# Parts per million - ppm

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

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

Parts per million is the mass ratio between the pollutant component and the solution and ppm is defined as

ppm = 1000000 m_{c}/ m_{s}

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

where

m_{c}= mass of component (kg, lb_{m})

m_{s}= mass of solution (kg, lb_{m})

In the metric system ppm 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 used are

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 are weight percent which can be expressed like

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 as 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

### ppm vs. Volume Pollutant per Volume Mixture

*ppm = 10^{6} v_{p} / v_{m} (2)*

*where*

*v _{p} = volume pollutant (m^{3}, ft^{3})*

*v _{m} = volume mixture or solution (m^{3}, ft^{3})*

#### 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

*(2)*to

*v _{p} = ppm v_{m} / 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 as

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.

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