DiscoBallOnMoon 2012-7-12 12:06 AM

## Molar Mass = Mass x Avogadro's number?

Okay, I know Molar Mass = Mass x Avogadro's number, but I don't quite understand the concept. Why is Molar Mass = Mass x Avogadro's number? Thank you.
jmlo 2012-7-12 01:27 AM

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Molar mass, by definition, is the mass of 1 mole of atoms. "Mole" here is a unit referring to the quantity of atoms. This unit is associated with a value of 6.022 x 10^23, which is commonly called Avogadro's number. In other words, "1 mole of atoms" is identical to "6.022 x 10^23 atoms".

Therefore, molar mass of an element, simply speaking, is the total mass of 1 mole of atoms of the element. If each of such atom has a mass of m, then its molar mass is just 6.022 x 10^23 times m. Same calculations can be done also for molecules.

Here you have to pay attention on the actual unit of molar mass. This quantity is given in units of g/mol. Since Avogadro's number bears no unit at all, the correct formula to calculate molar mass is indeed

Molar Mass = (Atomic Mass) x (Avogadro constant)

Avogadro constant and Avogadro's number are the same in magnitude (i.e., both are 6.022 x 10^23), but Avogadro constant has the unit of /mol.
DiscoBallOnMoon 2012-7-12 02:11 AM

Oh okay thanks. So if a question asks a polymer has a mass of x g, I would assume the mass is referring to the mass of each of such atom?

jmlo 2012-7-12 03:31 AM

If the mass quantity is in the unit of g, then it refers to the actual mass of the polymer. If it is given in the unit of g/mol, then it refers to the molar mass. Based on the given information, it is likely that x g is the total mass of the polymer.

Note that polymers are giant molecules made of hundreds (or thousands) of atoms. Moreover, there exists many different types of polymers whose compositions are different. Therefore, knowing only the total mass does not tell us how many polymer molecules are indeed present.