Information about Parts Per Million

The "parts-per" notations are used to denote low concentrations of chemical elements. Also known as mixing ratios, they are often used to denote the relative abundance of trace elements in the Earth's crust, trace elements in forensics or other analyses, dissolved minerals in water, or pollutants in the environment.

Parts-per notations (in particular ppm) are also used to specify the size of the errors of very precise measurements, such as gas pressure [1], voltage stability [2], and oscillator frequency.

The IEC suggests not to use the part-per notation to avoid misunderstanding. In most countries, a billion is 10¹² (a million²) and a trillion 10¹⁸ (a million³); in the U.S. a billion is 10⁹ and a trillion 10¹² (being a billion in Europe). Nevertheless the notation is still widely used.

Types of Parts-per notations

• Parts per hundred (denoted by "%" and very rarely "pph") — denotes one particle of a given substance for every 99 other particles. This is the common percent, or one part in 10² (100). This is equal to 0.6 second out of a minute, or (864 seconds) 14 minutes, 24 seconds of a day (exactly).
• Parts per thousand (denoted by "‰", the permille symbol, and occasionally "ppt") denotes one particle of a given substance for every 999 other particles. This is roughly equivalent to one drop of ink in a cup of water, or one second per 17 minutes. "Parts per thousand" is often used to record the salinity of seawater. One part in 10³.
• Parts per million ("ppm") denotes one particle of a given substance for every 999,999 other particles. One ppm is equivalent to 1 milligram of something per liter of water (mg/l) or 1 milligram of something per kilogram soil (mg/kg).This is roughly equivalent to one drop of ink in a 150 litre (40 gallon) drum of water, or one second per 280 hours (11 days, 16 hours). One part in 10⁶ — a precision of 0.0001%.
• Parts per billion ("ppb") denotes one particle of a given substance for every 999,999,999 other particles. One ppb represents one microgram of something per liter of water (ug/l), or one microgram of something per kilogram of soil (ug/kg). This is roughly equivalent to one drop of ink in a lane of a public swimming pool, or one second per 32 years. One part in 10⁹.
• Parts per trillion ("ppt") denotes one particle of a given substance for every 999,999,999,999 other particles. This is roughly equivalent to one drop of ink in a shipping canal lock full of water, or one second every 320 centuries. One part in 10¹².
• Parts per quadrillion ("ppq") denotes one particle of a given substance for every 999,999,999,999,999 other particles. This is roughly equivalent to a drop of ink in a medium-sized lake, or one second every 32,000 millennia. Very few analytical techniques can measure with this degree of accuracy; nevertheless, it is still used in some mathematical models of toxicology and epidemiology. One part in 10¹⁵.

Caveats

• Of all the pp variants, ppm is by far the one in most common usage; ppb is also frequently used, particularly in reference to trace gases present in the atmosphere; ppt is sparingly used in the same context. The others are little more than curiosities.
• ppma: parts per million (atomic), is used to indicate the ratio between the number of interesting atoms to ordinary atoms. Usage includes contaminants in semiconductor processing, and isotope abundance.
• Although "ppt" is usually used to denote "parts per trillion", it is also on occasion used to denote "parts per thousand". If there is any chance of ambiguity, one should describe the abbreviation in full.
• Users of ppb and beyond should be aware of the intercultural issues of the Long and short scales and the potential for misunderstandings.

It is a term with several variants in meaning, so the meaning should be made clear if this term is used. In particular, the ratio can be expressed in terms of particle count as above, volume (used in particular for gases) or mass. It can also be used as a mixed term, indicating mass per volume of liquid, as in mg/L, especially where the liquid density approximates that of water.

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.

Examples of parts per notation

The metric system is the most convenient way to express this since metric units go by steps of ten, hundred and thousand. For example, a milligram is a thousandth of a gram and a gram is a thousandth of a kilogram. Thus, a milligram is a thousandth of a thousandth, or a millionth of a kilogram. A milligram is one part per million of a kilogram thus, one part per million (ppm) by mass is the same as one milligram per kilogram. Just as part per million is abbreviated as ppm, a milligram per kilogram has its own symbolic form -- mg/kg, which unlike ppm is unambiguous.

• By mass:
• one milligram in a kilogram is 1 ppm by mass.
• one milligram in a metric tonne is 1 ppb by mass.
• By volume:
• one millilitre (or cubic centimetre) in a cubic metre (or kilolitre) is 1 ppm by volume. For most gases (those behaving much like an ideal gas) this is numerically equivalent to µmol/mol on the basis of molecules (not atoms). See Avogadro's law.
• By mass/volume ratio for dilute aqueous solutions (ppm w/v or ppm m/v):
• 1 litre (L) of water has mass of approximately 1 kg¹, so 1 milligram per litre (mg/L) is, loosely speaking, 1 ppm, and 1 microgram per litre (μg/L) is 1 ppb, for small concentrations in a water solution².
• By number of particles or moles:
• one micromole per mole can also be called 1 ppm.
• one nanomole per mole is 1 ppb.
• one picomole per mole is 1 ppt. This is 6.022·10¹¹ molecules.

Use

Examples of situations where parts per million are an appropriate measure include:

• relative abundances of trace elements in the earth's crust
• concentrations of pollutants in the environment

Inexact analogues

• one square centimeter in 1000 square feet is about .95 ppm
• one two-parent, two-child family in a city of about 4 million people is roughly 1 ppm
• one CD in the 1.57-million disc³ FreeDB catalogue is nearly 0.64 ppm

NIST caution

According to the U.S. National Institute of Standards and Technology (NIST) Guide for the Use of the International System of Units (SI), "the language-dependent terms part per million, part per billion, and part per trillion ... are not acceptable for use with the SI to express the values of quantities." NIST's Guide for the Use of the International System of Units (SI) has examples of alternative expressions. Acceptable SI units are:

1 millimole/mole = 1 part per thousand

1 micromole/mole = 1 part per million

1 nanomole/mole = 1 part per billion

1 picomole/mole = 1 part per trillion

Notes

1. Exactly one kg of pure water at maximum density (~4°C) and standard pressure was the definition of a litre from 1901 to 1964; today the litre is defined as exactly 1 dm³, the only distinction being whether the litre is calibrated to the international standard kilogram or to the  international standard meter, which are defined without reference to one another.
2. Properly speaking it is approximately 1 ppm by mass or by weight in solution. When solids dissolve, they can increase or decrease the total volume they occupy, and even increase or decrease the total volume of the solution. Adding 1 ppm by weight will rarely produce a solution that is 1 ppm by volume to the same precision. The notation ppm w/v or ppm m/v demonstrates the exact nature of the ratio and is therefore the most precise.
3. The definition given above is that parts per notation refers to numbers of particles (equivalent to moles), but the parts per notation can also be used by mass or volume. Those using the notation need to state their usage to avoid confusion.
4. In atmospheric chemistry and in air pollution regulations, the notation is commonly expressed as parts per million by volume (ppmv). This is useful only for gas concentrations (e.g., ppmv of carbon dioxide in the ambient air). For concentrations of non-gaseous substances such as aerosols, cloud droplets, and particulate matter in the ambient air, concentration is commonly expressed as mass per unit volume of air or other gas ( μg/m³ or mg/m³ meaning μg or mg of particulates per cubic metre of ambient air).
5. Note that using "parts per notation" as vol per total vol (ppmv), or any expression where the units in the numerator and denominator are identical, is technically not a concentration (eg. amount of substance per volume). More precisely, this is a mixing ratio. Mixing ratios can not be converted concentrations (eg. mol/volume, mg/L, etc) without additional knowledge of the system. For example to convert 1 ppmv to a concentration (say mol/volume), the pressure and temperature of the system must be taken into account.

See also

• Mole fraction