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20220815, 04:56 PM (ISO 8601)
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 Feb 2016
Why does everyone always overexplain moles and Avogadro's Number
Every explanation of these concepts always gets really complicated and longwinded, when really it can be explained in one sentence:
"It's the number of daltons (atomic mass units) in a gram"
That's it*. That's all it is. But almost anybody who tries to explain it will end up tripping over other parts of the lesson, (such as why we might need to convert from daltons to grams, and the history of calculating this conversion), even if they're otherwise capable of explaining things clearly and concisely. Why is that?
*If you want to get super technical, technically a mole is that amount specifically as a quantity of of discrete particles, but since it's a finite number I'm not sure that it being cardinal is really going to affect anything.Last edited by Bohandas; 20220815 at 05:16 PM.
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20220815, 06:11 PM (ISO 8601)
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 Dec 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
Honestly I find that explanation misleading too, because it completely hides 'why would you care?'. I'd say instead 'a mole is a unit for counting numbers of things that acts as a conversion factor between amu and grams. It's defined such that 1 mole worth of a given molecule has a mass in grams numerically equal to its atomic weight in amu'
Except for the fact that you might want to answer the question 'how much of this molecule whose atomic weight I know is in this macroscopic measure of material', there's no reason to care about moles. So while yes, it is the number of daltons per gram, unless you explain how to use that its not a very good explanation IMO.Last edited by NichG; 20220815 at 06:13 PM.

20220815, 08:35 PM (ISO 8601)
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 Feb 2016
Re: Why does everyone always overexplain moles and Avogadro's Number
Why you need to convert between daltons and grams definitely belongs in the same lesson for sure, I'm just saying that what avogadro's number is and what the significance of avogadro's number is are not strictly the same fact, and should be taught one after the other instead of trying to explain both at once and making a mess of things.
(Honestly, I still don't fully understand its significance. Mostnof the time it's mixed up with the third and more important fact that the relative atomic masses of the molecules in a chemical formula scale up to correspond to the relative masses of your reagents; I can tell without avogadro's number that to make 0.76 kilograms of salt with hydrochloric acid and sodium hydroxide I'll need 0.48kg of HCl and 0.52kg of NaOH)"we do not say anything in it, unless it is worth taking a long time to say, and to listen to" Treebeard
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20220815, 08:49 PM (ISO 8601)
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 Dec 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
Things are a lot easier when you don't see lessons as being just about conveying lists of facts. Connections between things are generally more important than the things themselves, and understanding why rather than what helps you basically rederive things at need without having to memorize. Knowing what Avogadro's Number is, is inherently valueless on its own.

20220817, 04:32 AM (ISO 8601)
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 Aug 2019
Re: Why does everyone always overexplain moles and Avogadro's Number
As a mathematician, I never understood what the fuss is about giving it two names. Both mole and avogadros number are just a number and the same one at that.

20220817, 04:40 AM (ISO 8601)
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Re: Why does everyone always overexplain moles and Avogadro's Number
Last edited by Eldan; 20220817 at 04:41 AM.
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20220817, 04:55 AM (ISO 8601)
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20220817, 06:00 AM (ISO 8601)
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Re: Why does everyone always overexplain moles and Avogadro's Number
I think there are a few important things to know about moles and Avogadro's number:
1: A mole is a number of particles equal to Avogadro's number.
2: Avogadro's number is the number of AMUs in one gram.
3: Therefore, the mass in grams of a mole of any substance, is the same as the mass in AMUs of any one of its particles.
4: You can use this fact without needing to know the actual value of Avogadro's number, and in fact you hardly ever need to know the actual value for practical purposes.
5: But in case you're curious, the value happens to be approximately 6*10^23.
Number four on that list is important because, in real life, it's hard to measure that value, and people were in fact doing chemistry using the concept before they ever knew that value. And it's also quite possible that a student might retain the concepts, without retaining the dry fact.
I also think that the "point oh two" that everyone learns is superfluous: It's still an approximation anyway, and giving the value to only a single decimal place happens to be good to a fraction of a percent precision. If you ever need more precision than that, then you're probably going to look it up and get even more digits.Time travels in divers paces with divers persons.
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20220817, 07:15 AM (ISO 8601)
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 Aug 2019

20220817, 08:27 AM (ISO 8601)
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 May 2016
Re: Why does everyone always overexplain moles and Avogadro's Number
You edited out the important bit  a mole is a number of particles; it isn't just a number. Your argument is basically that since a kilogram is a thousand grams then it's the same as the number one thousand, or like saying that since a milliliter of water and a gram of water are equivalent then milliliters and grams are just two different names for the same thing. 6.022e23 carbon atoms isn't the same as 6.022e23.
Last edited by Aeson; 20220817 at 08:35 AM.

20220817, 08:49 AM (ISO 8601)
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Re: Why does everyone always overexplain moles and Avogadro's Number
Last edited by Keltest; 20220817 at 08:49 AM.
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20220817, 09:14 AM (ISO 8601)
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 May 2016

20220817, 09:39 AM (ISO 8601)
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 Feb 2016
Re: Why does everyone always overexplain moles and Avogadro's Number
Right, so number four isn't really a fact about avogadro's number. It would still be true if the number's value were something else (Which it very well could've been, since it's based on the gram, which is a pretty arbitrary mass unit whose value was set partly by arbitrary historical factors*). And number four is also the important fact here, it's the fact that you're going to actually use. If anything the other facts are trivia about fact four.
*such as the meter being defined by a fraction of a meridian arc rather than an equatorial arc, which affected the size of the liter, which affected the amount of water they were measuring to define the original kilogram. As did atmospheric conditions to an extent. (Ironically this is one of the rare instances where it actually would have been good to go by a specific number of particles). All this in addition the the fact that the mass of a liter of water is pretty arbitrary basis to begin with.
The mole is strictly cardinal whereas avogadro's number can in theory be either cardinal or ordinal, even though it's only ever used as a cardinal since quantities of particles is the only context it ever comes up in. I don't know what possible use this distinction could have, but nevertheless it exists.Last edited by Bohandas; 20220817 at 09:44 AM.
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20220817, 09:54 AM (ISO 8601)
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 Dec 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
There's also generally the interaction with whole subject of dimensional analysis, which isn't strictly necessary 'to get the right numbers out', but is useful anyways both as a debugging check (track units and if the thing which is supposed to be a temperature comes out as Kelvin per moles carbon, you did something wrong) and as a way to derive simple scaling laws even if you don't know the full details of things.

20220817, 10:50 AM (ISO 8601)
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 Jul 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
Still, in terms of dimensional analysis, the mole is a dimensionless unit.
You can speak of a (possibly fractional) mole of any fungible things which are indivisible for the purposes of a specific analysis. I could say there are X moles of functioning automobiles on Earth, or Y moles of unspoiled jellybeans. It functions as a number. Its use merely means that something fungible and effectively identical for a particular analytical purpose is being counted.

20220817, 11:50 AM (ISO 8601)
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 Dec 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
Lets take something like 'I want to derive the ideal gas law just using dimensional analysis, without knowing any statistical mechanics'. We have quantities we want to build a relation out of: pressure (mass * distance^1 * time^2), temperature, volume (distance^3), and the number of particles present.
So if we want to make a dimensionless expression, we need constants or material properties that would cancel out mass, time, and temperature. We can note that PV has units of energy, and temperature is related to energy by a heat capacity, so PV/(heat capacity * T) is dimensionless, and can be written as a function of other dimensionless ratios.
If we treat 'number of particles present' as dimensionless, we're stuck at f(PV/[heat capacity]T, N, ...) = constant, where '...' would indicate any other independent dimensionless ratios that could be constructed for the system (which would require there to be additional dimensionful quantities describing that gas). So even if we know that there are no other dimensionful properties associated with the gas and '...' is empty, we still can't get a unique equation of state up to a constant because we're treating N as inherently dimensionless.
If we treat 'number of particles present' as having a dimension of 'number of things', then we know that we haven't actually cancelled out everything, and that we probably need to express that heat capacity as 'heat capacity per thing' * 'number of things', which then gets us a bit closer:
f(PV/([specific heat]NT), ...) = constant.
Now if there are no other dimensionful characteristics, this basically reduces to PV/([specific heat]NT) = f^1(constant) = constant, which is the ideal gas law, and it lets us basically interpret the Rydberg constant as being related to the specific heat inherent to the degrees of freedom associated with free particles.
Of course this is kind of a backwards construction... But it does show a bit how treating 'number of things' as if its just 'number' can lead to nonphysical equations of state.

20220817, 12:36 PM (ISO 8601)
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 Jul 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
Your way of doing it is a correct heuristic for avoiding pitfalls, and if you want to explicitly or implicitly use the Buckingham π theorem, as you have done. I suppose my thinking is a bit sloppy. But I also don't like it when people say a mole is a unit of mass.
I'm often working with heterogenous mixtures where the number of molecules and the bulk density are all that matter. Which probably isn't a proper excuse, but it's a narrow application that may have influenced my bad habit of shoving everything that isn't in mass, time, charge, temperature, or distance units into a proportionality constant and leaving that up to determine experimentally.

20220818, 02:31 AM (ISO 8601)
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Re: Why does everyone always overexplain moles and Avogadro's Number

20220818, 06:09 AM (ISO 8601)
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Re: Why does everyone always overexplain moles and Avogadro's Number
If you don't treat moles as a unit, then you also derive the Ideal Gas Law, just with Boltzmann's constant instead of Rydberg's constant.
Really, the question of whether "mole" is a number is the same as the question of whether "dozen" is a number. "Dozen" just means "twelve", except that it's always a count of some sort of object (eggs, donuts, etc.). In the same way, "mole" just means "Avogadro's number", except that it's always a count of some sort of object (molecules, ions, etc.).
All that said... Even though moles are really dimensionless, numbers that big realistically only show up when you're talking about macroscopic quantities of molecules or smaller particles. So, in practice, you can treat "mole" as a unit.Time travels in divers paces with divers persons.
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20220818, 07:49 AM (ISO 8601)
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 Apr 2009
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Re: Why does everyone always overexplain moles and Avogadro's Number
What's daltons and AMUs? You lost me at that point.
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20220818, 09:03 AM (ISO 8601)
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Re: Why does everyone always overexplain moles and Avogadro's Number
Atomic mass units. Roughly the weight of one proton/hydrogen atom, but officially defined as one twelfth the mass of an atom of carbon 12. Dalton is another name for the same thing.
Last edited by Eldan; 20220818 at 09:04 AM.
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20220818, 09:39 AM (ISO 8601)
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 Aug 2019

20220818, 10:15 AM (ISO 8601)
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 Jul 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
In many cases, that's because the answer to your question "doesn't matter" for the purpose at hand.
For example, if I'm using one of the engineers' favorite versions of the ideal gas law:
p=ρRT
Where R is the specific gas constant. That is, in this equation, R is the usual gas constant divided by the average molar mass of the molecules in the gas.
When using this, I don't need to care what elements, compounds, whatever the gas is made of. All I need is the average molar mass of all of that, and I can work from there to predict lots of mechanical, dynamical, and thermodynamic results given that gas. (As long as the chemistry of the gas and whatever solid and liquids I'm working with doesn't get...... interesting.)

20220818, 10:56 AM (ISO 8601)
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 Feb 2016
Re: Why does everyone always overexplain moles and Avogadro's Number
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20220818, 11:51 AM (ISO 8601)
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 Dec 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
To do that, you still need 'number of things' to be dimensionful. It's just that you're using units of '1 thing' rather than units of '6e23 things'.
If 'number of things' is dimensionless, you have an extra dimensionless group you can't exclude, meaning that you can't exclude equations of state where e.g. having 1023112 particles in the universe just has fundamentally different scaling laws than having 1023111 particles in the universe.

20220818, 01:27 PM (ISO 8601)
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 Jul 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
Tangent alert:
I just had a thought. Does anyone know offhand what if any effect suspended particulates have on the effective gas laws / equation of state.
Since the particulates would in most cases be big enough that you might not be able to treat every collision with a gas molecule as independent, and a particulate would have lots of degrees of freedom compared to one gas molecule..... I don't know? Does it end up mattering only in certain regimes? All or most of the time above a certain particulate density? Only for certain distributions of particulate mass/size/surface area?
Just curious. I don't think I've ever seen this covered.

20220818, 01:51 PM (ISO 8601)
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 Dec 2010
Re: Why does everyone always overexplain moles and Avogadro's Number
The issue in practice is that because particulates are much bigger than, say, nitrogen molecules, you also have comparatively far far fewer of them, so they don't actually contribute that much entropy to the gas itself. Now if you have particulates that are otherwise in a vacuum, those gasses behave very strangely  its basically a subproblem in granular physics, and there are these weird finite time singularities where in some finite amount of time an idealized rigidbody dissipative collision model will eventually produce an infinite number of collisions. So that sounds like 'yeah, that's an unphysical model so of course', but the interesting thing about that kind of singularity is that it means that properties of the grains/particles that you wouldn't think would be relevant actually can be mandatory for determining the behavior of the gas, not just a correction. E.g. you actually have to care about the Young's Modulus of your particles to understand how a dilute gas of those particles would behave, which is weird since normally the dilute limit is collisions > zero.
The speed of sound in granular gasses is also bizarre  it basically can take any value from zero to infinity (or well, speed of light...) based on the velocity of the thing that imparted the sound wave into the medium. Basically, in normal gasses, sound speed is a property of the gas, but in granular gasses its a semiconserved property of the fluctuation itself.