# How to interpret parts-per notations? Is 1 ppb equal to 1 μg/kg?

In an article I recently submitted, a reviewer asked that I provide a concentration in μg/kg instead of ppb (parts per billion), and mentions that the later is not correct. I am not a chemist, and I thought that 1 μg/kg = 1 ppb.

Is 1 ppb equal to 1 μg/kg ? What is a reason to consider ppb as incorrect?

• Just using ppb is ambiguous unless you state the basis (eg w/w for mass %). ppb could also be referring to molar proportion or volume proportion. Commented Apr 15, 2019 at 8:56

You are correct suggesting that 1 μg/kg implies 1 ppb, however the reverse is not true. For instance, 1 ppb can also be 1 nmol/mol, and the reader will never have a chance to deduce which one is it unless you explicitly define the usage of the "parts per something" in the text. This clutters the manuscript with redundant notes and causes overall confusion.

### Recommendations from authoritative sources

IUPAC

IUPAC's “Green Book” lists ppb and related symbols (ppm, ppt, ppb etc.) as deprecated [1, p. 98]:

Although ppm, ppb, ppt and alike are widely used in various applications of analytical and environmental chemistry, it is suggested to abandon completely their use because of the ambiguities involved. These units are unnecessary and can be easily replaced by SI-compatible quantities such as pmol/mol (picomole per mole), which are unambiguous. The last column contains suggested replacements (similar replacements can be formulated as mg/g, μg/g, pg/g etc.).

$$\begin{array}{lllll} \hline \text{Name} & \text{Symbol} & \text{Value} & \text{Examples} & \text{Replacement} \\ \hline \ldots & & & & \\ \text{part per billion} & \text{ppb} & 10^{-9} & \text{The air quality standard for ozone is a} & \pu{nmol/mol} \\ & & & \text{volume fraction of}~\varphi = 120~\text{ppb} & \\ \ldots & & & & \\ \hline \end{array}$$

ISO-80000-1

ISO-80000-1, section 6.5.5 The unit one [2, p.20] stresses out the necessity for the coherent usage of “per” units in general, and prohibits the usage of “parts-per” units:

Abbreviations such as ppm, pphm, ppb and ppt are language-dependent and ambiguous and shall not be used. Instead, the use of powers of 10 is recommended.

European Pharmacopoeia

According to European Pharmacopoeia, section 1.2. OTHER PROVISIONS APPLYING TO GENERAL CHAPTERS AND MONOGRAPHS [3, p. 4], in the absence of context ppm implies mass fraction:

The expression ‘parts per million’ (or ppm) refers to mass in mass, unless otherwise specified.

### Related incident

In 2020-02-26 there was a major accident with both engines stalling on the Airbus aircraft resulting in emergency landing due to the overdose of a biocide fuel additive. A base engineer was not familiar with the term “ppm”, and since the term was not defined in the maintenance manual, he incorrectly used an online calculator, which resulted in overshooting the correct biocide-to-fuel ratio 38 times. The fact that the instructions for two different biocides were not only extremely brief, but also referred to different ppm values by mass and by volume also greatly increased confusion:

Unit standardization

The dosage of biocide required was previously provided in ppm by weight for Biobor® JF and by ppm by volume for Kathon® FP 1.5. There is now industry-wide agreement to use mL/L unit for both Biobor® JF and Kathon® FP 1.5 biocides. Airbus maintenance procedures for all Airbus aircraft, the AMM for A300/A310/A320/A330/A340/A380, MP for A350 aircraft and AMP for A220 aircraft, were updated accordingly by removing the use of the ppm unit.

Luckily, the plane managed to land safely and there were no human casualties. This accident made the aircraft manufacturer to take action against using ppm notation in the future versions of technical documentation, and include transparent definitions for the “parts-per” notations still used in the current service manuals [4, p. 105].

### References

1. IUPAC “Green Book” Quantities, Units, and Symbols in Physical Chemistry, 3rd ed.; Cohen, R. E., Mills, I., Eds.; IUPAC Recommendations; RSC Pub: Cambridge, UK, 2007. (PDF)
2. ISO 80000-2:2009 Quantities and Units – Part 1: General; International Organization for Standardization: Geneva, CH, 2009.
3. Council of Europe; European Directorate for the Quality of Medicines & Healthcare. European Pharmacopoeia, 10th ed.; Council of Europe: Strasbourg, 2019. ISBN 978-92-871-8912-7.
4. Air Accidents Investigation Branch. Report on the Serious Incident to Airbus A321-211, Registration G-POWN at London Gatwick Airport on 26 February 2020; United Kingdom, 2021. (PDF)
• This difficulty with "parts-per" notations should probably be extended to percentages as well (given that, really, 'percent' is just 'parts per hundred'). I can't tell you how many times I've struggled to identify what kind of percentage is meant: % w/w? % w/v? at. %? % v/v? For % v/v, what are the bases? Is 10% one volume A for every 9 volumes of B? For every 10 volumes of B? For 10 volumes of final mixture/solution? Headaches, headaches, headaches, every dang time. Commented Apr 15, 2019 at 19:08
• @ andselisk, I am slightly confused by this new recommendation. My question is related to the denominator in nmol/mols. Suppose I prepare 100 ppb NaCl in water. Do I have 100 nmol of NaCl in 1 mol of water? How we practically prepare it. What if my solvent is a mixture such as air. How will we calculate moles of air? This new definition does not seem to be any better than the previous ones.
– ACR
Commented Apr 15, 2019 at 19:39
• @M.Farooq I'm not sure I understand, and this is not a novel directive, part-per-somehing has never been a favored/preferred notation as long as I remember myself. ppb is just a fraction, use whatever quantities of the same dimensions; you have to find out the amounts to calculate ppb anyways, why is this suddenly a problem? Commented Apr 15, 2019 at 19:49
• @andselisk, I am actually wondering about different scenarios. There is a very subtle difference in using nmol/mol vs. ug/kg. The typical definition of ppb is ug X in a kg of solution not the solvent. 100 ppb NaCl in water mean 100 ug NaCl "in" 1 liter of water solution. The total volume is 1 L. The analyte is a part of the solvent weight. With 100 ppm NaCl as 100 nmol NaCl dissolved in 1 mol water. In this case, NaCl is not a part of solvent. Similarly if I have a mixture as a solvent, whose moles should we use? The 1 L and kg definition do not care about the identity of the solvent system.
– ACR
Commented Apr 15, 2019 at 20:38
• @M.Farooq There are commonly used unambiguous quantities such as molar concentration for solutions, volume fraction for gas mixtures, molality if you want to use only the mass of the solvent etc. ppb and Co. is ambiguous, harder to use in calculations with units and always requires extra annotations. What's the point of making own life's harder? I'm sorry, but maybe you might want to ask a new question as I'm not getting what the problem here really is. Commented Apr 15, 2019 at 20:48