This example problem demonstrates how to convert molarity to parts per million.
A solution contains Cu2+ ions at a concentration of 3 x 10-4 M. What is the Cu2+ concentratrion in ppm?
Parts per million, or ppm, is a measure of the amount of a substance per million parts of solution.
1 ppm = 1 part "substance X"/ 1 x 106 parts solution
1 ppm = 1 g X/ 1 x 106 g solution
1 ppm = 1 x 10-6 g X/ g solution
1 ppm = 1 μg X/ g solution
If the solution is in water and the density of water = 1 g/mL then
1 ppm = 1 μg X / mL solution
Molarity uses moles/L, so the mL need to be converted to L
1 ppm = 1 μg X /( mL solution)x(1 L/1000 mL)
1 ppm = 1000 μg X / L solution
1 ppm = 1 mg X/L solution
We know the molarity of the solution, which is in moles/L. We need to find mg/L. To do this, convert moles to mg.
moles/L of Cu2+ = 3 x 10-4 M
From the periodic table, atomic mass of Cu = 63.55 g/mol
moles/L of Cu2+ = (3 x 10-4 mol x 63.55 g/mol)/L
moles/L of Cu2+ = 1.9 x 10-2 g/L
We want mg of Cu2+, so
moles/L of Cu2+ = 1.9 x 10-2 g/L x 1000 mg/1 g
moles/L of Cu2+ = 19 mg/L
Since 1 ppm = 1 mg/L
moles/L of Cu2+ = 19 ppm
A solution with 3 x 10-4 M concentration of Cu2+ ions is equivalent to 19 ppm.