Why is that molar mass has of a substance, which is the mass of one mole of a substance ($6.02\times 10^{23}$ particles of that substance) has the same value as molecular mass, which is the mass of one molecule which in some cases is just one of the particles stated above (one particle from a mole). Also why do they have different units?

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    $\begingroup$ Say, a coin weighs 2 g. Then a thousand coins weighs 2 kg. How come these values (2 and 2) are similar, and why are they in different units? $\endgroup$ – Ivan Neretin Feb 17 '19 at 14:53
  • $\begingroup$ Thank you that was surprisingly the most useful answer I have gotten throughout but are you sure it is correct $\endgroup$ – Taofeek Feb 17 '19 at 15:55
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    $\begingroup$ An answer? I never gave you any. I merely asked a rhetorical question; if it made you think in the right direction, good for you. Just what part of my comment could be mistaken for something that may or may not be correct? That a certain real-world coin actually weighs 2 g? I never said that. Or that 1000 times 2 g makes 2 kg? Well, yes, I guess I can say so with a good deal of confidence. $\endgroup$ – Ivan Neretin Feb 17 '19 at 16:08
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    $\begingroup$ Related: Quick and simple explanation of molar mass, molecular mass and atomic mass $\endgroup$ – Loong Feb 17 '19 at 19:25

molar mass of a substance is the mass of one mole of a substance

This is not quite correct. If you said the speed of a car is the distance it travels in one hour, cars would go at speeds of 120 miles (race car) or 30 miles (in town). However, speed is defined as distance traveled per time. As a result, speed has the dimension of distance divided by time, and a typical unit (at least where I live) is miles per hour.

Molar mass is defined as the mass per amount of substance. The dimensions are mass divided by amount of substance, and typical units are g/mol.

Why does molar mass have the same value as molecular mass?

If the molar mass is given in g/mol and the molecular mass is given in u (unified atomic mass unit) or Dalton, the number is the same. The reason is that both the mole (at least until May 2019) and the Dalton are based on the mass of the carbon-12 isotope. A mole of a substance is defined as the amount that has the same number of particles as present in 12 grams of carbon-12. The Dalton is define as 1/12th of the mass of a carbon-12 atom.

From these definitions, you will find that the molar mass of the carbon-12 isotope is 12 g/mol, exactly, and the molecular mass of carbon-12 is 12 Dalton, exactly.

What will change in May 2019?

The mole will be defined as "One mole contains exactly 6.02214076×10^23 elementary entities." The molar mass of carbon-12 will be an experimentally determined quantity.

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  • $\begingroup$ I'd change the sentence "If the molar mass is given in g/mol and the molecular mass is given in u..." to If the molar mass is given in g/mol and the molecular mass is given in u/atom ..." $\endgroup$ – MaxW Feb 17 '19 at 18:48
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    $\begingroup$ I would argue that molar mass by definition is the mass of 1 mole of substance. Otherwise you can call it something else. The term "molar" speaks for itself, just as in other molar quantities. $\endgroup$ – Buck Thorn Feb 17 '19 at 19:31
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    $\begingroup$ @Try_Hard : As long as it is clear that the dimensions are mass divided by amount of substance, either definition is fine. I'm not a native English speaker, so to me the mass of 1 mole of substance sounds like the dimensions would be mass, while the mass per amount of substance (or the mass divided by the amount of substance) sounds like the dimensions are mass divided by amount of substance. Some definitions just add "expressed in g/mol" to make that clear, which is fine too. $\endgroup$ – Karsten Theis Feb 17 '19 at 22:41
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    $\begingroup$ @MaxW : I think it is fine to say in the text that this refers to the mass of one atom (or call the quantity $m_\mathrm{atom}$), but I'm not so sure about putting it into the units. What is the dimension of "atom"? What is the value of "atom". If it is 1, the statements are still true. The definition of molecular mass already includes that it refers to a single molecule (or atom). $\endgroup$ – Karsten Theis Feb 17 '19 at 22:46
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    $\begingroup$ Kirsten basically the Avogadro number will be taken as exactly that. So we shall expect in principle little change in the atomic mass for atoms different than C 12. It is a shame but I cannot quickly figure it out $\endgroup$ – Alchimista Feb 18 '19 at 10:18

Like "1 dozen", "1 mole" refers to an exact number. Molar mass refers to the mass of a very specific number of molecules/atoms: 1 mole. The molar mass is the mass divided by the amount (number of individual entities such as atoms or molecules) of substance measured in moles.

Now 1 mole is equal of course to Avogadro's constant $\pu{N_A}$. To make matters clear $\pu{N_A = 6.022 \times 10^{23}/mol}$ but it is usually ok to speak of Avogadro's number as equal to the number of particles in 1 mole. It is therefore fair in practice to make the following substitution when performing computations:

$$\pu{1 mole = N_A = 6.022 \times 10^{23}}$$

withthe understanding that $\pu{N_A}$ always refers to the number of entities in 1 mole.

Now lets say we take 1 mole of carbon-12 atoms and determine its mass. It's $\pu{m = 12.0 g}$, which means the molar mass is

$$\pu{M = 12.0 g/1 mole = 12.0 g/mol}$$

But what if we want to know the mass of 1 atom of $\ce{^{12}C}$? Ok, substitute "1 mole" with Avogadro's number. That's just

$$\pu{M_{molecule} = 12.0 g/N_A = 12.0 g/6.022 \times 10^{23} = 1.66\times 10^{-27} kg = 1.66 yg}$$

But $\pu{1.66\times 10^{-27} kg}$ is a really tiny and cumbersome number, and the "yoctogram" is very rarely used. However we can define an atomic mass unit:

$$\pu{1 amu = 1 g/N_A (exactly)} $$


$$\pu{M_{molecule} = 12.0 amu}$$

This is much tidier! But that's the same as before, except that we changed "g/mol" with "amu", so the units are practically exchangeable.

However they are not always interchangeable (sometimes you should be careful): the mass of an atom or molecule refers rather obviously to a single atom or molecule, whereas the mass of a mole is a sum over all species in that mole, which may contain for instance a mix of isotopes. Of course, if you refer to an "average mass" then amu and g/mol are interchangeable.

[3]: Actually, chemical engineers distinguish between lb-mol and g-mol and so forth, but I'm a plain chemist, so I stick to chemist's (or SI) convention.

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  • $\begingroup$ Avogadro constant is not dimensionless, its unit is $\pu{mol-1}$. Also, if you use an equal sign in the first equation, then probably use CODATA's value of $\pu{6.022140857(74)e23 mol-1}$ (I didn't downvote). @downvoter it would be nice if you share the reason for downvoting so that the answer could be improved further. $\endgroup$ – andselisk Feb 18 '19 at 10:17
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    $\begingroup$ Act as you wish, I only underline the issues I instantly noted that could lead to downvoting. And no, $\pu{mol-1}$ is not redundant, it's common sense. If you don't trust me, have a look at CODATA paper, IUPAC Green Book, ACS Style Guide or any other normative document you trust. $\endgroup$ – andselisk Feb 18 '19 at 10:30
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    $\begingroup$ @andselisk I appreciate bringing this point to my attention. Thing is in practice one is free to substitute Avogadro's constant (the number) for the unit of 1 mole in calculations, at least afaik. $\endgroup$ – Buck Thorn Feb 18 '19 at 10:41

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