5 ms·

Instead of having Avogadro's number at all, chemists could just count using numbers like we do for everything else. We already have the prefixes to make 10^+/-2

Instead of having Avogadro's number at all, chemists could just count using numbers like we do for everything else. We already have the prefixes to make 10^+/-24 easy. No need to re-define it, just stop using it. It's nothing more than a conversion factor between two parallel unit systems that somehow both coexist within SI.

Ekaros 2y ago
Avogadro's number is for making calculations including weight simpler. If I have x grams of carbon how many grams of oxygen I need to burn it all. And then how many grams of carbon dioxide I end up with. Value is somewhat arbitrary. And could also be tied to some other isotope. It is really about the ratios between all the elements including their isotopes. Picking carbon and there of isotope C-12, and saying this is exactly 12 grams is not unreasonable selection.
- saalweachter 2y ago
  And now that we actually know how big particles are, we could work the other direction [if restandarizing an industrialized civilization wasn't impossible] -- pick an arbitrary number of particles that is a nice number for some reason or another (eg, 4!!), take the simplest thing that has mass (monatomic hydrogen), and declare your unit of mass to be equal to 4!! hydrogen atoms. Sure, it's not easy for a primitive scientist to take a box of an exact number of hydrogen atoms and weigh them, but any advanced civilization should know exactly what a hydrogen atom masses.
  - EnigmaFlare 2y ago
    That system would last only as long as nobody wanted any more precision than you could get from measuring hydrogen atoms. Then they're do what they've always done and redefine it to something uglier but which can be measured more accurately. > any advanced civilization should know exactly what a hydrogen atom masses. Nobody can know that exactly. Just giving it a name isn't the same as knowing it. We already have a name for it - "the mass of a hydrogen atom".
    - saalweachter 2y ago
      There's a validity to your criticism that I'm not enough of a domain expert to really dismiss, but also -- We're already like, really good at measuring the mass of atoms. We know the hydrogen atom's mass to ten or eleven significant figures, something like one part in ten billion. It's not the most precise measurement we have, those are at around one part in a trillion or so, but it's still pretty darn good.
      - EnigmaFlare 2y ago
        Are you suggesting we're already good enough at measuring the mass of atoms and no further precision will ever be needed? Otherwise, your statement would have been equally valid 100 years ago by just taking some significant figures off. By the way, 4!! ~= N_A was a funny surprise! If you were starting from scratch though, you could make it even simpler and define the unit of mass to be 1e27 times the mass of a hydrogen atom which is 1.7 kg. But again, you might find some other more accurate way and have to redefine it to include an ugly conversion factor just to get practical work done in some high-precision future world.
        saalweachter 2y ago
        Factorials are a base-independent way to make large numbers. You could go 10^27 or 10^25 or some other random power of ten, but why powers of ten over powers of two? And then once you choose a base, why 10^27 versus 10^25 versus 10^24? Which makes one the more natural choice than another? On the other hand, once you choose factorials over exponents, and furthermore, double-factorials, there's really only one option. 3!! is is 720, which is not really much of anything, in the grand scheme of things. 5!! is something like 7e198, which is probably more than there is of anything in the universe, or at least, in the known universe. 4!! is the only double-factorial which is a useful number of particles. The more annoying thing is that mass and electric charge are so far apart. If you were starting from scratch, it'd be really cool to have 1 number-unit of something be the mass unit, and 1 number-unit of electrons be the charge-unit. But 4!! electrons is like 100,000 coulombs, which is just a lot. 2^64 electrons is more like 3 coulombs, which is more workable, but 2^64 daltons is only around 30 migrograms, which is a helluva mass unit if roughly human-sized is the scale of most intelligent life forms. (Incidentally, powers of two have an even closer coincidence to Avogadro's number -- 2^79 is within half a percent of N_A. But 79 is such an ugly number -- there's nothing particularly elegant about 10^1001111.) Re: measurement, we're presumably going to get better at measuring the mass of a hydrogen atom over time. We might even eventually be able to calculate it from first principles (which is really just saying we might be able to establish an exact relationship between the mass of a proton, electron and various physical constants; according to a random search, a 2008 paper was able to calculate the mass of a nucleon within about 3% of experimental results, which isn't great accuracy wise but is still pretty interesting). (Aside #2: You could also pick a larger particle to try to bridge the gap between mass and charge. The Higgs Boson, for instance, masses around 130x the hydrogen atom.)
- EnigmaFlare 2y ago
  Let me try to do it without Avogadro's number approximately: m_oxygen / m_carbon = (n_oxygen * A_oxygen) / (n_carbon * A_carbon) m_oxygen = x * (2 * 16) / (1 * 12) = 2.7 x and more accurately: m_oxygen / m_carbon = n_oxygen * m_oxygen / n_carbon * m_carbon m_oxygen = x * (2 * 26.567 yg) / (1 * 19.945 yg) = 2.664 x Can you do it more easily using Avogadro's number?
  - Ekaros 2y ago
    Where did you get the A_oxygen and A_carbon in first part? Take the same calculation, use 12,01 for carbon and 16,00 for oxygen. Values in one reference book, get 2,66444629475 or the 2,644. Avogadro's number is just number of atoms in the mole. Making atomic masses sensible numbers. Carbon dioxide is actually relatively bad example as both values are close to integers. Chloride with atomic mass 35,45 starts to be more reasonable example where you have pretty simple number. As shown dealing with very small numbers like counting together masses of neutrons, protons and electrons and then removing binding energy gets very tiny numbers. Which make calculations more error prone or even complex to do by hand. Using atomic masses which include Avogadro's number makes it much simpler process.
    - EnigmaFlare 2y ago
      Those are the mass numbers from the periodic table which are exact integers and chemists probably know in their heads. If you have to look up a 4-digit number, it's not easier to look up or use 12.01 u instead of 19.95 yg, especially with higher atomic masses where they're less integer-like, as you say. But using u involves more conceptual complexity because you're mixing two different mass units (u and g) in the same calculation. That's the part that's hard to do in your head. Chemistry students often struggle with this whole concept, which comes with a whole parallel collection of formulas and quantities to work with the alternative mass unit. They more easily understand SI prefixes which is just reusing an existing well-known concept. You don't need to struggle with doin math on very tiny numbers any more than electrical engineers have to struggle with picofarads and nanoseconds.
      - 2y ago

Ekaros 2y ago

Avogadro's number is for making calculations including weight simpler. If I have x grams of carbon how many grams of oxygen I need to burn it all. And then how many grams of carbon dioxide I end up with. Value is somewhat arbitrary. And could also be tied to some other isotope. It is really about the ratios between all the elements including their isotopes. Picking carbon and there of isotope C-12, and saying this is exactly 12 grams is not unreasonable selection.

saalweachter 2y ago
And now that we actually know how big particles are, we could work the other direction [if restandarizing an industrialized civilization wasn't impossible] -- pick an arbitrary number of particles that is a nice number for some reason or another (eg, 4!!), take the simplest thing that has mass (monatomic hydrogen), and declare your unit of mass to be equal to 4!! hydrogen atoms. Sure, it's not easy for a primitive scientist to take a box of an exact number of hydrogen atoms and weigh them, but any advanced civilization should know exactly what a hydrogen atom masses.
- EnigmaFlare 2y ago
  That system would last only as long as nobody wanted any more precision than you could get from measuring hydrogen atoms. Then they're do what they've always done and redefine it to something uglier but which can be measured more accurately. > any advanced civilization should know exactly what a hydrogen atom masses. Nobody can know that exactly. Just giving it a name isn't the same as knowing it. We already have a name for it - "the mass of a hydrogen atom".
  - saalweachter 2y ago
    There's a validity to your criticism that I'm not enough of a domain expert to really dismiss, but also -- We're already like, really good at measuring the mass of atoms. We know the hydrogen atom's mass to ten or eleven significant figures, something like one part in ten billion. It's not the most precise measurement we have, those are at around one part in a trillion or so, but it's still pretty darn good.
    - EnigmaFlare 2y ago
      Are you suggesting we're already good enough at measuring the mass of atoms and no further precision will ever be needed? Otherwise, your statement would have been equally valid 100 years ago by just taking some significant figures off. By the way, 4!! ~= N_A was a funny surprise! If you were starting from scratch though, you could make it even simpler and define the unit of mass to be 1e27 times the mass of a hydrogen atom which is 1.7 kg. But again, you might find some other more accurate way and have to redefine it to include an ugly conversion factor just to get practical work done in some high-precision future world.
      - saalweachter 2y ago
        Factorials are a base-independent way to make large numbers. You could go 10^27 or 10^25 or some other random power of ten, but why powers of ten over powers of two? And then once you choose a base, why 10^27 versus 10^25 versus 10^24? Which makes one the more natural choice than another? On the other hand, once you choose factorials over exponents, and furthermore, double-factorials, there's really only one option. 3!! is is 720, which is not really much of anything, in the grand scheme of things. 5!! is something like 7e198, which is probably more than there is of anything in the universe, or at least, in the known universe. 4!! is the only double-factorial which is a useful number of particles. The more annoying thing is that mass and electric charge are so far apart. If you were starting from scratch, it'd be really cool to have 1 number-unit of something be the mass unit, and 1 number-unit of electrons be the charge-unit. But 4!! electrons is like 100,000 coulombs, which is just a lot. 2^64 electrons is more like 3 coulombs, which is more workable, but 2^64 daltons is only around 30 migrograms, which is a helluva mass unit if roughly human-sized is the scale of most intelligent life forms. (Incidentally, powers of two have an even closer coincidence to Avogadro's number -- 2^79 is within half a percent of N_A. But 79 is such an ugly number -- there's nothing particularly elegant about 10^1001111.) Re: measurement, we're presumably going to get better at measuring the mass of a hydrogen atom over time. We might even eventually be able to calculate it from first principles (which is really just saying we might be able to establish an exact relationship between the mass of a proton, electron and various physical constants; according to a random search, a 2008 paper was able to calculate the mass of a nucleon within about 3% of experimental results, which isn't great accuracy wise but is still pretty interesting). (Aside #2: You could also pick a larger particle to try to bridge the gap between mass and charge. The Higgs Boson, for instance, masses around 130x the hydrogen atom.)
EnigmaFlare 2y ago
Let me try to do it without Avogadro's number approximately: m_oxygen / m_carbon = (n_oxygen * A_oxygen) / (n_carbon * A_carbon) m_oxygen = x * (2 * 16) / (1 * 12) = 2.7 x and more accurately: m_oxygen / m_carbon = n_oxygen * m_oxygen / n_carbon * m_carbon m_oxygen = x * (2 * 26.567 yg) / (1 * 19.945 yg) = 2.664 x Can you do it more easily using Avogadro's number?
- Ekaros 2y ago
  Where did you get the A_oxygen and A_carbon in first part? Take the same calculation, use 12,01 for carbon and 16,00 for oxygen. Values in one reference book, get 2,66444629475 or the 2,644. Avogadro's number is just number of atoms in the mole. Making atomic masses sensible numbers. Carbon dioxide is actually relatively bad example as both values are close to integers. Chloride with atomic mass 35,45 starts to be more reasonable example where you have pretty simple number. As shown dealing with very small numbers like counting together masses of neutrons, protons and electrons and then removing binding energy gets very tiny numbers. Which make calculations more error prone or even complex to do by hand. Using atomic masses which include Avogadro's number makes it much simpler process.
  - EnigmaFlare 2y ago
    Those are the mass numbers from the periodic table which are exact integers and chemists probably know in their heads. If you have to look up a 4-digit number, it's not easier to look up or use 12.01 u instead of 19.95 yg, especially with higher atomic masses where they're less integer-like, as you say. But using u involves more conceptual complexity because you're mixing two different mass units (u and g) in the same calculation. That's the part that's hard to do in your head. Chemistry students often struggle with this whole concept, which comes with a whole parallel collection of formulas and quantities to work with the alternative mass unit. They more easily understand SI prefixes which is just reusing an existing well-known concept. You don't need to struggle with doin math on very tiny numbers any more than electrical engineers have to struggle with picofarads and nanoseconds.
    - 2y ago