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In science, engineering, and in fairly common usage, concentration is the measure of how much of a given substance there is in a given mixture of substances.

## Concentration expressions and notation

There are many different notations and quantitative expressions of concentration. The most commonly used expressions are discussed below:

### Mole fraction and mole percent

The mole fraction is a measure of the concentration of a component substance in a mixture of substances. It is defined as the number of moles of a component substance in a mixture divided by the total number of moles of the mixture.

The mole percent or molar percent is usually denoted by mole % and is equal to 100 times the mole fraction.

### Mass fraction and mass percent

The mass fraction is also a measure of the concentration of a component substance in a mixture of substances. It is defined as the mass of a component substance in a mixture divided by the total mass of the mixture. It is most commonly referred to as the weight fraction.

The mass percent is equal to 100 time the mass fraction. It is most commonly referred to as the weight percent and is usually denoted as wt %, weight % or percent by weight.

### Volume fraction and volume percent

The volume fraction is another measure of the concentration of a component substance in a mixture of substances. It is defined as the volume of a component substance in a mixture divided by the total volume of the mixture.

The volume percent is equal to 100 time the volume fraction and is usually denoted as vol %, volume %, % v/v or percent by volume.

### Mass per volume

There are a number of concentration expressions that involve an amount of mass contained in an amount of volume. For example:

### Mole per volume

In chemistry, concentration often indicates what amount of moles is present in a given volume (usually measured in units of litres or cubic metres).

### Parts-per notation

The parts-per notation is used in science and engineering as a measure of the concentration of a component substance in a mixture of substances and usually when the concentration is very small. The most commonly used parts-per notations are:

• Parts per million (ppm): In most countries, 1 million is 1×106 and thus 1 part per million parts (1 ppm) has a numerical value of 1×10-6.
• Parts per billion (ppb): In the United States, 1 billion is 1×109 and thus one part per billion parts (1 ppb) has a numerical value of 1×10-9. This terminology should be used with great caution because
• Parts per trillion (ppt): In the United States, 1 trillion is 1×1012 and thus one part per trillion parts (1 ppt) has a numerical value of 1×10-12. This terminology should also be used with great caution because:
• In the United Kingdom and other nations using British English, France and continental Europe, 1×1012 is 1 billion and 1 trillion is 1×1018
• Concentrations are sometimes expressed as ppt meaning parts per thousand which conflicts with ppt meaning parts per trillion.

The International Organization for Standardization technical standard ISO 80000-1:2009, clause 6.5.5 advocates the use of powers of ten per cubic meter or per kilogram rather than any of the parts-per notation (i.e., ppm, ppb or ppt). Complying with ISO standard would avoid any of the problems associated with the various definitions of billion and trillion in countries other than the United States.

The United States' National Institute of Standards and Technology includes this statement in their NIST Guide to the SI :

Because the names of numbers 109 and larger are not uniform worldwide, it is best that they be avoided entirely (in many countries, 1 billion = 1 × 1012, not 1 × 109 as in the United States); the preferred way of expressing large numbers is to use powers of 10. This ambiguity in the names of numbers is one of the reasons why the use of ppm, ppb, ppt, and the like is deprecated.

Despite the above stated positions of the International Organization for Standardization and the United States' National Institute of Standards and Technology, the technical literature continues to use the parts-per notation quite often. Also, in some cases, the use of the parts-per notation is required by law.

### Molarity, molality and normality

Molarity, normality and molality are terms used in chemistry to denote the concentration of solutes in solutions or solvents.

#### Molarity

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 c with SI units of mol/m3 or other SI acceptable units.. This recommendation has not been universally implemented in academia or chemistry research yet.

#### Normality

Normality, as a concentration term with symbol N, 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. 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 the International Union of Applied Chemistry (IUPAC) now consider that the term normality is obsolete.

#### Molality

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.

## Clarity of notation

Some of the concentration notations must be carefully defined or referenced 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 at stated ambient conditions of temperature and pressure, the concentrations are commonly expressed as μg/m3 or mg/m3 (i.e., μg or mg of particulates per cubic metre of ambient air). Since the concentration of gaseous substances in the air may also be expressed as μg/m3 or mg/m3, it is quite important to state those ambient conditions so that such gaseous concentrations can be converted to ppmv as is sometimes needed.

In fact, when any expression (or notation) is based upon measurements at some standard state or some Reference conditions of gas temperature and pressure, to avoid any possibility of confusion, it is important to clearly state the specific standard or reference conditions rather than simply stating "Standard state" or "Standard conditions" or "STP".

The usage of terminology is generally fixed inside most specific branches of science, leading some workers in those specific sciences to believe that their own terminology is the only correct one. This, in turn, leads them not to clearly define or reference their terminology in their publications and others may therefore misinterpret their results. Many scientific, engineering and other technical publications, that are otherwise excellent, fail to define their usage of the parts-per notation. The difference between expressing concentrations as ppm by volume or ppm by mass or weight is very significant when dealing with gases and it is most important to define 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.