A student weighs out 6.84 g of sucrose, C12H22O11. How many molecules of sucrose are present in this sample? (Molar masses: C = 12.0 g/mol, H = 1.0 g/mol, O = 16.0 g/mol; Avogadro constant = 6.02 × 10^23 mol^-1)

Correct answer

A. 1.20 × 10^22

Principle or equation

The number of entities (molecules) in a sample is calculated by first converting the mass to moles using the molar mass, then multiplying by Avogadro's constant. The molar mass of a compound is the sum of the atomic masses of all atoms in its formula.

Why this answer is correct

Calculate the molar mass of sucrose: C12H22O11 has 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms. Molar mass = 12(12.0) + 22(1.0) + 11(16.0) = 144.0 + 22.0 + 176.0 = 342.0 g/mol. Moles of sucrose = mass / molar mass = 6.84 g / 342.0 g/mol = 0.0200 mol. Number of molecules = moles × Avogadro constant = 0.0200 mol × 6.02 × 10^23 mol^-1 = 1.204 × 10^22, which rounds to 1.20 × 10^22.

Example

For a 0.100 mol sample of water, the number of molecules is 0.100 × 6.02 × 10^23 = 6.02 × 10^22.