Convert Molarity to Parts Per Million Example Problem

Concentration Unit Conversion

Molarity and ppm are expression of concentration of a solution.
Molarity and ppm are expression of concentration of a solution. Sami Sarkis

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 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, 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 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.