Calculator of Alexandria

Grams to moles calculator

Convert between grams, moles and number of particles using molar mass and Avogadro's number, with the reasoning shown.

I know the

NaCl is 58.44 g/mol. Add up atomic masses from the periodic table.

Amountnn
Mass
g
Particles

Formula

n=mM,N=n NAn = \frac{m}{M}, \quad N = n\,N_A
How it's derived

The formula

n=mMn = \frac{m}{M} N=n NAN = n\,N_A

nn is the amount in moles, mm the mass in grams, MM the molar mass in g/mol, NN the number of particles, and NA=6.02214076×1023 mol−1N_A = 6.02214076 \times 10^{23}\ \text{mol}^{-1} is Avogadro’s number.

Where it comes from

Atoms are far too small to count one by one, so chemists count them in batches. A mole is a batch of exactly 6.02214076×10236.02214076 \times 10^{23} particles. Since 2019 this number is fixed by definition, like a dozen is fixed at twelve.

The batch size was chosen so that the numbers line up with the periodic table. One atom of carbon-12 has a mass of 12 atomic mass units, and one mole of carbon-12 has a mass of 12 grams. So an element’s atomic mass in the table is also the mass of one mole of it, in grams. For a compound, add up the atoms: NaCl is 22.99+35.45=58.4422.99 + 35.45 = 58.44 g/mol.

If each mole weighs MM grams, then mm grams contains m/Mm/M moles. Multiplying by the batch size gives the number of particles.

Worked example

10.0 g of table salt (NaCl, 58.44 g/mol):

n=10.058.44=0.171 moln = \frac{10.0}{58.44} = 0.171\ \text{mol} N=0.171×6.022×1023=1.03×1023 formula unitsN = 0.171 \times 6.022 \times 10^{23} = 1.03 \times 10^{23}\ \text{formula units}

Watch out for

  • Molecules vs atoms. One mole of water molecules (H2O\text{H}_2\text{O}) contains two moles of hydrogen atoms.
  • Hydrates. Copper sulfate pentahydrate (CuSO4⋅5H2O\text{CuSO}_4 \cdot 5\text{H}_2\text{O}, 249.69 g/mol) weighs much more per mole than the anhydrous salt (159.61 g/mol). Use the molar mass printed on the bottle you have.

Sources

Last checked