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(This needs a lot of work)

In science, engineering and often in common usage, concentration is the measure of how much of a given substance there is mixed with another substance.

Notation
There are a number of different ways to quantitatively express concentration, including those listed below:

Molarity, molality and normality of liquid solutions

 * Molarity or molar concentration (in units of mol/L) denotes the number of moles of a given solute per litre of solution. The units of mol/L are commonly replaced by the symbol M. The National Institute of Standards and Technology (NIST) of the United States considers the term molarity and the symbol M to be obsolete and recommends using the term amount-of-substance concentration of B (or concentration of B) and the symbol cB with SI units of mol/m3 or other SI acceptable units. . This recommendation has not been universally implemented in academia or chemistry research yet.


 * Molality or molal concentration (in units of mol/kg) denotes the number of moles of solute per kilogram of solvent (not solution). The units of mol/kg are commonly replaced by the symbol m (not to be confused with symbol m for metre). NIST also considers the term molality and the symbol m to be obsolete and recommends using the term molality of solute B and the symbol bB or mB with SI units of mol/kg or other SI acceptable units.


 * Normality, as a concentration term, has been used for decades in chemistry. In solution, salts are dissociated into reactive solute species (ions such as H+, Fe3+, or Cl-). A normal solution has one gram equivalent of a solute ion per liter of solution. The definition of a gram equivalent depends on the type of solute: acid, base, redox species, or ions that will precipitate. It is critical to note that normality measures a single ion which is part of an overall solute. For example, one could determine the normality of the hydroxide ion or sodium ion in an aqueous solution of the overall solute sodium hydroxide (NaOH), but the normality of sodium hydroxide itself has no meaning. However, both NIST and

Mole fraction
The mole fraction Χ, (also called molar fraction) denotes the number of moles of a component as a proportion of the total number of moles. The mole percentage or molar percentage, denoted "mol %" and equal to 100% times the mole fraction, is sometimes quoted instead of the mole fraction.)

Mass percentage and mass fraction)
Mass percentage denotes the mass of a substance in a mixture as a percentage of the mass of the entire mixture.

"Parts-per" notation
The parts-per notation is used in some areas of science and engineering because it does not require conversion from weights or volumes to more chemically relevant units such as normality or molarity. It describes the amount of one substance in another. It is the ratio of the amount of the substance of interest to the amount of that substance plus the amount of the substance it is in.


 * Parts per hundred (denoted by '%' [the per cent symbol], and very rarely 'pph') - denotes the amount of a given substance in a total amount of 100 regardless of the units of measure as long as they are the same. e.g. 1 gram per 100 gram. 1 part in 102.


 * Parts per thousand (denoted by '‰' [the per mille symbol], and occasionally 'ppt', though this should be avoided) denotes the amount of a given substance in a total amount of 1000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per gram, or 1 gram per kilogram.  1 part in 103.


 * Parts per million ('ppm') denotes the amount of a given substance in a total amount of 1,000,000 regardless of the units of measure used as long as they are the same. e.g. 1 milligram per kilogram.  1 part in 106.


 * Parts per billion ('ppb') denotes the amount of a given substance in a total amount of 1,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per tonne.  1 part in 109.


 * Parts per trillion ('ppt') denotes the amount of a given substance in a total amount of 1,000,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per kilotonne. 1 part in 1012.


 * Parts per quadrillion ('ppq') denotes the amount of a given substance in a total amount of 1,000,000,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per megatonne. 1 part in 1015.

Clarity of notation
The notation is used for convenience and the units of measure must be denoted for clarity though this is frequently not the case even in technical publications.

In atmospheric chemistry and in air pollution regulations, the parts per notation is commonly expressed with a v following, such as ppmv, to indicate parts per million by volume. This works fine for gas concentrations (e.g., ppmv of carbon dioxide in the ambient air) but, for concentrations of non-gaseous substances such as aerosols, cloud droplets, and particulate matter in the ambient air, the concentrations are commonly expressed as μg/m³ or mg/m³ (e.g., μg or mg of particulates per cubic metre of ambient air). This expression eliminates the need to take into account the impact of temperature and pressure on the density and hence weight of the gas.

The usage is generally quite fixed inside most specific branches of science, leading some researchers to believe that their own usage (mass/mass, volume/volume or others) is the only correct one. This, in turn, leads them not to specify their usage in their research, and others may therefore misinterpret their results. For example, electrochemists often use volume/volume, while chemical engineers may use mass/mass as well as volume/volume. Many academic papers of otherwise excellent level fail to specify their usage of the part-per notation. The difference between expressing concentrations as mass/mass or volume/volume is quite significant when dealing with gases and it is very important to specify which is being used. It is quite simple, for example, to distinguish ppm by volume from ppm by mass or weight by using ppmv or ppmw.