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The practical benefit of Avogadro's constant is to manage error bounds. The point is that we can measure the weight of atomic-scale objects very accurately in
by planede 4y ago
The practical benefit of Avogadro's constant is to manage error bounds.
The point is that we can measure the weight of atomic-scale objects very accurately in Daltons (1/12 the mass of a Carbon atom).
The weight of macroscopic objects can be measured very accurately in kilograms.
Avogadro's constant is the conversion factor between Daltons and grams, and currently we can't measure it as accurately.
So if you have an accurate weight measurement in kilograms, then you can lose significant accuracy by expressing the same weight in Daltons. Same for the other way around.
edit:
Huh, I did not know about the 2019 redefinition of Avogadro's constant, so this analysis might not stand:
https://en.wikipedia.org/wiki/Avogadro_constant#SI_redefinition_of_2019 https://en.wikipedia.org/wiki/Avogadro_constant#SI_redefinit...
Or at least there is still a conversion factor between atomic weight unit (Da or u) and grams, it's just no longer the Avogadro's constant?
edit2:
Hmm, interesting:
> In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram.[1][2] Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (kB), and the Avogadro constant (NA), respectively.
Anyway, accuracy was a major concern for retiring the old kg standard. This effectively means that now in SI macroscopic weight measured in kg has one-to-one correspondence to measurement in atomic weight units. But this development was quite recent.
https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_ba...
- kragen 4y agointeresting, i didn't realize that the redefinition meant that avogadro's constant was no longer the ratio between daltons and grams. unsurprisingly this is controversial: https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units#Mass_and_the_Avogadro_constant https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_ba... i think it's good to be specific about what you mean by 'very accurately' though; maybe i misunderstand but i think the uncertainty of measurement is about 10⁻¹⁰ in all three cases if we were designing the metric system today instead of in 01795 we would probably define the unit of mass as something like 10²⁴ atoms of silicon-28 (about 47 grams)
- planede 4y ago> I didn't realize that the redefinition meant that avogadro's constant was no longer the ratio between daltons and grams No, I was wrong about that. It's still the ratio, but now this ratio is defined as an exact number. Basically grams defined in terms of daltons.
- kragen 4y agoi thought they defined grams in terms of an integer number of atoms of silicon-28, but the mass of a silicon-28 atom in daltons is not an exact number; it's an empirically measured number, because of the binding energy mass defect, and because the dalton is referenced to a different atom, the carbon-12 atom but all in all it's very confusing