Avogadro's Number Example Chemistry Problem

Question: Calculate the mass in grams of 2.5 x 10⁹ H₂O molecules.

Solution

Step 1 - Determine the mass of 1 mole of H₂O

To obtain the mass of 1 mole of water, look up the atomic masses for hydrogen and oxygen from the Periodic Table. There are two hydrogen atoms and one oxygen for every H₂O molecule, so the mass of H₂O is:

mass of H₂O = 2 (mass of H) + mass of O
mass of H₂O = 2 ( 1.01 g ) + 16.00 g
mass of H₂O = 2.02 g + 16.00 g
mass of H₂O = 18.02 g

Step 2 - Determine the mass of 2.5 x 10⁹ H₂O molecules

One mole of H₂O is 6.022 x 10²³ molecules of H₂O (Avogadro's number). This relation is then used to 'convert' a number of H₂O molecules to grams by the ratio:

mass of X molecules of H₂O / X molecules = mass of a mole of H₂O molecules / 6.022 x 10²³ molecules

Solve for mass of X molecules of H₂O

mass of X molecules of H₂O = ( mass of a mole H₂O · X molecules of H₂O ) / 6.022 x 10²³ H₂O molecules

mass of 2.5 x 10⁹ molecules of H₂O = ( 18.02 g · 2.5 x 10⁹) / 6.022 x 10²³ H₂O molecules
mass of 2.5 x 10⁹ molecules of H₂O = ( 4.5 x 10¹⁰) / 6.022 x 10²³ H₂O molecules
mass of 2.5 x 10⁹ molecules of H₂O = 7.5 x 10^-14 g.

Answer

The mass of 2.5 x 10⁹ molecules of H₂O is 7.5 x 10^-14 g.