Metric System Units

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Brief Historical Survey

The first standardized system of measurement, based on the decimal was proposed in France about 1670. However, it was not until 1791 that such a system was developed.

It was called the "metric" system, based on the French word for measure. The driving force was the growing importance of weights in the sciences, especially chemistry. At that time, every country had their own system of weights and measures. England had three different systems just within its own borders!!

On May 20, 1875, delegates of 17 countries signed the Meter Convention. It was amended in 1921 and today 48 countries are signatories.

The modern metric system has been renamed Systeme International d'Unites (International System of Units) and is denoted by the letters SI. SI was established in 1960, at the 11th General Conference on Weights and Measures. It was then that units, definitions, and symbols were revised and simplified.

There are three major parts to the metric system: the seven base units, the prefixes and units built up from the base units. Here is a list of the base units which make up the metric system:

Physical Quantity Name of SI unit Symbol for SI unit
length metre (meter) m
mass kilogram kg
time second s
electric current ampere A
temperature Kelvin K
amount of substance mole mol
luminous intensity candela cd

Prefixes were also agreed on in 1791 The set from kilo- down to milli- was developed then. For the multipliers (prefixes greater than 1), Greek was used and for the fractions (prefixes less than 1), Latin was used.

In 1958, the International Committee on Weights and Measures added Mega-, Giga-, and Tera- to the multipliers and micro-, nano-, and pico- to the fractions. In 1960, at the 11th General Conference on Weights and Measures, everything was officially adopted.

Since that time, additional prefixes have been added as the need arose. Typically, as scientific instruments get better and better, smaller and smaller quantities can be detected. So, new fractional prefixes need to be added. When they are, new multipliers are added also, to keep the system symmetrical. A brief mention about when the adoptions took place can be found here.

Non-SI Units Commonly Used

(a) Liter: symbol = L. The SI unit for volume is m3 (cubic meter). One dm3 (cubic decimeter) equals one L. A cubic decimeter is a cube 0.1 m on a side. The fact that 1 dm3 equals 1 L is used often in metric unit conversions. Remember it!

(b) cubic centimeter: symbol = cm3. Often used for measuring the volume of solids, one cm3 equals one milliliter (mL). This equality between 1 cm3 and 1 mL is used often in metric unit conversions. Remember it!

(c) Ångström: symbol = Å. One Å equals 10¯8 cm. This unit, named for Anders Jonas Ångström, is often used for the wavelengths of electromagnetic radiation as well as the length of chemical bonds. Its use is being replaced by nm and pm, respectively. However, you still see questions that use Å. Even though its use is low, you still need to know it. The fact that it is in low usage makes it attractive for test questions!

Definitions of the Units

I. The Meter

The meter has a most interesting history. The original definition was one ten-millionth of the distance from the North Pole to the Equator. From that, French scientists made a bar of 90% platinum and 10% iridium and put two marks on it to signify the meter distance.

This particular alloy was used because it resisted expansions due to temperature very well and it could take a high polish, resulting in the ability to take a very fine line. This reduced the error due to the width of the lines.

As science moved into the 1900s, it was becoming apparent that wavelength measurements were among the most accurate ones in all of science. In 1907, the red line of cadmium at 6438 Å was adopted as a new meter standard, however many continued to advocate the green line at 5460 Å in mercury's spectrum. By the way, using a particular wavelength of light as a standard for measurement was made as early as 1829. It took almost 80 years for the technology of measurement to become exact enough for use as an international standard.

In 1960, the orange line at 6058 Å of krypton-86 was adopted. The wavelength was specified as :

λvac = 6057.802106 Å

so that one meter equaled:

1,650,763.73 Hz¯1

If you want to be really technical, this is the 2p10 to 5d5 transition (following the notation of Paschen). It can also be written: 2P10 to 5d5. So there!

The definition was changed once again, in 1983, to the following:

The meter is the length of path travelled by light in vacuum during a time interval of 1 / 299,792,458 of a second.

By the way, this definition depends on the fact that the speed of light is defined (not measured) as exactly 299,792,458 meters per second.

I think the meter's definition journey is over.

II. The Kilogram

In 2019, the kilogram received a new definition. It is now defined thusly:

1 kg exactly equals 6.62607015 × 10-34 kg m21

You can read a bit more about it here.

An interesting fact about the kilogram is that it is the only SI base unit to incorporate a prefix. (By the way, teachers have been known to test that fact.) Why wasn't the gram used? I don't know for sure, but the gram is such a small amount of stuff that it would be easy to make a mistake in creating a physical standard. So I suspect they decided to deal with a larger amount of material.

Below are my older comments about the kilogram, from before the 2019 re-definition:

Here is the definition of the kilogram, adopted in 1901:
it is equal to the mass of the international prototype of the kilogram.

What that means is that there is a cylinder of 90% platinum/10% iridium in a vault in Paris, France and that lump of stuff weighs exactly one kilogram, by definition. I have heard, although I have no proof, that it has been removed for use only 4 times during the 1900s.

The kilogram is the only unit still based on a single lump of stuff. All the other definitions can be reproduced with a high degree of accuracy in any laboratory with the proper equipment. Interestingly enough, the kilogram is losing weight and scientists are calling for the kilogram to be redefined in a more accurate way.

III. Amount of Substance (The Mole)

In 2019, the mole was newly-defined to this:

1 mole contains exactly 6.02214076 × 1023 elementary entities

The article I linked above contains a mention of this change.

Below are my older comments about the mole, from before the 2019 re-definition:

In 1860, at the first ever international meeting of chemists, it was decided that hydrogen would serve as the standard for all atomic weights. It was defined as weighing exactly one atomic mass unit (amu). (The concept of mole had not yet been introduced into chemistry.) In 1906, oxygen was made the standard. There wasn't anything wrong with hydrogen, it was just that oxygen formed compounds with almost every element known and hydrogen did not. So oxygen was defined to weigh exactly 16 amu.

However, in 1929, the discovery of the O-17 isotope and later the O-18 isotope (both stable) changed matters, even though the two isotopes comprised only 0.24% of all oxygen atoms. Also, it was discovered that oxygen from different sources world-wide had slightly different mixes of the three isotopes. This was a BIG problem. In response, the physics community defined the amu as 1/16 the weight of the lightest oxygen isotope (which was O-16), while chemists do not come up with a new definition so fast. This meant that the atomic weights used by people in physics were different than those used in chemistry. This situation could not be tolerated.

During the years 1958-1961 this issue was first debated by the world-wide chemistry and physics community and then voted upon. What emerged from the debate were two possible new standards: fluorine and carbon. The final vote showed carbon as the winner. Although fluorine had the advantage of only one natural isotope, carbon is much the safer element to handle. Also, while carbon has two natural, stable isotopes, the isotopic mix between carbon-12 and carbon-13 is well known and stable world-wide.

These years were at the height of the Cold War between the USA and the Soviet Union. Despite this, the Soviet physics and chemistry communities was well-represented in the debate and the voting. As a personal note, the ChemTeam was in elementary school during those years. I can still hear the air raid siren being tested every Friday at 10AM and I remember the drop-and-cover drills in case of nuclear attack (!).

From 1971, the official wording (unchanged to the present day) is as follows:

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. 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.

By the way, some books will rearrange the definition. For example:

The amount of a substance of specified chemical formula, containing the same number of formula units (molecules, atoms, ions, electrons, etc.) as there are in 0.012 kilograms (exactly) of the pure nuclide carbon-12.

This definition came from a reference book published in 1972 and is, of course, saying the same thing as the first definition.

IV. The above article on new definitions also mentions new definitions for the ampere and the Kelvin. I will leave those (and the other two) undiscussed.

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