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Parts per million

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Overview

The concentration in parts per million can be expressed as:

Concentration in parts per million is equal to mass of solute divided by total mass of solution and multiplying the resultant by 10 raise to the power 6.
Concentration in parts per million is equal to mass of solute divided by total mass of solution and multiplying the resultant by 10 raise to the power 6.

In the above equation we are multiplying by 106 because that is what a million is. Note that it is important to use the same units of mass for each substance.

Remember that for water based solutions 1 mL of water has a mass of 1g and 1 L has a mass of 1000g.

Example

What is the concentration, in ppm, when 2g of a pollutant is dissolved in 1L of water?

The video below shows the systematic approach to solving the above problem.

Audio icon This video contains sound.

The process of solving problems like these can be simplified by following a series of steps.

The first step is to extract from the problem statement the information that has been provided and the information being asked for.

The information we are provided with is:

We have 2 grams of pollutant and 1 Litre of water.

The information we are asked for is:

Concentration in parts per million of the solution resulting from dissolving pollutant in water.

The second step is to identify the formula to find out the information being asked for.

In this problem we are being asked to find concentration in parts per million or ppm. The formula to calculate concentration in ppm is:

Concentration in parts per million is equal to mass of solute divided by total mass of solution and multiplying the resultant by 10 raise to the power 6.

The third step is to match the information provided in the problem statement with the formula. As pollutant is dissolved in water, therefore pollutant is the solute i.e. 2 grams and water is the solution i.e. 1 litre.

The fourth step is to ensure that the information being used in the formula is in the correct units. When calculating concentration in ppm, the units of mass of both solute and the solution should be the same. This isn�t the case here as the pollutant is in grams and water is in litres. Water needs to be converted from litres to grams.

1 litre has a mass of 1000 grams, therefore mass of water in grams is 1000.

Now that we have both the pollutant and water in grams, we go ahead with the calculations. We get:

Therefore the concentration in parts per million is 2000 which is our answer.