Calculating the Concentration in PPM (Parts per Million)

The concentration in ppm (parts per million) is the number of parts of solute dissolved in one million parts of solution.

A concentration of |1\ \text{ppm}| can be written in the following ways.

|1\ \text{ppm}=\dfrac{1\ \text{g}}{1\ 000\ 000\ \text{g}}=\dfrac{1\ \text{g}}{1\ 000\ \text{kg}}=\dfrac{1\ \text{mg}}{1\ \text{kg}}|

When we have an aqueous solution at room temperature, we can also conclude that a concentration of |1\ \text{ppm}| corresponds to the following.

|1\ \text{ppm}\approx \dfrac{1\ \text{g}}{1\ 000\ 000\ \text{mL}}=\dfrac{1\ \text{g}}{1\ 000\ \text{L}}=\dfrac{1\ \text{mg}}{1\ \text{L}}|

Therefore, for an aqueous solution, the mass to mass ratio is approximately equivalent to the mass to volume ratio.

|1\ \text{ppm}=1\ \text{mg/kg}\approx 1\ \text{mg/L}|

However, if the solvent in the solution is not water, the mass to mass ratio and the mass to volume ratio are not equivalent.

The concentration in ppm can be determined using the following formula.
||C=\dfrac{m_\text{solute}}{m_\text{solution}}\times 1\,000\,000||
where
|C| stands for the concentration (ppm)
|m_\text{solute}| stands for the mass of the solute (g)
|m_\text{solution}| stands for the mass of the solution (g)

The concentration in ppm can also be determined by cross multiplication.

At the Sept-Îles wharf, inspectors want to measure the quantity of pollutants released into the water by a commercial ship. In a |100\ \text{L}| volume of water collected near the ship, they found |25\ \text{mg}| of pollutants. What is the concentration in ppm of pollutants near the ship?

Here is the data of the problem. Since the solution is aqueous (the solvent is water), it will be possible to convert the volume into mass, given that |1\ \text{g}| of water corresponds to a volume of |1\ \text{mL}.|

|m_{solute} = 25\ \text{mg} = 0.025\ \text{g}|
|V_{solution} = 100\ \text{L} = 100\ 000\ \text{mL}|
When we know that |1\ \text{mL}| of water has a mass of |1\ \text{g}| at room temperature, we can say |m_{solution} = 100\ 000\ \text{g}|.

Using the formula shown below, the concentration in ppm can be determined.
|C=\dfrac{m_\text{solute}}{m_\text{solution}}\times 1\,000\,000|
|C=\frac{0.025\ \text {g}}{100\,000\ \text{g}}\times 1\,000\,000|
|C=0.25\ \text{ppm}|

The same result can be obtained by cross multiplication.
|\dfrac{0.025\ \text{g}}{100\ 000\ \text{g}} =\dfrac{x}{1\ 000\ 000\ \text{g}}|
|x=\dfrac{0.025\ \text{g} \times 1\ 000\ 000\ \text{g}}{100\,000\ \text{g}}|
|x = 0.25\ \text{ppm}|

There is therefore a |0.25\ \text{ppm}| concentration of pollutant in the water near the ship.