Convert Molarity to Parts Per Million Example Problem

Molarity and parts per million (ppm) are two units of measurement used to describe the concentration of a chemical solution. One mole is equivalent to the molecular or atomic mass of the solute. Parts per million, of course, refers to the number of molecules of solute per million parts of a solution. Since both of these units of measurement are commonly referred to in chemistry, it's helpful to understand how to convert from one to the other. This example problem demonstrates how to convert molarity to parts per million.

Molarity to ppm Problem

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

Solution

Parts per million, or ppm, is a measure of the amount of a substance per million parts of a 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, the 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
In dilute solutions 1 ppm = 1 mg/L.
moles/L of Cu²⁺ = 19 ppm

Answer

A solution with 3 x 10^-4 M concentration of Cu²⁺ 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 of 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 now 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 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.