Two basic sets of units are used by the engineering and science community. They are:
a. US-CS (United States Customary units) (e.g., pounds, inches, degrees Fahrenheit)
b. SI (International System of Units) (e.g., grams, meters, degrees Celsius)
The typical units used depend on the matrix studied.

Concentrations of substances in a solid are generally given as mass of substance per unit mass of solid. For example, the concentration of DDT (a now-banned, but once commonly used insecticide to control the spread of malaria) in the tissue of a bird would be given as m g DDT/kg tissue. The concentration of PCB (a highly chlorinated recalcitrant organic once commonly used for a variety of purposes including as a hydraulic fluid in electric generators) in sediments would be given as mg PCB/kg sediment.
For solids:
1 m g/kg = 1 ppb (part per billion – by weight)1 mg/kg = 1 ppm (part per million by weight)

Concentrations of substances in a liquid (for CEE 1503, that will usually mean water) are generally given as mass of substance per unit volume of solution. Conventional units are mg/L, mg/L, ng/L (mg = milligram, L = liter, mg = microgram, ng = nanogram). Things get confusing when we have to deal with ppm or ppb units. Part of the confusion originates from the definition of ppm or ppb. One should really define ppm (or ppb, ppt, etc.) in terms of whether the units are on a weight (w/w) or volume (v/v) basis, or a combination of the two (w/v or v/w) basis.
Note, the equality:
1 mg/L = 1 ppm (w/v or weight/volume)1 m g/L = 1 ppb (w/v)
does not depend on the specific gravity of the solution.

If we are dealing with ppm (or ppb, etc.) on a weight (w/w) basis, things get a little more complicated. For dilute solutions, where 1 liter of solution weights approximately 1000 g (i.e., the specific gravity of the solution is 1.0) the following set of equivalencies are true.
1 mg/L = 1 g/m3 » 1 ppm (w/w)1 m g/L = 1 mg/ m3 » 1 ppb (w/w)
In some situations, the solution is concentrated or we must deal with a non-aqueous liquid (such as gasoline), the specific gravity may not be equal to 1.0 and
mg/L = ppm (w/w) ´ Specific gravity of the solutionm g/L = ppb (w/w) ´ Specific gravity of the solution
For example, a sediment – water mixture contains 1 m g/L of PCBs (polychlorinated biphenyls). The specific gravity of the sediment – water mixture is 1.06. What is the concentration of PCBs in ppm (w/w)?

For most air pollution work, it is customary to express pollutant concentrations in volumetric terms. For example, the concentration of a gaseous pollutant in ppm units is the volume of the pollutant per million volumes of the air mixture:

One can use the notation (v/v) or by volume to denote that the concentrations are given in volumetric units.
At times, gaseous concentrations are expressed using mixed units of mass per units volume (e.g., m g/m3 or mg/m3). The relationship between ppm (v/v) and mg/m3 depends on the density of the pollutant which depends on its pressure, temperature and molecular weight.
The ideal gas law (PV = nRT, where P = pressure (atm), V = volume (1), n = mass of substance (moles), R = ideal gas constant (0.082 atm L mol-1K-1), T = absolute temperature (°C + 273) in degrees Kelvin) is used to convert units.
Standard temperature and pressure are defined as 1 atm and 0 °C (273 K). Under these conditions one mole of an ideal gas occupies a volume of 22.4 L.

Using Boyle’s Law (PV = constant or P1V1 = P2V2) for constant temperature conditions and Charles’s Law (V/T = constant or V1T1 = V2T2) for constant pressure conditions, we can develop an equation to convert ppm to mg/m3 or visa versa.

Thus, as you raise the temperature of a gas mixture, the volume of the mixture increases. Since the pollutant mass is constant, the concentration in units of mg/m3 must decrease. As you raise the pressure of a gas mixture, the volume of the mixture decreases. Since the pollutant mass is constant, the concentration in units of mg/m3 must increase. (Remember the mass of the pollutant is independent of pressure).

Question: Suppose the average concentration of sulfur dioxide (SO2) is measured to be 400 mg/m3 at 25 °C and 1 atm. Does this exceed the Federal Air Quality Standard of 0.14 ppm (given for 1 atm and 25 °C)?
Solution: The molecular weight of SO2 is (32.06 amu) + 2(16.00 amu) = 64.1 g/mol.
Cppm = 0.15 ppm

Therefore, the Federal Air Quality Standard has been exceeded.