# What is the relation between the amu and avogadro’s number? [closed]

I know that the relation between Avogadro’s number and amu is a reciprocal relationship but the relation is slightly unclear.

Could anyone give me more clarification?

• $$N_{A} = \frac{m_{\mathrm{in\ amu}}}{m_{\mathrm{in\ grams}}}$$
– Zhe
Mar 9, 2017 at 23:15

## 3 Answers

$\pu{1amu}$ is defined as one twelfth of the mass of one carbon-12 atom.

Avogadro's number is defined as the total number of entities in $\pu{12g}$ of carbon-12.

$N_\mathrm A=6.022\times10^{23}$

It is a measuring criteria, just like a dozen, which is used to put a number to a certain item. A dozen means 12 items (items like bananas, atoms, molecules, etc) and 1 mole means $6.022\times10^{23}$ items (items like bananas, atoms, molecules, etc).

So, $\pu{12g}\ \ce{^12C}$ contains $N_\mathrm A$ atoms

Therefore, 1 atom of carbon-12 weighs $\frac{12}{N_\mathrm A}\ \mathrm{g}$.

As per the defintion of atomic mass unit, $$\pu{1amu}=\frac{1}{12}\frac{12}{N_\mathrm A}\mathrm{\ g}=\frac{1}{6.022\times10^{23}}\ \mathrm{g}$$

Hence, $\pu{1amu}=\pu{1.6\times10^{-27}kg}$

• I don’t know where your obscure unit gram-metres derive from, but I’m reasonably sure you were trying to talk about grams all across this answer so I corrected that.
– Jan
Oct 8, 2017 at 15:00
• It wasn't meant to be interpreted as $gram-meter$, I used to the notation 'gm' for gram. However, thanks for the edit. Oct 8, 2017 at 17:37
• If you wanted to write grams, please use the standard SI-conform abbreviation $\mathrm g$ and not any made-up non-standard ones. Everything else will cause confusion.
– Jan
Oct 8, 2017 at 17:46
• Yeah, I got that. Oct 8, 2017 at 17:47

The atomic mass unit (amu or simply u) is the $1/12$ of the mass of a $\ce{^12C}$ atom.
Avogadro's number ($N_\mathrm A=6.022\times10^{23}$) is the number of atoms contained in $\pu{12g}$ of $\ce{^12C}$.

The relation between them has to do with relative atomic mass ($A_\mathrm r$), which is basically the number of atomic mass units an atom is equal to. One can easily understand that carbon is equal to $\pu{12u}$, hydrogen to $\pu{1u}$, helium to $\pu{4u}$, etc. (I'm referring to the most common isotopes)

Now, $N_\mathrm A$ atoms (or $\pu{1 mol}$) weigh $A_\mathrm r\ \mathrm{g}$. For example, $N_\mathrm A$ atoms of hydrogen weigh $\pu{1g}$. This is because they are the $1/12$ of $N_\mathrm A$ atoms of carbon (which weigh $\pu{12g}$).

There is a lengthy discussion of what an amu is, as well as on Avogadro's constant in Wikipedia. see https://en.wikipedia.org/wiki/Unified_atomic_mass_unit and see https://en.wikipedia.org/wiki/Avogadro_constant. An amu is a unit of mass, like a pound, gram, microgram, or tonne. An amu is a very, very small unit of mass, defined, as you know by now, as being exactly the mass of 12 isolated 12C atoms in their ground state (which is just a way to eliminate kinetic or potential energy which would give the atoms more mass (remember E = mc²)). Avogadro's Number is just like a dozen, a pair, a score, a gross - it is a definite number of things, of particles. It is, like "dozen" and the rest, dimensionless. A very important note is that the term has been depreciated by the IUPAC (the consensus "Authority" for Chemistry (and some Physics)). You should not be taught about Avogadro's Number; it has been replaced by Avogadro's Constant. Avogadro's Constant is not dimensionless - which is the big difference between the two. The Constant has units of reciprocal quantity. If that quantity is reciprocal moles, then the numerical value of the Constant and the Number are identical, but the quantity could be something else, for instance reciprocal pound-moles. This shouldn't confuse you, because it is almost always reciprocal moles, the important point is that it has units while Avogadro's Number does not. Unfortunately, both are symbolized NA, and it appears by your question that your teacher has failed to (or is unable to ) distinguish between the two. {Consider the common terms Atomic Weight and Molecular Weight. They are not weights, but masses and we are taught that. IUPAC also depreciates them for their "Mass" alternative, yet they are widely used, while Molecular Mass is rarely used (I don't see MM ever, but I see MW all the time). This is a similar situation, where the historical term persists although it has been depreciated.} One dalton, 1 Da, is one amu, is one u, but guess what? Da is preferred as being more clear. (Guess whether amu has been depreciated...) In a perfect world, one mole would be a specific integer number of particles. Unfortunately, our measuring instruments aren't accurate to 24 decimal places, so the actual number is only specified to 10 to 12 decimal digits and there is a proposal to define the Constant to be exactly 6.022140 or 6.022141 x 1023 - they are, last I heard, still arguing over it. My point here is that the number itself has no fundamental importance, just like a baker's dozen is 13 pieces, while a dozen is 12, as long as we all know how many we're talking about either is fine. So 12 Da of 12C has a mass in grams of 12 ÷ NA. You may find it interesting to show this answer to your teacher and listen to what s/he says about it.