Molarity and parts per million (ppm) are two units of concentration of a chemical solution. This example problem demonstrates how to convert molarity to parts per million.

### Molarity to ppm Problem

A solution contains Cu^{2+} ions at a concentration of 3 x 10^{-4} M. What is the Cu^{2+} 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 10^{6} parts solution

1 ppm = 1 g X/ 1 x 10^{6} 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 Cu^{2+} = 3 x 10^{-4} M

From the periodic table, the atomic mass of Cu = 63.55 g/mol

moles/L of Cu^{2+} = (3 x 10^{-4} mol x 63.55 g/mol)/L

moles/L of Cu^{2+} = 1.9 x 10^{-2} g/L

We want mg of Cu^{2+}, so

moles/L of Cu^{2+} = 1.9 x 10^{-2} g/L x 1000 mg/1 g

moles/L of Cu^{2+} = 19 mg/L

In dilute solutions 1 ppm = 1 mg/L.

moles/L of Cu^{2+} = 19 ppm**Answer:**

A solution with 3 x 10^{-4} M concentration of Cu^{2+} ions is equivalent to 19 ppm.

### ppm to Molarity Conversion Example

You can perform the unit conversion the other way, too. Remember, for dilute solutions, you can use the approximation that 1 ppm is 1 mg/L. Use the atomic masses from the periodic table to find the molar mass of the solute.

For example, let's find the ppm concentration of chloride ions in a 0.1 M NaCl solution.

A 1 M solution of sodium chloride (NaCl) has a molar mass 35.45 for chloride, which you find from looking up the atomic mass or chlorine on the periodic table and noting there is only 1 Cl ion per NaCl molecule. The mass of sodium doesn't come into play, since we're only looking at chloride ions for this problem. So, you know have the relation:

35.45 gram/mole or 35.5 g/mol

You either move the decimal point over one space to the left or else multiply this value times 0.1 to get the number of grams in a 0.1 M solution, to give you 3.55 grams per liter for a 0.1 M NaCl solution.

3.55 g/L is the same as 3550 mg/L

Since 1 mg/L is about 1 ppm:

A 0.1 M solution of NaCl has a concentration of about 3550 ppm Cl ions.