# Parts per million

Auxiliary unit of measure
Unit name Millionth, English 'parts per million'
Unit symbol ${\ displaystyle \ mathrm {ppm}}$
Formula symbol ${\ displaystyle {\ mathit {p}}}$
Type quotient
definition ${\ displaystyle \ mathrm {1 \, ppm = 1 \, \ cdot 10 ^ {- 6} = 0 {,} 000 \, 001}}$
Named after English parts per million , "shares per million"

One millionth stands for the number 10 −6 and, as an auxiliary unit of measurement, is comparable to the percent (%) for the number 10 −2 and the per mille (‰) for the number 10 −3 .

The English expression parts per million (abbreviated ppm , literally translated as “parts per million”) is also widely used . Due to the high degree of misunderstanding of the terms ppm, ppb and ppt, the use of these terms has been discouraged since 1992.

One ppm is one percent of one percent of one percent or one per mille of one per mille .

## Basics

### parts per million (ppm) and parts per trillion (ppt)

The international standard ISO 31-0 Quantities and units - Part 0: General principles from 1992 recommends avoiding the term ppm. This should especially the risk of misunderstandings with the analog formed terms ppb ( parts per trillion ) and ppt ( parts per quintillion or parts per thousand ) prevention, because trillion and quintillion mean in American usage 10 9 ( trillion , German billion ) or 10 12 ( trillion , German Billion ) - see also long and short scale . Therefore, any information in one of these units should always be interpreted with caution. However, e.g. For example, in the geosciences, the term ppm continues to be widely used, as well as ppb and ppt, particularly in rock analysis.

### conversion

• 10 −20 = 1 hundredth = 1 % - corresponds to 10 ‰ or 10,000 ppm
• 10 −30 = 1 thousandth = 1 - corresponds to 1,000 ppm
• 10 −40 = 1 ten-thousandth = 1 bp ( base point ) - corresponds to 0.1 or 1 or 100 ppm
• 10 −50 = 1 hundred thousandth = 1 pcm ( per cent mille ) - corresponds to 0.01 or 0.1 or 10 ppm
• 10 −60 = 1 millionth = 1 ppm ( part per million ) - corresponds to 0.001 or 0.01
• 10 −90 = 1 billionth = 1 ppb ( part per billion )
• 10 −12 = 1 trillionth = 1 ppt ( part per trillion )
• 10 −15 = 1 billiardth = 1 ppq ( part per quadrillion )

### Mixing ratios

Volume mixing ratios are indicated by a trailing "v" (for volume or volume ) (for example ppmv, ppbv, pptv). The abbreviation vpm is also used for ppmv. The above-mentioned risk of confusion is also given here.

Weight or mass mixing ratios are indicated by a subsequent “w” (for weight ) (examples ppmw, ppbw, pptw). ppmw is related to percent by weight as ppmv is to percent by volume.

## use

### Substance concentrations

A millionth (ppm) corresponds as a mass fraction to one milligram per kilogram , as a volume concentration to one milliliter per cubic meter and as a mole fraction to one micromole per mol .

#### Solid and liquid substances

The ppm is often used in mass spectrometry , e.g. B. to measure the impurities in a pure substance or to specify the accuracy of the measurement (mass accuracy). For the certificate of analysis that is enclosed with a chemical, ppm refers to the mass of the substance. Here, one ppm corresponds to a contamination of 1 µg per gram of the chemical.

In chemistry, the ppm is used when specifying the concentration of aqueous solutions of the dissolved substances. This means that 1 µg of a substance is contained in one gram of the solution or mixture. For the dissolved substances of similar density, 1 ppm means around 1 mg / l. Even with the same density of dissolved substances, only approximately 1 ppm ≈ mg / l applies. Nevertheless, the ppm is still often used incorrectly when specifying the concentration of aqueous solutions. To simplify matters, it is assumed that 1 liter of the aqueous solution has a mass of 1 kg.

#### Gases

For gases, volume fractions are usually considered instead of mass fractions. For example, 8 ppm of carbon monoxide in air means 8 μl of CO per liter of air. Here, too, it is advisable to specify the reference units. According to the ideal gas law, there is always the same number of particles in a gas volume regardless of the size (gravity) of the particles. That is why reference is often made to the particle numbers for gas mixtures with ppm data.

The DFG MAK value commission calculates with a molar volume of 24.1 l at 20 ° C and an (atmospheric) pressure of 1013 hPa (= 1013 mbar). From the equation

• Gas concentration (related to particles) = (molar volume / molar mass) · gas concentration in g / m³

thus arises

• Gas concentration (related to particles) = (0.0241 m³ / mol) / (molar mass) · (gas concentration in g / m³).

A common application is air measurements in environmental protection : If the amount of immission is given as a mass fraction per volume, for example in µg per m³ air, the conversion to ppm is based on the ratio of the number of molecules.

Example: 0.1 µg lead in one m³ of air corresponds to (0.1 · 10 −6  / 207) mol lead in (10 3  / 22.414) mol air. So there are about 10 11 air molecules per lead atom (0.1 µg lead per m³ air corresponds to about 10 ppt lead in air). The following were used for this calculation: molar mass of lead = 207 g / mol and number of moles of gas particles at T = 0 ° C and p = 1 atm per liter = 1 / 22.414 mol (with pV = nRT ).

Despite the ISO rejection, especially when measuring the concentration of natural gas in air, the proportions of the gas are measured with gas concentration measuring devices or gas detection devices in ppm or, in the case of higher concentrations, in percentages or proportions by volume .

The carbon dioxide content of the air is around 410 ppm today. This means that there are 410 molecules of CO 2 for every million molecules in dry air .

### Device accuracy

In geodesy , the accuracy of devices for measuring distances is often given in ppm. The specification is then to be understood as millimeters per kilometer .

### Chemical shift

In NMR spectroscopy, the ppm is used to indicate the chemical shift .

### Error rates

In the automotive industry in particular, failure frequencies (error rates) are expressed in ppm, for example in the case of the electronics in the control units installed . The automakers are demanding strict ppm rates from their suppliers. This means that out of a million control units produced, a maximum of a certain, relatively small number may be defective (see table). The following table is intended to provide an exemplary comparison of the required error rates for a semiconductor manufacturer who installs its processors in both entertainment electronics and the automotive industry:

 Consumer electronics 1000 ppm Automotive industry 20 ppm

### electronics

In electronics, in addition to error rates, temperature or age-dependent changes to the component parameters are specified in ppm. The aging rate ( drift characteristic or aging rate ) indicates the relative change in the characteristics of a component or a component over a certain period of time. For example, 5 ppm / month stands for 5 · 10 −6 / month, i.e. 5 millionths per month.

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