- 15,759
- 5,758
Note: If we wanted "nice" numbers, then we would probably define a reasonably sized length unit such that the speed of light would be ##10^9## of that length unit per second ... Oh wait! That is within 2% of a foot, can't have that ...
Avagadro's Number looks a lot less ugly to me now than it did before. Now it's an integer. It used to have an uncertainty to it, that seems more ugly to me.I admire that goal, and I think that the old definition of Avogadro's number was the last piece of the SI to still exemplify that, without the ugly numbers.
Bwa Ha Ha! You caught on to my sinister plot for Imperial supremacy!Note: If we wanted "nice" numbers, then we would probably define a reasonably sized length unit such that the speed of light would be ##10^9## of that length unit per second ... Oh wait! That is within 2% of a foot, can't have that ...
Well yes... meaningful quantitative statements do tend to have uncertainty... only tautological ones don't.Avagadro's Number looks a lot less ugly to me now than it did before. Now it's an integer. It used to have an uncertainty to it, that seems more ugly to me.
Nobody has said otherwise. It has been argued that it would be more natural to define it as a number or symbol.the "mole" is not defined as a number; it is defined as an 'amount of substance' (symbol, n)
You should update your notion of how the SI defined today. Don't worry, the change officially got into effect only in May this year :-).I prefer 'Avogadro's Constant (Na) = 6.022E23/mol
the "mole" is not defined as a number; it is defined as an 'amount of substance' (symbol, n)
and 1 mol of anything is the amount of that thing that has 6E22 entities.
Somebody mentioned that the mole is a conversion unit. It surely is. It is a miracle constant. It instantly converts atomic mass numbers into grams. From the micro world to the macro world. What is the value of this constant? Who gives a damn'? (OK, it's the inverse of the atomic mass unit expressed in grams)
If the value of Avogadro's constant were 42/mol, a chemist's life would be horrible. The poor chemist would have to deal with one number if he/she is thinking about atoms and molecules, and a different number if he/she were in the lab with bottles of stuff. It doesn't bear thinking about.
But it IS defined as a number:Nobody has said otherwise. It has been argued that it would be more natural to define it as a number or symbol.
It is not defined as a number in the sense we typically use in the meaning of having no physical dimension. Although the Avogadro number is defined by its numerical value and represents the number of entities in a mole by definition, amount of substance (and hence the unit mole) has its own physical dimension within SI. A mole is therefore not dimensionless and neither is Avogadro's number (even if it is called "number").But it IS defined as a number:
The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly ##6.02214076 \cdot 10^{23}## elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit ##\text{mol}^{−1}## and is called the Avogadro number.[7][49] The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.
For details about the new SI, see the Wikipedia article
https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units
It is clear from this that the mole (which is a unit of the base quantity amount of substance) has non-trivial physical dimension and therefore is not just a number under the current SI definition. The argument made here is that it would be more natural to define it as being dimensionless.Physical quantities can be organized in a system of dimensions, where the system used is decided by convention. Each of the seven base quantities used in the SI is regarded as having its own dimension.
The dimension of Avogadro's number is 1/N, not 1/mol. The mole is a unit for quantities of dimension N.The SI is not supposed to provide "natural units" but well-defined precise units that can be reproduced everywhere (by assumption of the cosmological principle even everywhere in the entire universe) to be used FAPP under everyday circumstances.
According to the definition 1 mole is the amount of substance consisting of a specific number of entities (relevant degrees of freedom I'd translate it). That's why the Avogradro number in the SI has the dimension 1/mol, i.e., you have ##\simeq 6 \cdot 10^{23}## entities per mole.
I suggest you read the official document where it is made clear that mol is a unit of dimension N (amount of substance), it is not a dimension in and of itself. Saying that something has dimensions of mol is like saying that a distance has dimensions of meters (it does not, it has dimensions of length L). This is described in section 2.3.3 of the SI brochure. Units are not the same thing as physical dimension although the concepts are somewhat related.The Avogadro number in the SI has the dimension 1/mol
Angles are dimensionless in the SI so the situation is not equivalent. Again, there is a distinction between the physical dimension and the units used to describe quantities of those dimensions.The same is true for angles: I'm not sure what's the status in the SI. I remember there was some debate concerning angles and solid angles, i.e., whether you should write rad or sr in the sense of units. If you do so, angles and solid angles get a dimension of rad or sr, respectively though the natural measure is again dimensionless.
This is not entirely true. You can still express a meter in Planck units. It would just be a number used to relate to other numbers, much like mol would be a number used to relate to other numbers if you define amount of substance to be dimensionless.Then everything is dimensionless, and you have no more units for any quantity.
I admit I was a floating voter here, but this post suggests to me that the dimensions of a mole, if it is to make any sense, must be different for every substance.Somewhat tangentially related to the recent discussion. Perhaps a chemist can answer.
For mass it makes sense to add a kg of glucose and a kg of NaCl to get a total mass. Would you ever add a mol of glucose to a mol of NaCl to get a total amount of substance?
Or if you add 1 mol of Na and 1 mol of Cl would you ever say you had 2 mol of anything?
I'm not convinced. In principle you can add lengths or masses. A physical process may not support simple addition, but that's not the issue. Another example would be relativistic velocity addition. It's not simple addition, but you can manipulate velocities mathematically regardless of what's moving.Well, my chemistry is quite rusty, but wouldn't I get some Na, Cl but also NaCl? I'd say I've less than 2 moles of substance, depending on the conditions. For full equilibrium the question, how many moles I get is answered by the mass-action law.
Then the issue with mass is also not that trivial. According to relativity mass is not conserved, i.e., if you have an exothermic (endothermic) reaction your total mass gets smaller (larger) by the amount ##\delta Q/c^2## (the true meaning of the most misunderstood but most famous formula of physics ##E=mc^2##). In chemistry that's of course usually negligible, not so in nuclear reaction like fission!
In the SI Avogadro’s number is dimensionful. If you would instead make amount of substance dimensionless, 1 mol would be exactly the number that the SI currently defines as the avogadro number’s measured value in 1/mol. The Avogadro number is then just a conversion factor with value 1 just like c in natural units but it is still 1 = 6.xxxe23 / mol.But why then do they write
NA=6.xxx⋅10231molNA=6.xxx⋅10231mol
N_A=6.xxx \cdot 10^{23} \frac{1}{\text{mol}}
oif molmol\text{mol} had the dimension of NNN (which dimension is in fact 1). That's very confusing. Maybe I get something wrong here.
Sure, it is a matter of convention what you give physical dimension to. The argument here is that it is more natural not to give amount of substance a physical dimension contrary to the SI convention. Much similar to it being natural to have dimensionless velocities in natural units.Maybe I'm using the expression "dimension" wrong, but which dimension a quantity takes, depends on the system of units used, i.e., in the HEP natural units masses, energies, momenta, and temperatures have the same dimension. The same holds for lengths and times. Velocities are dimensionless.
The SI brochure first defines all of the units and then define the physical dimensions used by stating that each base unit has its own independent physical dimension. This was by no means necessary. The SI could just has well just have defined meters and seconds to be different units for length, which would make velocities dimensionless but have c as a dimensionless conversion factor.Of course, you can also specify "dimensions" independent from units. Is it this sense the SI brochure uses the word "dimension"? Than it's clear that I used the wrong meaning in context of the SI.
That two numbers have the same physical dimension is a prerequisite for an addition to make sense. However, there is no guarantee that having the same physical dimension implies that the sum makes sense. For this, we need modelling.Somewhat tangentially related to the recent discussion. Perhaps a chemist can answer.
For mass it makes sense to add a kg of glucose and a kg of NaCl to get a total mass. Would you ever add a mol of glucose to a mol of NaCl to get a total amount of substance?
Or if you add 1 mol of Na and 1 mol of Cl would you ever say you had 2 mol of anything?
In SI it is the same dimension.What I am interested in is the idea of “amount of substance” as a dimension. Does it behave that way? Specifically, is there any use case for adding moles of different substances. Does “amount of substance” in general behave as a dimension under addition, or is each “amount of substance X” a separate dimension.
This to me sounds no different from ”is there any use case for adding m/s of velocity components in different directions?”Specifically, is there any use case for adding moles of different substances.
Correct. For which you gave the standard formula ##\sqrt{v_x^2+v_y^2}## which when expanded clearly is the addition of lots of terms of dimension L/T.This to me sounds no different from ”is there any use case for adding m/s of velocity components in different directions?”
It is the addition of two terms of dimension (L/T)^2 and then taking the square root of that.which when expanded clearly is the addition of lots of terms of dimension L/T.
Did my post #46 not convince you, with its simplicity?I admit I was a floating voter here, but this post suggests to me that the dimensions of a mole, if it is to make any sense, must be different for every substance.
If you have a mole of oranges, then either you have a dimensionless number of you have a unit of orange.
This SI unit of "a number of whatever thing you are talking about" seems to me neither one thing nor the other.
What's the counterargument?