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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 mc / ms  

       = 106 mc / ms                                          (1)

where

mc = mass of component (kg, lbm)

ms = mass of solution (kg, lbm)

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 mc / ms                                  (2)

ppm vs. Mass per Unit Volume

The concentration of a component can be measured as mass per unit volume - like mg/liter, mg/cm3 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 = 106 vp / vm                               (3)

where

vp = volume pollutant (m3, ft3)

vm = volume mixture or solution (m3, ft3)

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 m3 of air can be calculated by modifying (2) to

vp = ppm vm / 106 

    = (400 ppm) (1 m3) / 106

    =  0.0004 m3/m3

Percent by Volume

Volume percent can be expressed as volume per unit volume:

percent by volume = 100 vc /(vc + vs)                               (4)

where

vc = volume component

vs = 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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