how to find the molar mass of an unknown substance that has 4.204x10^22 atoms

Question

the substance is unknown, but the mass is measured to be 13.5 grams. Now I have to find the molor mass, but the number of moles is unknown. 

Answer 1

First you want to divide by Avogadro's number to convert the value over into Moles

Moles = # of Atoms / Avogadro's Number

Moles = 4.204 x 10^22 / (6.022 x 10^23) = 0.0698 mol

Then you can find the Molar Mass by taking

Molar Mass = Mass / Moles

Molar Mass = 13.5 g / 0.0698 mol

Molar Mass = 193.38

meaning that the Molar Mass of the unknown substance is approximately 193.38 g/mol

Answer 2

Hi Myca,

In this problem, you have to use Avogadro's Number to solve this: 6.0221367 x 10²³

1g = 6.0221367 x 10²³ amu                                amu= atomic mass unit

mass of 1 atom = mass of a mole of atoms / 6.022 x 10²³

Molecular mass - sum of the atomic masses (in amu) in the molecule
Molar mass - the mass (in kg or g) of 1 mole of units of its amu

Don't let this confuse you; it is very important always to bear in mind that the mole is a number and not a mass. But each individual particle has a mass of its own, so a mole of any specific substance will always correspond to a certain mass of that substance.

     1 mol (substance)      =     1                   

molar mass (substance)

 

           1 mol (substance)             =     1

6.022 x 10²³ (substance) atoms

 

Use second equation and you'll get:

      4.204 x 10²² atoms             = 0.6981 x 10-1 = 0.06981 mol
6.022 x 10²³ (substance) atoms

So, let's go back to that "substance." It has a mass of 13.5 grams. To get the molar mass, you have to have 1 mole of substance.

13.5 grams / 0.06981 = 193.382 grams    =   193 grams / mol   (for 3 sig figs)


I hope you understand / understood what I did / represented.

 

Good luck to you.

 

Yohan Chu   (LV  NV)

 

Here are molar mass for other known substances:
molar mass of H₂O = 18.002 grams
molar mass of CO₂ = 44.01 grams
molar mass of NH₃ = 17.033 grams

We use this (molar mass) ( X grams / 1 mol) in stoichiometry