Convert Molarity to Parts Per Million Example Problem

This example problem demonstrates how to convert molarity to parts per million.

Problem:

A solution contains Cu²⁺ ions at a concentration of 3 x 10^-4 M. What is the Cu²⁺ concentratrion in ppm?

Solution

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⁺ = 1.9 mg/L

Since 1 ppm = 1 mg/L

moles/L of Cu²⁺ = 1.9 ppm

Answer:

A solution with 3 x 10^-4 M concentration of Cu²⁺ ions is equivalent to 1.9 ppm.