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.
