The parts per million, and in general "parts per *notation*«, is a pseudo unit of measure used to describe relational phenomena such as «parts of a whole», for example concentrations. Specific, **one ppm represents 1 part of a million, that is 1/1000000 or 1×10 ^{-6}**:

It is similar to the concept of percentage. 1% would be a part of 100 (10^{two}) while 1 ppm would be a part of 10^{6}. The equivalence between percentage and ppm is as follows:

EITHER

A very important characteristic of parts per million is that they are **ratios or fractions between two values without a unit of measure that relates them**, that is, it is a direct quantity-for-quantity comparison. In this sense, **ppm is not recognized in the International System of Units** (YES), as the percentages are not either.

For example, an SI concentration of 1 mg/kg would be equivalent to a concentration of 1 ppm, since one mg is one millionth of 1 kg.

## Examples of use: measurement of concentrations

The most common use of ppm is in chemical analysis for the measurement of very dilute concentrations. It is also used in other fields of science, for example in physics and engineering, to **express the measure of some proportional phenomena**. Below we will see some of the most common usage examples.

### mass ppm/mass

The concentration in parts per million expressed as mass/mass is calculated by dividing the mass of the solute (m_{s}) divided by the mass of the solution (m_{d}sum of the mass of the solute and the mass of the solvent), both expressed in the same unit and multiplied by 10^{6} (1 million). It is usually named as ppmm:

For example, we can express both masses in grams. If to 1500 g of water we add 0.01 g of a solute:

C_{ppm} = ( 0.01 / 1500.01 ) × 10^{6} = **6.66 ppm**

Therefore, a solution of 0.01 g in 1500 g of solvent has a concentration of 6.67 ppm. In the SI it would be equivalent to a concentration of 6.66 mg/kg (1 ppm = 1 mg/kg).

As most of the times that parts per million are used, the solute is very diluted, it is common to neglect it in the denominator and simply divide the mass of the solute by the mass of the solvent.

If we do not know the mass of the solvent but do know its volume and density, we can calculate the mass as the volume times the density, since the density (ρ, kg/m^{3} in SI) is:

Remember that if the solvent is water, the density is practically equal to 1 kg/L, which means that 1 L of water has a mass approximately equal to 1 kg. Therefore, if 1 ppm = mg/kg, in the case of water it would be equivalent to 1 mg/L.

### ppm by volume/volume

The expression of a concentration in parts per million volume-volume is similar to the expression mass-mass. It is obtained by dividing the volume of solute (V_{s}) divided by the volume of the solution (V_{d}volume of solute plus volume of solvent) and multiply by 10^{6}. It is usually named as ppmv:

For example, if we dissolve 1 ml of acetone in 2 L of water (2 L = 2000 ml):

C_{(volume/volume)} = ( 1 / 2001 ) x 10^{6} = 499.75 ppmv

In the International System of Units it would be equivalent to 499.75 μl/L (1 ppm = 1 μl/L), since a μl is one millionth of 1 L.

One of the most common examples of the use of parts per million by volume/volume is for **measure concentrations in the air**. For example, in this news it can be read as the average concentration of CO_{two} in the Earth's atmosphere it exceeded 400 ppm. This means that each liter of air contains 400 μl of CO_{two}or what is the same, that 0.04% of the atmosphere is CO_{two} (remember that 1 ppm = 0.0001%).

### ppm mass/volume

Concentration is often expressed as the mass of solute in a given volume of solution. Parts per million by mass/volume are calculated by dividing the mass of the solute in grams by the volume of solution in milliliters and multiplying by 10.^{6}:

What would be equivalent to the mass of the solute in mg divided by the volume in liters:

In the case of water, or any other solvent with a density equal to 1 kg/L, we know that 1 kg has a volume of 1 L. For other solvents we can obtain their volume in liters if we know their mass and density. For example, we have 0.5 mg of solute and 0.2 kg of a solvent with a density of 0.95 kg/L. The volume in liters of the solvent would be:

V = 0.2 / 0.95 = 0.21L

And the concentration in ppm mass/volume would be:

C _{(mass/volume}) = 0.5 / 0.21 = 2.38 ppm

## Relationship with other parties *notation*

Name | Notation | Coefficient |
---|---|---|

Percent | % | 10^{-two} |

Per thousand | ‰ | 10^{-3} |

Parts per million | ppm | 10^{-6} |

parts per billion | ppb | 10^{-9} |

parts per trillion | ppt | 10^{-12} |