Chemistry · General chemistry I · Worked example

Convert a number of atoms to grams

What is the mass of 1.50 × 10²⁴ iron atoms?

1.50 \times 10^{24} atoms Fe \to mol \to g

Plan the path through moles

Particles and grams are not connected directly. Go from atoms to moles with Avogadro’s number, then from moles to grams with the molar mass of iron, 55.85 g/mol.

Atoms to moles

Divide by Avogadro’s number: put 6.022 × 10²³ atoms in the denominator so atoms cancel. 1.50 × 10²⁴ / 6.022 × 10²³ = 2.49 mol.

1.50 \times 10^{24} atoms Fe \times \frac{1 mol Fe}{6.022 \times 10^{23} atoms Fe} = 2.49 mol Fe

\begin{array}{c} 1.50 \times 10^{24} atoms Fe \\ \times \frac{1 mol Fe}{6.022 \times 10^{23} atoms Fe} \\ = 2.49 mol Fe \end{array}

Moles to grams in one chain

Multiply by the molar mass, keeping the whole chain so the rounding happens once: 2.4908… × 55.85 = 139.1, or 139 g to three significant figures.

1.50 \times 10^{24} atoms Fe \times \frac{1 mol Fe}{6.022 \times 10^{23} atoms Fe} \times \frac{55.85 g Fe}{1 mol Fe} = 139 g Fe

\begin{array}{c} 1.50 \times 10^{24} atoms Fe \\ \times \frac{1 mol Fe}{6.022 \times 10^{23} atoms Fe} \\ \times \frac{55.85 g Fe}{1 mol Fe} = 139 g Fe \end{array}

Check the size of the answer

1.50 × 10²⁴ is about 2.5 times Avogadro’s number, and 2.5 moles of iron at about 56 g/mol is about 140 g. The answer fits.

Result

1.50 × 10²⁴ iron atoms have a mass of 139 g.

Your turn

How many atoms are in 5.00 g of aluminum?

Show the answer and explanation

1.12 × 10²³ atoms.

5.00 g ÷ 26.98 g/mol = 0.1853 mol, and 0.1853 mol × 6.022 × 10²³ = 1.116 × 10²³, which is 1.12 × 10²³ atoms.

5.00 g Al \times \frac{1 mol Al}{26.98 g Al} \times \frac{6.022 \times 10^{23} atoms}{1 mol} = 1.12 \times 10^{23} atoms

\begin{array}{c} 5.00 g Al \times \frac{1 mol Al}{26.98 g Al} \\ \times \frac{6.022 \times 10^{23} atoms}{1 mol} \\ = 1.12 \times 10^{23} atoms \end{array}

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