# How is a mole (the unit) different from the number 6.02214179e23?

That’s no more of a problem than it was when, say, the meter was redefined in terms of the second and the speed of light. Once you get the technology to the point where you can count out atoms more precisely than you can measure the physical artifact in some French city or other, then you measure the old standard using the new one, and use the best-measurement number in the definition of the new standard. To the extent that the numerical values of physical constants would change with the new definition, it’d only be noticeable to folks doing experiments at least as precise as the experiment you’re doing to set the standard. And since you should be using the most precise experiment available to set the standard, it shouldn’t present a problem for anyone at all.

The way it was taught to me, it was a matter of two factors; one, the mole had been in place before we were able to count atoms, and two, “working in terms of the weight of a particle within the SI would be a PITA; let’s find the conversion factor (i.e., the count) between ‘the weight of a particle’ and ‘the weight that’s easily expressed in grams, where the weight of individual isotopes has no decimals’”. Speaking in terms of moles when you’re talking about “large amounts of particles” is no different from giving a person’s weight in kg or a production batch’s in metric tons.

Going back to the OP’s question, “mole” is the unit, the number is one of its many conversion factors. “kg” is a unit, 1000 is one of its many conversion factors; you can not say that “a mole is Avogadro’s number” any more than you can say “a kilogram is one thousand” (or “one kilogram is one thousandth,” or “one kilogram is one million”…).

Yeah, the meter was, at one time, “one ten-millionth of the length of the Earth’s meridian along a quadrant, that is the distance from the Equator to the North Pole.” So it was a unit of measure derived from a natural feature of the world, and as tools became more precise, so did the standard. To define a mole as “as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 0.012 kg of the isotope carbon-12 (12C)” seems perfectly consistent to me.

(Both quotes taken from Wikipedia.)

Unless, of course, you were a chemist. http://en.wikipedia.org/wiki/Molarity

(Was I just whooshed?) To expand on my above post, molarity (moles per liter) is a very convenient unit to work with for solutions of acids, bases, and salts (or any reactive species, for that matter.)

Reactions occur as molecule-molecule interactions. As such, calculations revolve around concentrations of the molecules in solution, not mass concentrations of the substances. For example, if you want to neutralise a given amount of HCl (an acid) with NaOH (a base), you need the same molar concentration of each. However, the masses of each substance is very different. In this case, one would need 36.4609g of HCl to neutralise 39.997g of NaOH, or in moles, 1 mole of each. Molar calculations simplify the situation.

So basically, if you are running through dozens of calculations in a given day, it’s much easier to keep writing small numbers in moles instead of fractions of 6.02x10^23.

This is the key point. I remember even from high school chemistry, when we needed to figure out how much of substance A was needed to react with a certain amount of substance B, the amounts needed to be converted to moles to do the calculation.

The exact number represented by a mole wasn’t important; the concept was.

There’s a huge difference, here. 1000 is the conversion factor from kilograms to grams, and is only something inherent to “kilograms” in so far as you consider “grams” somehow fundamental. But 6.02e23 is the conversion factor from “moles” to “1”, and there’s no disputing that “1” really is fundamental. If I say that I have a mole of particles, that’s exactly the same thing as saying that I have 6.02e23 particles.

Protons and neutrons, isn’t it? Because the example of 1 Mole of Carbon-12 weighing 12 grams is based on its 6 protons and 6 neutrons - or have I misunderstood?

Yup, and technically electrons, but they’re so light comparatively speaking that ignoring them makes no practical difference.
Back in the days when Avagadro’s number was 6.023e23 instead of 6.022e23 (up through the early 80’s) we used moles as an easy intermediate step in figuring out how many grams of O[sub]2[/sub] we needed to mix with X grams of H[sub]2[/sub] to get it to all burn up.

A proton and neutron have the same mass (almost). Maybe it would have been even clearer to say “The mass of a proton or neutron is 1/6E23 grams”.

This is very sensible. In fact, isn’t there some sentiment to the effect that numbers in general are conversion factors to units (in the sense of ones, not in the sense of dimensioned things)? There was a proposal some time back that there should be a unit whose value was the dimensionless number one, named a “uno”, and using it would complete some kind of symmetry in the expression of all quantities.

Referring again to BIPM and “When the mole is used, the elementary entities must be specified…”, the more I look at our discussion, the more convinced I feel that in careful use of the word “mole” it is logically interchangeable with “dozen”, “pair”, “google”, and so forth. That opposing argument I was looking for seems ever more conspicuous by its absence.

Nitpick: “Google” is the search engine. “Googol” is the large number.

There’s a lot of leeway in deciding what counts as a “fundamental unit”. You can say that you need one fundamental unit for each fundamental physical quantity, but that just pushes the problem farther back.

For example, if you take relativity seriously, duration and distance are the same quantity; a second is just 1/c meters. (In fact, in some areas of work, people often use Planck units, where c is set to 1, and a “Planck time” is the exact same unit as a “Planck length”.)

In fact, you can do this with all of the fundamental quantities, reducing everything to just meters (or kg, or Planck lengths, or whatever you want) and a bunch of constants. (http://en.wikipedia.org/wiki/Fundamental_units explains this, although the explanation isn’t as clear as it could be.)

Once you’ve done that, the question is, what good does your one left-over unit do? In what sense is it different from a dimensionless quantity? When you’re, e.g., working at the Planck scale, you normally don’t bother writing time, distance, energy, etc. in terms of Planck lengths; you just leave the units out. But it’s still sometimes useful to write in the units to make sure they all cancel out. In that case, you could just as well use something like “uno” for your unit.

So, there’s nothing special about moles. Like all other SI units (and non-SI units that people use anyway, like radians and steradians), they’re there because they make physics (well, in this case, chemistry) easier to do, not because they’re an essential measure of some quantity that couldn’t otherwise be described.

Of course in most cases, there are also historical factors–at the time the unit was invented, it was a measure of some quantity that couldn’t otherwise be described. The same is true for many units that SI doesn’t treat as fundamental, of course. People still regularly use volts rather than watts/amp or joules/coulomb. SI is just one of many possible choices of “fundamental” units, that turns out to be handy for doing science.

I wouldn’t think of a mole as a number. After all, no one sits down and counts out 6.02e23 molecules. A mole is an particular mass of something, but unlike a kilogram, it’s a mass that varies with the substance being measured. One mole of carbon-12 is 12 g. One mole hydrogen is 1 g. When you think of it that way, and realize that multiples and fractions of those amounts are especially useful in chemistry, it makes a lot more sense.

Alan, it sounds as though you wouldn’t think of a million as a number, either.

I understand why it is useful. What I don’t get is why it was promoted to the rank of SI base unit. I mean, it isn’t even consistent with the other ones. A mole of C12 atoms doesn’t weigh a kilogram, it weighs 1/1000 kg. So there is now a factor of 1000 connecting it to other SI units.

First nitpick: A second is not 1/c meters, it’s 1/299792458 meters. The number 299792458 is not c. Second nitpick: It’s actually fairly rare to use Planck units in physics (that amounts to picking your units such that G, c, and [del]h[/del] are all equal to 1), since so little is known about quantum gravity. But folks working in relativity often use units where G and c are both 1, and particle physicists often use units where c and [del]h[/del] are both 1, and so in both cases measure lengths and times in the same units.

And if you reduce everything to one unit (like relativists measuring lengths, time, and masses all in the same units), then dimensional analysis is still relevant, since you can have different powers of that unit. For instance, a relativist might measure mass in meters, but would then measure angular momentum in square meters.

Agreed; stupid mistake.

Agreed. I should have said “natural units”, and given Planck units as just one example of natural units (not the most common, but a good one for showing how to eliminate as many fundamental quantities as possible, as simply as possible–although I didn’t bother to show most of them anyway).

Agreed; that’s what I meant by “write in the units to make sure they all cancel out”, which was a bad attempt at simplifying the idea.

But the point is that there’s nothing inherently “fundamental” about the 7 fundamental quantities that SI uses; you can get by with 1, and you can pick pretty much any one that you want. Depending on your choice of what’s fundamental, the second is as superfluous as the mole. The only question that matters for SI is whether they’re useful for “doing science”.

It depends. A million what? A million mg is a unit. A million molecules isn’t in SI, but it could be. A million photons isn’t, but it could be. So could a million wavelengths.