# How do I determine Avogadro's number with this information?

Using the volume, density and molar mass of carbon, determine Avogadro's number.

Density of C: 3.51

Volume:2.60x10^-25

Molar Mass:12.01

I just don't know how to use these numbers to arrive at the number. (note) the volume may be off because of experimental error, i just need to know the correct set up

Thanks

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• 9 years ago

You could at least type in the units. The density figure looks like grams/cc density of diamond. The tiny size of the volume suggests that it the volume in cubic somethings occupied by an atom in whatever form of carbon you are looking at.

If so, and volume in cm^3 or cc units, then you have:

ρ = 3.51 g / cm^3

V = 2.60x10^-25 cm^3 / atom

M(C) = 12.01 g/mol

Multiplying ρV gives the mass of an atom in grams:

ρV = (3.51 g/cm^3) * (2.60 x 10^-25 cm^3 / atom) = 9.13 x 10^-25 g / atom

Avogadro's number N₀ is the number of atoms in a mole. Multiplying N₀ times the mass of an atom gives the mass of a mole of atoms, or:

ρVN₀ = M(C)

N₀ = M(C) / (ρV)

With your data, that's N₀ = (12.01 g/mol) / (9.13 x 10^-25 g/atom)

N₀ ~~ 1.32 x 10^25 atom/mol

That's well above 6.02x10^23, so either my guesses were bad or your data is lousy. That's an inclusive "or".