a measured response

March 2, 2007 1:17 AM

Redefining Avogadro's Number.A mole is the number of molecules in a gram of water: ~6.022 x 10²³. Unfortunately "a gram" is defined by a chunk of metal in a vault in France, the last of the seven SI units still defined by a physical artifact. Since the reference mass (known as "Le Gran K") is actually changing over time (due to cleaning, handling, etc), the definition of a gram is currently temporally unstable. Now a new proposal has been put forward to explicitly define the number to be a known integer: 602,214,141,070,409,084,099,072, which would fundamentally change the way we define a gram. Le Gran K could become a historical curiosity like the original platinum meter stick.
posted by dkg (39 comments total)

Elegant. I like it, not that my A$0.02 makes any difference.
posted by ozjohn at 1:32 AM on March 2, 2007

Second link is bad.

Those silly scientists. Everyone knows there are 28,2 grams in an a ounce of weed, so 1 gram is 1/28,2 of a OZ (on Earth, of course, gram being a unit of mass and ounce is a unit of weight.)

In space, you get a much bigger counts.
posted by three blind mice at 1:39 AM on March 2, 2007 [2 favorites has favorites]

A marijuana joke in the first 2 comments.

MeFi is in stellar mode today.
posted by dreamsign at 1:44 AM on March 2, 2007

i bought three ounces of weed on the moon, and by the time i returned, it had magically grown to over a pound! i've finally found a legitimate commercial application for space travel, hooray!
posted by bruce at 2:05 AM on March 2, 2007

My understanding (vaguely recalled and possibly wrong understanding) was that we've been sticking with the lump-of-metal for the kg definition for now as the gradual changes in that mass are smaller than our measurement errors in N_A anyway, so it's still a better definition to use than defining N_A and working backwards. I don't see how things have changed on this front.

Although defining N_A as a perfect cube is admittedly cunning.
posted by edd at 2:25 AM on March 2, 2007

Why can't they say something like "a gram is the mass of x atoms of element y"?
posted by rongorongo at 2:38 AM on March 2, 2007

isn't it 6.023 X 1023?
posted by milkwood at 2:44 AM on March 2, 2007

There's a joke involving a chemist, a mole and 1Kg of avocados in here somewhere...
posted by algreer at 2:46 AM on March 2, 2007

There's no physical significance to units anyway; they're designed to make things easy and intuitive for the humans that have to do the calculations. So let's ditch kilograms altogether (having a prefix in the name of a base unit is almost as inelegant as defining it by an artifact), and create a new unit of mass, the whomp, defined as the mass of exactly 10^24 carbon-12 atoms.

Hmm, or maybe not.
posted by hoverboards don't work on water at 3:09 AM on March 2, 2007 [1 favorite has favorites]

yeah cos that new number will fit on my calculator screen
posted by cardamine at 3:21 AM on March 2, 2007

rongorongo: the problem is that you can't count out x atoms of element y very easily. If you tried to do it repeatedly your final kg would differ by a substantial amount on each attempt.

Unless someone's come up with a good way of counting the atoms in something accurately you'll be scuppered (and you'll need to consider the isotopic make-up of element y too, so that you know how contaminated your, say, carbon-12 is with carbon-13, and how heavy carbon-13 is - which won't be exactly 1/12 more - but that's probably not too hard to do well with a mass spectrometer or something).

It's a much harder problem than measuring wavelengths of light for defining metres and seconds and so on, and it's the measurement issue which is the core of the problem. It doesn't really matter what we choose for a kg as long as we can consistently and accurately measure it. Having one lump of metal in Paris is actually not an awful way of doing this, even though it's an inelegant way of defining it.
posted by edd at 3:59 AM on March 2, 2007

I definitely understand the importance of having standards for constants, but this one, frankly, has always blown me away:

Under the International System of Units, the second is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K (absolute zero). The ground state is defined at zero magnetic field. The second thus defined is equivalent to the ephemeris second.

I always thought it was incredibly complex and convoluded way to establish an immutable standard for a basic measure of time. After all, didn't Einstein say it was all relative anway?
posted by psmealey at 4:11 AM on March 2, 2007

A mole is the number of molecules in a gram of water:

No. It's not. There are 18.02 grams in a mole of water. /chemist
posted by hangashore at 4:56 AM on March 2, 2007 [3 favorites has favorites]

incredibly complex and convoluded

The most stable time reference available to science happens to be somewhat exotic. That's not especially surprising.


didn't Einstein say it was all relative anway

International atomic time has corrected for gravitational time dilation since midnight January 1, 1977.
posted by ryanrs at 5:06 AM on March 2, 2007

Yep. A mole is basically the number of protons in a gram of pure ionized Hydrogen.
posted by snoktruix at 5:07 AM on March 2, 2007 [1 favorite has favorites]

That's not especially surprising.

Probably not to you, if you are a scientist. But in freshman chemistry it was a real eye opener. I enjoyed every bit of it.
posted by psmealey at 5:09 AM on March 2, 2007

snoktruix: no, that's not accurate either. It has to be the carbon-12 definition. 12 grams of carbon-12. The nuclear mass defect is not insignificant.
posted by edd at 5:11 AM on March 2, 2007 [1 favorite has favorites]

Yeah, true. And I guess the electrons in the carbon are rolled in as well, even without considering the nuclear mass defect (wonder which is more?).
posted by snoktruix at 5:38 AM on March 2, 2007

Mole.
posted by LordSludge at 5:48 AM on March 2, 2007

So why not just use the mass of the moon, or something like that? I bet it's pretty easy to measure.
posted by noble_rot at 5:57 AM on March 2, 2007

The binding energy of an electron to a nucleus is on the order of electronvolts, but nuclear binding energies are in the mega-electronvolt range, so they're millions of times more important.

The nuclear binding energies are about ten times the mass of an electron (which is about half a MeV), but the electron masses are easy to count and add up compared to the nuclear binding energies which are not exactly easy to calculate, so you don't have to worry about them for this.

It's easiest to figure out by looking at the mass of a proton in atomic mass units (defined so that C-12 is 12 amu). It's about 1.007, so 12 of them are 0.7% heavier than a C-12 nucleus. The electron is about 0.05% of a proton mass.
posted by edd at 6:05 AM on March 2, 2007

psmealey, I hope you've seen the definition of the ampere:

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2×10–7 newton per meter of length.

At least the definition of a second is based on a physical measurement that's potentially possible, rather than a measurement involving two infinitely long one-dimensional wires.

In a similar way to the kilogram, you could in theory redefine the ampere in terms of a particular (large!) number of electrons passing a boundary in a second.
posted by chrismear at 6:07 AM on March 2, 2007

Those silly scientists. Everyone knows there are 28,2 grams in an a ounce of weed, so 1 gram is 1/28,2 of a OZ (on Earth, of course, gram being a unit of mass and ounce is a unit of weight.)

I guess now researchers will have to state the size of their dealer's cut as well as their margin of error.
posted by nebulawindphone at 6:26 AM on March 2, 2007 [1 favorite has favorites]

Chrismear, the ampere's definition doesn't have to be directly physically measurable; since we (think we) know all the relevant formulas, we can convert the given definition, as you say, to the electron flux passing through a boundry. (I'm not sure how the definition of the second is "potentially possible", though, given that it involves 0K...)

Does anyone know if "Le Gran K" is on display? I'm going to be in Paris soon, and I make it a point to see at least one astonishingly geeky thing anywhere I go.
posted by phooky at 6:30 AM on March 2, 2007

Does anyone know if "Le Gran K" is on display? I'm going to be in Paris soon, and I make it a point to see at least one astonishingly geeky thing anywhere I go.

Definetly not, they keep it in a safe and only take it out ocasionally in order to double check their copies. All other times, copies are used. I think they only take it out once a year, or even more rarely then that.
posted by delmoi at 6:41 AM on March 2, 2007

There is a list of other spesific proposals to define the Kg on the wikipedia page for it.
posted by delmoi at 6:46 AM on March 2, 2007

Very interesting post. And special thanks to edd for explaining why Having one lump of metal in Paris is actually not an awful way of doing this, even though it's an inelegant way of defining it. I am now better educated than I was before entering this thread.
posted by languagehat at 6:50 AM on March 2, 2007

delmoi, did you mean this?
posted by languagehat at 6:51 AM on March 2, 2007

I don't know about you guys, but I really like mole sauce on my avocados.
posted by psmealey at 7:19 AM on March 2, 2007

"Le Gran K?" Is that a Catalan kilogram or something?
posted by gubo at 7:42 AM on March 2, 2007

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2×10–7 newton per meter of length.

So in other words, it is made up.
posted by Ynoxas at 7:49 AM on March 2, 2007

The thing about this proposal (and similar ones like the Russian crystal counting one) is that it pushes the problem out to how accurately we can infer mass from number of atoms. This problem is right at the heart of one of the great mysteries of physics.

You can do this two ways: either by weighing a known number of atoms (using gravity) or by measuring the force response through Newton's third law. This implies that there are two kinds of mass. gravitational mass, defined by Newton's law of gravitation F=G m₁ m₂/r; and dynamic mass from Newton's third law of motion, F=m_d a. The masses m₁ (or m₂) and m_d are spookily equivalent. There's no widely-held explanation for this equivalence; it could be just a coincidence as far as we know. This remains one of the great mysteries of physics.

The thing is, it's really not possible to isolate yourself from gravity anywhere we know of, not to the precision that's needed for a mass standard. So, using F=ma isn't good enough. Also, unfortunately, Einstein (and many others) have shown that Newton's law of gravity isn't perfect either, so we need to use general relativity to figure out the relationship between number and mass, specifically relativistic mass, the mass of E=m_r c². (Eerily, m_r  still seems to be exactly equivalent to m_d, and even m_d's big brother, the mass used in quantum mechanics. This gave everyone goosebumps for most of the early Twentieth century. This is also responsible for the mess that is String Theory).

What this all boils down to is that to get from Avogadro's number to a reference mass unit, you need to measure the general relativity quantity equivalent to G, which depends on on your experimental geometry and where you are on the planet, and make sure that you are measuring the right number of atoms. Both are very hard measurements.

The reason this is such a big advance is that it's possible at all. Measuring the local gravity can be done well enough using a very sensitive balance. Prepping a crystal of known number is discussed in the article, a big breakthrough. Now units of mass can be first class citizens again, based on fundamental constants, like time and current (or charge) are, rather than based on a lump of platinum/iridium in Paris.
posted by bonehead at 7:53 AM on March 2, 2007 [3 favorites has favorites]

I feel obligated to link the Dinosaur Comic about the prototype kilogram.
posted by sindark at 8:06 AM on March 2, 2007

dang. sorry about the busted second link. Here's the correct link to Le Gran K.
posted by dkg at 8:19 AM on March 2, 2007

And double-dang. Sorry about the wrong definition of a mole. That shows you how much attention i paid in chemistry class. Thanks for the corrections, hangashore, snoktruix, and edd.
posted by dkg at 8:34 AM on March 2, 2007

delmoi, did you mean this?
er, yes
posted by delmoi at 9:35 AM on March 2, 2007

That shows you how much attention i paid in chemistry class.

S'okay, sometimes it (still) puts me to sleep. Nice links, dkg.
posted by hangashore at 10:15 AM on March 2, 2007

Before we redefine 'mass', maybe we could give the final and most bashful member of the cast of the standard model of elementary particles, the Higgs boson, mass-bearer, a few more chances to make its initial appearance on one of our supremely lavish accelerator stages. Who knows what it may choose to disclose about itself in the initial soliloquy?
posted by jamjam at 10:17 AM on March 2, 2007

There's no widely-held explanation for this equivalence

Well, General Relativity proposes that gravitational mass is caused by inertial mass; they're the same because what gravity is doing is accelerating spacetime out from under you, rather than acting directly on you. This is the "equivalence principle".
posted by hattifattener at 11:11 AM on March 2, 2007