# Parts per million - ppm

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

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*Parts per million - ppm* - is commonly used as a measure of small levels (concentrations) 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:

*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

### 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:

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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