PPM

Parts Per Million (PPM)

A unit of concentration often used when measuring levels of pollutants in air, water, body fluids, etc. One ppm is 1 part in 1,000,000. The common unit mg/liter , is equal to ppm. Four drops of ink in a 55-gallon (208 liters) barrel of water would produce an "ink concentration" of 1 ppm.

       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 = 1,000,000 mc / ms      

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

Alternatively mass related units to measure very small concentration levels used are
ppb - parts per billion (1 / 1,000,000,000)
ppt - parts per trillion (1 / 1,000,000,000,000)

An alternatively mass related unit to measure larger concentration levels are weight percent which can be expressed like
weight percent = 100 mc / ms        
Volume related Concentration Units
Mass per Unit Volume

The concentration of a component can be measured as mass per unit volume as 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

    = 1 microlitre ( μL ) per liter

    = 0.001 gram per litre

    = 8.345 pounds per million gallons of water

Percent by Volume
Volume percent can be expressed as volume per unit volume as
percent by volume = 100 vc /(vc + vs)      
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 dissolved in one kg (mass) of the solution.

Parts per Million by Weight in Water

The concentration in ppm of gas in water is meanly meant by weight. To express this concentration with metric units the density of water is needed. 

The density of pure water has to be by definition 1000.0000 kg/m3 at a temperature of 3.98°C and standard atmospheric pressure, till 1969. Till then this was mean definition for the kilogram. Today's the kilo is defined as being equal to the mass of the international prototype of the kilogram. Water with a high purity (VSMOW) at a temperature of 4°C (IPTS-68) and standard atmospheric pressure has a density of 999.9750 kg/m3. 

The density of water is effected by the temperature, pressure and impurities, i.e. dissolved gasses or the salinity of the water. Even the concerning concentration of gas dissolved in the water is affecting the density of the solution. By nature there's a chance that water contains a certain concentration of Deuterium which influences the density of the water. This concentration is also called the isotopic composition. 

Accurate calculations on these conversions are only possible when the density of the water is measured. In practice the density of water is therefore set to 1.0 ·103 kg/m3. When calculating the conversion with this value you gets: