Question

Suppose the mole number of Ca2+ ions in a 50 mL water sample is quantified as 1.5 × 10^−5 mol. What is the concentration of Ca2+ ions in the water sample in ppm CaCO3?

Answer 1

The definition of parts per million: 1 g solute per 1,000,000 g solution

Now, divide both values by 1000 to get a new definition for ppm: 0.001 g per 1,000 g solution

or ppm = 1 mg solute per 1 kg solution

Then, for an aqueous solution, we have this definition:

ppm = 1 mg solute per liter of solution

This last definition is based on the fact that most solutions where ppm is used are so dilute that the density of the solution is 1.00 g/mL or 1 kg/L.

Your problem

1.5 × 10^−5 M in Ca2+ ions means 1.5 × 10^−5 M in CaCO3. So, in one liter, we have 1.5 × 10^−5 mole of CaCO3. Let's see how many grams that is:

1.5 × 10^−5 mol times 100.086 g/mol = 0.0015 g

Change 0.0015 g to mg

0.0015 g times (1000 mg / g) = 1.5 mg

1.5 mg / 0.050 L of solution = 30 ppm