# Parts per million - ppm

## ppm - parts per million - commonly used as a unit of concentration

*Parts per million - ppm* - is commonly used as a dimensionless measure of small levels (concentrations) of pollutants in air, water, body fluids, etc.

*Parts per million* is the molar mass, volume or mass ratio between the pollutant component and the solution. *ppm* is defined as

ppm = 1,000,000 c / s

= 10^{6}(1)c / s

where

c = molar mass, volume or mass of component (mole, m^{3}, ft^{3},kg, lb)_{m}

s =molar mass, volume or massof solution(mole, m^{3}, ft^{3},kg, lb)_{m}

In the metric system *ppm* for mass can be expressed in terms of *milligram versus kg* where

1 mg/kg = 1 part per million

*ppm* can be also be expressed as

*1 ppm = 10*^{-6}= 0.0001 % = 0.001 ‰*1 000 ppm = 0.1**%**10 000 ppm = 1%*

Alternatively - mass related units to measure very small concentration levels:

*ppb - parts per billion (1 / 1,000,000,000 or 10*^{-9})*ppt - parts per trillion (1 / 1,000,000,000,000 or 10*^{-12})*ppq - parts per quadrillion (1 / 1,000,000,000,000,000 or 10*^{-15})

An alternatively mass related unit to measure larger concentration levels is *weight percent* which can be expressed as

weight percent = 100 m_{c}/ m_{s}(2)

### ppm vs. Mass per Unit Volume

The concentration of a component can be measured as mass per unit volume - like *mg/liter, mg/cm*^{3} etc.

Weight of substance added to one unit volume of water to give one *part per million (ppm)*

1 ppm

= 2.72 pounds per acre-foot

= 1,233 grams per acre-foot

= 1.233 kilograms per acre-foot

= 0.0283 grams per cubic foot

= 0.0000624 pounds per cubic foot

= 0.0038 grams per US gallon

= 0.058419 grains per US gallon

= 0.07016 grains per Imperial gallon

= 1 milligram per liter (mg/L)

= 1 microlitre ( μL ) per liter

= 0.001 gram per litre

= 8.345 pounds per million gallons of water

#### Example - Volume Concentration of Carbon Dioxide in Air

The concentration of carbon dioxide in air is aprox. *400 ppm*. The volume of carbon dioxide in one *1 m ^{3}* of air can be calculated by modifying

*(1)*to

*c = ppm s / 10^{6} *

* = (400 ppm) (1 m^{3}) / 10^{6} *

* = 0.0004 m ^{3}/m^{3}*

### Percent by Volume

Volume percent can be expressed as volume per unit volume:

percent by volume = 100 v_{c }/(v_{c}+ v_{s}) (3)

where

v_{c}= volume component

v_{s}= volume solvent

### Molarity

Molarity is the number of moles of solute (substance of interest - pollution, etc.) dissolved in one liter (volume) of the solution.

### Molality

Molality is the number moles of solute divided by kilograms of solvent.