Chemistry · General chemistry I · Worked example

Convert grams to moles and molecules

How many moles of water, and how many water molecules, are in 25.0 g of H₂O?

25.0 g H_{2} O \to mol \to molecules

Find the molar mass

Water has two hydrogen atoms (1.008 each) and one oxygen atom (16.00). Their sum, 18.016, is reported as 18.02 g/mol: a sum keeps the fewest decimal places of its terms, and 16.00 has two.

M (H_{2} O) = 2 (1.008) + 16.00 = 18.02 g/mol

\begin{aligned} M (H_{2} O) & = 2 (1.008) + 16.00 \\ = 18.02 g/mol \end{aligned}

Convert grams to moles

Divide by the molar mass by writing it as 1 mol over 18.02 g, so grams cancel. 25.0/18.02 = 1.387…, which is 1.39 mol to three significant figures, the precision of 25.0 g.

25.0 g H_{2} O \times \frac{1 mol H_{2} O}{18.02 g H_{2} O} = 1.39 mol H_{2} O

\begin{array}{c} 25.0 g H_{2} O \times \frac{1 mol H_{2} O}{18.02 g H_{2} O} \\ = 1.39 mol H_{2} O \end{array}

Convert moles to molecules

Multiply by Avogadro’s number. Continue the chain from the measured mass rather than from the rounded 1.39 mol, so rounding happens once, at the end: 1.387… × 6.022 × 10²³ = 8.35 × 10²³ molecules.

25.0 g H_{2} O \times \frac{1 mol H_{2} O}{18.02 g H_{2} O} \times \frac{6.022 \times 10^{23} molecules}{1 mol} = 8.35 \times 10^{23} molecules

\begin{array}{c} 25.0 g H_{2} O \times \frac{1 mol H_{2} O}{18.02 g H_{2} O} \\ \times \frac{6.022 \times 10^{23} molecules}{1 mol} \\ = 8.35 \times 10^{23} molecules \end{array}

Why not multiply 1.39 by 6.022 × 10²³?

1.39 × 6.022 = 8.37, because 1.39 is already rounded. Carrying the unrounded amount, or the whole chain, gives 8.35. The last digit also depends on the constants you use: with the unrounded molar mass, 18.016 g/mol, the chain gives 8.36 × 10²³.

Check the size of the answer

25 g is a little more than one mole of water (18 g), so the count should be a little more than 6 × 10²³. 8.35 × 10²³ fits. Each molecule has three atoms, so the sample holds about 2.51 × 10²⁴ atoms.

Result

25.0 g of H₂O is 1.39 mol, or 8.35 × 10²³ molecules.

Your turn

What is the mass of 0.250 mol of carbon dioxide, CO₂?

Show the answer and explanation

11.0 g.

M(CO₂) = 12.01 + 2(16.00) = 44.01 g/mol. Multiply the amount by the molar mass so moles cancel: 0.250 × 44.01 = 11.0025, which is 11.0 g to three significant figures.

0.250 mol {CO}_{2} \times \frac{44.01 g {CO}_{2}}{1 mol {CO}_{2}} = 11.0 g {CO}_{2}

\begin{array}{c} 0.250 mol {CO}_{2} \times \frac{44.01 g {CO}_{2}}{1 mol {CO}_{2}} \\ = 11.0 g {CO}_{2} \end{array}

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