholes someone can detect from it using language.

For example if we really would have defined an atomic mass unit in this different way, we would have also defined Avogadro's number as number of atoms in $\pu{24 g}$ of $\ce{^{12}C}$. Even $\ce{^{12}C}$ would have been written as $\ce{^{24}C}$!

The takeaway is that the scientific idea and origin of all these units was(and is) always there but it's just the nuance of defining it in such a way that it doesn't create such problems was the problem. That's the only reason all the standard units were restandardized recently. It's a sad reality that schools are still teaching the old definitions even after we have said them a good bye.

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  • $\begingroup$ My understanding is that if we consider Avogadro number to be a constant then mass of 1 mole shouldn't be affected by changing the definition of 1 amu as it would affect only the relative mass of elements. The absolute mass would still remain the same right? So why should the mass of 1 mole change on changing definition of 1 amu? $\endgroup$
    – dumb
    May 20, 2021 at 16:25
  • $\begingroup$ @dumb We initially defined moles on the basis of gram-equivalents. $\pu{12 g}$ of carbon-12 was selected because we assumed that mass of $\ce{^{12}C}$ to be $\pu{12 amu}$. If it was $\pu{24 amu}$ we would call $\pu{24 g}$ of carbon-12(24) a mole. Nothing is special even with a gram. If they decided at that time to use imperial units than the mole would be defined in that way(eg. Calling 24lb of carbon-12(24) a mole) . A mole of substance really isn't something special, other than the fact we made it the standard one. $\endgroup$
    – Nisarg Bhavsar
    May 20, 2021 at 16:37

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