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2017 Newsletter Article 4, Textbooks and the SI Base Units. A Challenge for Authors and Editors.


Peter F. Rusch


The vast number of chemistry textbooks and their many revisions provide opportunity for advancing the fundamentals of chemistry.  Among those fundamentals are the SI (Système International) Base Units for: time; length; mass; thermodynamic temperature; electrical current; intensity of light; and amount of substance.  All of these are significant in the practice of chemistry.

Presently, an international effort is underway to redefine each of the SI Base Units.  Led by the International Committee on Weights and measures (CIPM), there is a growing consensus on the new definitions with the prospect of their formal adoption by the next General Conference on Weights and Measures (CGPM) in 2018. Originally, the SI Base units were based on physical observations of terrestrial phenomenon to which anybody could relate.  The revised definitions are all based on physical constants considered to be invariants of nature.

How these new definitions will be represented in chemistry textbooks is an open question with few authors and editors aware of the forthcoming changes.

The present system of physical units has developed over the last two centuries.  Originally, the important units for science and commerce were weights and measures.  Indeed, those remain in the names of the relevant organizations that are responsible for units.

Prior to the French Revolution, there were thousands of different weights and measures in what we know as Western Europe.  Never mind those in other parts of the world most of which were unknown to the French revolutionists.  As a part of that great upheaval, it was decreed that there would be a single system of weights and measures in the new republic.  Science was highly developed in France and the scientists were charged with the development of this “universal” system.  From these beginnings came the present and widely-accepted SI (Système International).

For measures, the meter was defined as 10-7 (or one ten-millionth) of a quadrant of the Earth’s circumference.  Happily, such a quadrant (one-fourth of a great circle of the Earth) ran through France from Dunkirk on the north coast to Barcelona just outside southern France.  Measuring this distance and calculating that fraction of the measured quadrant was left to the surveyors who had at their disposal a highly accurate method of measuring angles.  Starting with a single linear measurement of the base of a single triangle two teams set out to measure hundreds of triangles across France on the way between Dunkirk and Barcelona.  They met near the town of Rodez.  All that remained was to calculate the linear distance using simple trigonometry.  Thus, the meter (or metre) was based on the dimension of the Earth and was easily understood.

For weight the kilogram was defined as a cubic decimeter of water at 4°C that was known to be the temperature of greatest density of water.  Interestingly, the kilogram depended on the meter as it was necessary to have that linear measurement to determine the volume of water.  How could this be done as the meter itself was not yet known?  Each of the units, meter and kilogram, were determined as “provisional” until the calculation of the meter was completed.  Thus, the kilogram was based on a terrestrial phenomenon that was easily understood.

We now recognize the seven SI Base Units shown in figure 1.

Figure 1. SI (Système International) Base Units

In the late 1700’s prototypes of the meter and kilogram were rendered as a durable objects made of metal.  They were deposited in the archives of the French Republic in December 1799.  In May 1875, seventeen countries signed the Metre Convention that established the International Bureau of Weights and Measures (BIPM)[1].  In 1921 the convention was extended to all physical measurements.  The United States of America was one of the original signers of the Metre Convention.  Now, more than fifty countries are members of this convention.

Later, forty standard kilograms were produced using a platinum-iridium allow and each measuring 39 mm in diameter and 39 mm in height.  They were cast in London by George Matthey and were “hammered, polished and adjusted” to match the kilogram in the French archive.  In 1889, 34 of these “witnesses“ were distributed while six remained in France.  In 1890, K4 and K20 arrived in the US where K20 was designated the primary standard kilogram for the US.

Following the distribution of the standard kilograms it was decided to return them periodically to France for comparison to the standard kilogram referred to as “le Grand K.”  Results of these comparisons are shown in Figure 2.




Figure 2. Comparison of standard kilograms to le Grand K.


Because le Grand K is the standard, it is always used as the reference; le Grand K is at the top of the hierarchy of standard kilograms.  The results clearly show that the mass of the witnesses is changing relative to le Grand KThere is the possibility that le Grand K itself is changing mass but it cannot be compared to any other mass as it is the standard.  It is this consistent drift over time that has led to the proposal to eliminate the “artefact” know as le Grand K.

Redefining the kilogram by eliminating le Grand K requires some other basis for the definition of the kilogram.  Since 1968 the definition of the second has been based on the radiation of the 133Cs atom.  Since 1983, the meter has been defined on the speed of light.  In each case, the definition is a physical constant believed to be an invariant of nature.  Prompted by the need to redefine the kilogram, all SI Base Units will be defined on invariants of nature.  Consensus values for the constants will be adopted as exact values with uncertainty.

While all seven SI Base Units are of importance in the practice of chemistry, the new definitions of the kilogram, kelvin and mol required particular attention as they are more complicated to understand and teach.

Unit of amount of substance (mole)

In 1971 the following definition was adopted:

  1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is “mol.”
  2. When the mole is used, the elementary entities must be specified and may be atoms, molecules ions, electrons, other particles, or specified groups of such particles.

This is the current definition of the mole that will be replaced.  The definition is based on the agreement that the mass of an atom of carbon-12 is exactly 12 and that agreement is enshrined in the definition.  All atomic and molecular weight measurements are referenced to this exact number by definition.

It’s a well-known chemistry fact that Avogadro’s number (or the Avogadro constant) is related to this definition.  Accordingly, the proposed redefinition uses the Avogadro constant as an invariant of nature:

  • The mole is the unit of amount of substance of a specified elementary entity which may be an atom, molecule, ion, electron, other particle or specified groups of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly  6.022 141…x 1023 when it is expressed in the unit mol-1.

This might be an easier way to introduce the Avogadro constant as it will be the basis of the definition of the mole.  What is lost is the fundamental concept of the mass of an atom of carbon-12 is exactly.  Most likely the agreement on the mass of carbon-12 will remain fundamental in chemistry even though it is lost in the proposed definition of the mole.

Much discussion has led to the belief that “amount of substance” is an ambiguous and inappropriate term for the mole concept.  Most likely the term “chemical amount” or “amount of chemical substance” will gain favor.  This, too, may be clarifying and pedagogically more pleasing.

Unit of thermodynamic temperature (kelvin)

Presently, the definition is:

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Once again there is a terrestrial phenomenon used to define the SI Base Unit.  It is easily understood and realized.  For consistency however, there is a problem: Exactly what is water?  It is known that for most elements the distribution of the stable isotopes is not consistent throughout the world.  Accordingly, in 2005 the definition was enriched:

This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios:  0.000 155 76 mole of 2H per mole of 1H, 0.000 379 9 mole of 17O per mole of 16O, and 0.002 005 2 mole of 18O per mole of 16O.

The proposed definition is:

The kelvin, K, is the unit of thermodynamic temperature its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380 65… 10-23 when it is expressed in the unit s-2 m2 kg K-1, which is equal to J K-1.

The proposed definition has the advantage of not requiring a further definition of water.  It has the disadvantage of explaining the Boltzmann constant and visualizing just how that defines thermodynamic temperature.

Comparison of the present and proposed definitions of thermodynamic temperature provides an opportunity to illustrate the concept of “mise en practique” so important to the SI Base Units.  Roughly translated it means put into practice.  It is imperative that we convey the notion that mise en practique is entirely separate from the definition.

Note that the present definition provides the mise en practique; obtain the correct, isotopically balanced water and lower the temperature until ice appears.  Under normal atmospheric pressure that’s the triple point of water.

With the proposed definition, there is no such guidance.  What is the experiment or procedure that will relate in a practical way the Boltzmann constant to thermodynamic temperature?



Author’s Note – Presented at the ACS National ACS Meeting in San Francisco April 3, 2017


[1] “BIPM is an intergovernmental organization under the authority of the General Conference of Weights and Measures (CGPM) and the supervision of the International Committee for Weights and Measures (CIPM)”

05/01/17 to 05/03/17


Hi, Peter,

Can you tell us anything about how the standard kilograms are stored?  Are they all stored in the same way?  How are they handled?  What kind of variation is there in the handling of the standards?  I'm trying to understand what might be causing these minute but systematic variations in their masses.


As you may know, the IPK (international prototype of the kilogram) is stored at BIPM under vacuum insided triple bell-jars.  I don't know for sure but believe that the other "copies" or "witnesses" are stored similarly.

Roy Jensen's picture

And every time they are compared, there is considerable drift. I can't find the article I recently read, but you have a picture in your post that illustrates this drift.


Bob Belford's picture

Hi Peter,

First, I would like to thank you for sharing this paper with us and giving us a chance to discuss such an important topic.  I actually have two questions.

First, you state, "Prompted by the need to redefine the kilogram, all SI Base Units will be defined on invariants of nature. Consensus values for the constants will be adopted as exact values with uncertainty."

What is meant by "exact values with uncertainty".  I thought uncertainty was a property of inexact values.  For example, the number of letters in this sentence is an exact value, with no uncertainty. But once printed, the weight of the ink has uncertainty, and is an inexact value.  Do you mean, it is an exact value with an agreed upon number of significant digits?

Second, and please forgive me if I am missing the obvious, but I thought the new definition of the Kilogram was based on Planck's constant, but I am not seeing that in the article.   



I understand the interest in defining the SI base units in terms of “physical constants believed to be invariant of nature”, but I wonder if it will make a difference in real-world measurements. For example, are there ways to determine temperature that would yield different values based on the current and proposed definitions of the kelvin? In other words, at least for temperature, is this an abstract exercise with no practical effect?

I also find it curious that the definitions are based in part on defining nature’s constants as exact, even though we don’t know what the exact values are. For example, the kelvin would be described as, “The kelvin, K, is the unit of thermodynamic temperature its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380 65… 10-23 when it is expressed in the unit s-2 m2 kg K-1, which is equal to J K-1.” Wikipedia says that the Boltzmann constant is 1.38064852(79)×10−23 J/K. If this value (or some other more accurate value) is used to calibrate temperature measuring instruments, what happens to this calibration when we develop ways to determine the constant more accurately? Are we still stuck with the problem of a drifting definition?

Mark Bishop

In effect, yes, this is an abstract exercise regarding the practice of chemistry as we know it. Keep in mind that there is to be a continuity; the kelvin will remain what it is today.  Only the definition will change.   Also, yes, there is experimental error in measurements and the several values for the Boltzmann constant is exactly what one expects.  Part of the new definitions is that a single value will be selected by CODATA based on the best measurements.  There will be no drifitng values unless and until someone somewhere raises the isse.  The metrologists pont out that once the speed of light was selected to define the meter (metre) no one was interested in measuring it any more.   

If the definition of kelvin changes, how can the "kelvin...remain what it is today", or do you mean the the "kelvin will stay essentially the same to the limits of our ability to measure temperature"? Is the Boltzmann constant going to be defined to keep the kelvin the same??? If so, does this mean that the Boltzmann constant used in the definition (which may be the best value available) will be defined as a value that is almost certainly not the exact value for the true Boltzmann constant? Doesn't that defeat the purpose of defining the base units in terms of constants that are assumed to be invariant? If I understand the plan, wouldn't it be more true to define the kelvin as, "“the unit of thermodynamic temperature for which the magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380 65 10-23 (which is close to the true value of the Boltzmann constant) when it is expressed in the unit s-2 m2 kg K-1, which is equal to J K-1.” If the number associated with the Boltzmann constant is going to be fixed with an exact value, why are there dots in the number in the definition (1.380 65... 10-23)? Can we assume that at some point the kelvin would be redefined using a more accurate value for the Boltzmann constant that may be determined in the future?

One of the things I do is edit scientific papers for Chinese scientists who want to publish in English-language journals, and the editor in me really doesn't like the "its" in the kelvin definition. Note that I substituted "for which the" for "its".

Mark Bishop

The new definitions do not change the SI Base Units; the kilogam is still a kilogram; one degree kelvin is still one degree kelvin.  The exact values of the fundamental constants used in the definitions will be consensus values that will be accepted as "true" values for the purpose of the defintions.  As these values are not yet accepted by the International Conference on Weights and Measures that will meet in 2018, the dots appear to indicate present uncertainty in the value. 

The science of metrology is all about traceability and uncertainty.  Usually the variety of measurements of any physical constant group around a central value; often these values are assumed to be in a Gaussian distribution.  Once the value of each of the defining physical constants is selected it will be assumed to have no uncertainty.  Similar to the mass of carbon-12 that is 12.0000000000000...  Each value will have it's own number of significant digits.  The currently proposed values are listed in the draft of NISTS's Brochure 9  for the SI. It's in draft as the values are fully accepted by the International Conference on Weights and Measures that willmeet in 2018.  

You are correct.  I don't know how that could be missed in the paper., 


The kilogram, kg, is the unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly 6.626 068… x 10-34 when it is expressed in the unit s-1 m2 kg, which is equal to J s. 

SDWoodgate's picture

I think that the new definition of the mole will be easier to teach.  It was always a bit of a stretch to get students to grasp that the number of particles in a mole of substance was the same as in 12 g of carbon-12.  It is much better to tell them the number.  Personally I like the term chemical amount because we use mol in a more general way than just for substances as in kJ per mol of reaction for enthalpy changes.

Yes, it's useful to bring the value of the Avagadro constant into the definition of the mole.  What is lost in doing so is the basis of the atomic mass scale of carbon-12 as exactly 12.00000... as it is no longer part of the definition.  It's a small matter as the uncertainty introduced in the mass of carbon-12 makes little difference in the practice of chemistry.   

Hi Peter,

Thanks for sharing your paper.

I am afraid I found two items in this paper that require a correction. If I'm wrong, please let me know.

The first item is Fig. 1. I think capitalization of unit names does not agree with SI specifications. As far as I now, the 7 basic units names must be in lower case, except for electrical current A and temperature T

The second item is statement "Under normal atmospheric pressure that’s the triple point of water". I think the triple point has nothing to do with atmospheric pressure; indeed, pressure is one of the two parameters that make up the triple point (the other is temperature).

I too do not understand what is meant by the statement: "Note that the present definition provides the mise en practique; obtain the correct, isotopically balanced water and lower the temperature until ice appears.  Under normal atmospheric pressure that’s the triple point of water."

This quote means that the present definition of thermodynamic temperature is a fraction of the triple point of water.   That definition also provides the means of achieving the definition, the mise en practique.  The new definnition uses the Boltzmann constant and does not also contain the mise en practique.  Indeed, all of the new definitions are independent of their respective mise en practique.  My concern about the redefinition of the kiogram is that the new definition presently relies on the use of a Watt balance that is a method of achieving the definition.  In my view, that's not the stated intention of the new definitions;  they are promoted to be independent of the mise en practique.           

Roy Jensen's picture


You've hit on something that is a pet peeve of mine -- the adherence to international standards by textbooks. Specifically the lack thereof. Sigh. Consider:

 * SATP/STP were changed in 1982. Today, only about half of first-year textbooks present the correct information.

 * inorganic nomenclature (IUPAC Red Book) was substantially revised in 2005. Basically zero textbooks present the correct information.

 * states of matter: are the subscript? italicized? To the best of my knowledge, this has never changed. Why are first-year textbooks still all over the map with this?

Sorry about the rant. I enjoyed reading about the upcoming new standards, but I doubt textbooks will change anytime soon. But I will update my textbook when they become official.


My few discussions with textbook editors from major publishers have been about just doing what the users demand.  If true, the CHED and others should lobby the textbook editors for the content they want.  

DelmarLarsen's picture

Or just make a viable alternative.... 

Roy Jensen's picture

I disagree. There is no reason to make a "viable alternative", when there is logic to the established standard. 

1. spaces separate words

2. subscripted and superscripted labels apply to the entity *immediately* preceeding or postceeding them.

3. variables are italicized; labels are not


WRONG: 35.4mL, 35.4 mL

CORRECT: 35.4 mL

WRONG: HCl(aq), HCl(aq)


and a myriad of others that are still used incorrectly.

DelmarLarsen's picture

My reference was short and perhaps subject to confusion. I was referring to making an alternative to textbook publishers so you do not need to try to convince anyone.... that is the topic of the next newsletter.

However, since we are on the topic, it is clearly important to establish and use standards as much as possible in both teaching and research. However, as with all ideologies, dogmatic adherence and aggressive proselytizing of a specific standard (IUPAC approved or otherwise) can be detrimental to future advances (in the lab and otherwise); we must remember that science is dynamic. I personally, could care less if a phase is subscripted in a chemical reaction as long as it is clear what it means and no one gets confused.

Try to remove the wavenumber unit from my research and my fellow spectroscopists and I would revolt. We should be teaching our students flexibility in their education (within reason), not rigid ideologies.


Permit me to speak in defense of the textbook publishers on the question of applying IUPAC rules.

I was involved a few years back in writing a textbook to help introduce students to chemistry.  When it came time to print balanced equations, my proofreader applied what was cited as a relatively new IUPAC standard deciding that no space should be permitted between coefficients and molecular formulas.

I argued that the space between the coefficients and formulas be put back in.  My argument was reading comprehension. When learners of a language are initially taught to “decode text” (translate alphabetic words into constituent sounds), generally instruction starts with short words that have spaces between them, rather than starting with cyclooctatetraene. 

When students balancing an equation write Co(OH)2 .in handwriting, in my experience it takes a while for them to learn to make some letter o cases small and some large in a manner that lets them distinguish these cases, especially when reading their own handwriting. while solving a problem   Co(CH3CO2)2 can be especially troubling given how small some textbook fonts print subscripts on print and on the screen.  . 

I personally think writing   2 Co(CH3CO2)2  instead of 2Co(CH3CO2)2  is a bit more “student centered” for beginners who are trying to learn to count atoms, and my co-author and publisher graciously allowed the space.

Experts read the language fluently either way, but I don’t see the downside to putting the space after the coefficient as had long been the practice, and I think it helps students in breaking the  terms into their constituent parts.

In chem problems, should we adopt SI units -- and state all of our volumes in cubic meters?

-- rick nelson

Yes, I think we should model good behavior and use all SI units, except for examples of how to convert other units into SI units.

The liter is an accepted SI unit. The liter is a derived unit that is defined as exactly 0.001 m3.

I vote for no space between coefficients and formulas.

Roy Jensen's picture

I've run into that in my province, and actually convinced the Ministry of Education to adopt IUPAC standards. Now if I could convince my colleagues to do the same. 

Specific to your statement: the knowledgable capitulate to the ignorant? Good Grief!


I too have been dismayed by the slowness of uptake of Nomenclature rules and in some cases of authors making their own rules for use in their textbooks. I did a quick survey of the dozen or so texts available in our library for a first year course back in 1987 and commented on it in Journal of Chemical Education, 1987, 64, 900-1.

For laboratory courses where names are expected, the more recent changeover from chloro to chlorido may take a generation ??!!

With respect to errors I can't forget when in high school the Physics teacher handed out a piece of paper for circulation to the class and told each student to mark 1 foot according to the ruler we all carried around in those days. When the 30-40 of us had finished it was amazing to see that the difference between the shortest and longest foot was about half an inch!

Sounds to me like a re-play of Gauss' well-known experiment.