How Many Molecules Are in 36.0 g of Water?

Given

• Mass of water sample: m = 36.0 g

• Molar mass of H2O: M = 18.015 g/mol

• Avogadro's number: N_A = 6.022 x 10^23 mol^-1

Find

The number of water molecules in the sample.

Principle

A mole is the chemist's counting unit: one mole of anything contains exactly 6.022 x 10^23 particles. To count molecules from a weighed mass, first convert grams to moles with the molar mass, then convert moles to molecules with Avogadro's number. Both conversions use factors equal to one, so the chemistry does not change — only the counting unit does.

Formula

Solution

1. Molar mass of water: M(H2O) = 2(1.008) + 15.999 = 18.015 g/mol.

2. Convert grams to moles: n = m / M = 36.0 g / 18.015 g/mol = 1.998 mol of H2O.

3. Convert moles to molecules: N = 1.998 mol x 6.022 x 10^23 mol^-1 = 1.203 x 10^24 molecules.

4. Rounded to three significant figures: 1.20 x 10^24 molecules.

Unit check

Dividing grams by grams-per-mole leaves moles; multiplying moles by particles-per-mole leaves a pure particle count. Every unit cancels except the count of molecules, which is exactly what was asked for.

What this means physically

A mere 36 g of water (about two tablespoons) holds roughly a trillion trillion molecules. That gives a concrete sense of how enormous Avogadro's number is and why chemists weigh chemicals but think in moles.