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# What is a Mole, Checking Out the Mole

#### Description

An overview of the meaning of this unit for measuring quantities of molecules by Joseph Herbert and Tom Buck.

# What is a Mole?

by Joseph Herbert

When the world was younger and simpler, various people interested in what passed for science in those days investigated gases as a way to find out more about matter in general. Amedeo Avogadro, Conte di Quaregna e Ceretto (1776-1856), was one of these people. Now this was not too long after people had discovered that there even were different gases. For example, oxygen was discovered in 1774 (by Priestly) and shown to be a singular entity (an element) in around 1777 by Antoine Laurent Lavoisier (later killed in the Terror following the French Revolution). By 1811 when Avogadro was working, the idea of gases as elements was fairly strongly established and the relationships of temperature and pressures and volume of gases had been investigated by Boyle and Charles and Gay-Lussac. There were some problems with these gas relationships and those were related to the weight of the identical volumes of different gases. Common gases show a wide range of weights for a given volume and this represented a problem. How do you compare the behavior of different gases when you don't really know how much of any gas you have in your sample?

Fortunately for Conte Avogadro, the ideas of atoms and molecules had been discovered and distributed. Molecules had been shown to be combinations of specific atoms and these combinations of atoms as molecules had constant properties and behaviors. As the idea of atoms developed, a relative scale of ATOMIC WEIGHTS was developed. In the early version of this scale, Oxygen was taken as equaling 16 units. Later the scale was changed so Carbon was equal to 12 units (the difference was a matter of a fraction of a percent). These arbitrary units were units of relative atomic weight and (roughly) hydrogen is 1, oxygen is 16, and other elements have other weights. Molecules, which are combinations of atoms, have weights equal to the combined weights of the atoms that make up the molecule. For example, Hydrogen gas is made of molecules that contain two hydrogen atoms and so weigh 2 units on the relative atomic weight scale. Oxygen gas, which is also made of two atom molecules, has a weight of 32 units. An example of the molecular weight of a larger molecule is Whiting, calcium carbonate, which weighs 100 units. The atoms involved are calcium (40 units) carbon (12 units) and three oxygens (48 units).

What Avogadro was able to show was that for gases, identical volumes of any gas at a standard identical temperature and pressure will contain the equal number of molecules. If you then weigh the identical volumes for several different gases, you find that the weight of the gas in the volume varies so that the weight of the volume of gas is proportional to the sum of the atomic weights of the atoms that make up the molecules of the gas. Once this idea, that a particular volume of gas was proportional to molecular weight, was shown to be true, it became possible to select a volume of gas that would have a convenient weight. The convenient weight is the molecular weight of the gas expressed in grams. This is called the Gram Molecular Weight.

In the experiments that surround this idea, the standard temperature chosen is 25 degrees C. and the pressure on the gas is chosen as one atmosphere or 760 millimeters of mercury. There is nothing special about these values, the temperature is about average room temperature and the pressure is average atmospheric pressure at sea level. It is only important that everyone doing the experiments uses the same temperature and the same pressure (or makes appropriate corrections). It was eventually shown that a Gram Molecular Weight of a gas, at standard temperature and pressure, would occupy 22.4 liters of volume. Or saying it the other way, 22.4 liters of a gas at standard temperature and pressure contains the number of molecules that weigh as much as the molecular weight of the gas expressed in grams. The number of molecules contained in this volume of gas was given the name MOLE just to confuse future generations of chemistry and biology students.

Once the volume of the gas is related to a weight that is related to a number of molecules, a logical question is, "What is that number of molecules that weighs in grams what the molecule weighs in relative atomic weight units?" The number, named after Avogadro, is 6.0221367 x 10 exp23, a very large number, indeed. This is the number of molecules in 22.4 liters of gas at standard temperature and pressure, but it is also the number of molecules in a sample of any material that weighs as much as the molecular weight of the substance expressed in grams. A Gram Molecular Weight of any substance contains Avogadro's number of molecules.

So, it turns out that an amount of any chemical compound that is equal to the combined atomic weights or the molecular weight, expressed in grams, contains 602,213,670,000,000,000,000,000 molecules. This means that 18 grams of water is composed of this many water molecules. 2 grams of hydrogen is this many hydrogen molecules (Hydrogen exists as H2, a diatomic molecule). 12 grams of carbon is this many carbon atoms. 44 grams of CO2 is this many molecules of carbon dioxide. 100 grams of whiting contains this many calcium carbonate molecules. 238 grams of Uranium is this many Uranium atoms. The list goes on.

The utility of the concept of a MOLE (and the associated Avogadro s Number) as an amount of a material is that it allows you to relate the weight of the material to the number of molecules in that weight. The mole idea also allows you to combine equal amounts (numbers of molecules in each) of two compounds. If you have a gram molecular weight of one compound and a gram molecular weight of another compound, there are equal numbers of molecules in the two weights. If you wanted the two compounds to combine so there was one molecule of each material available to combine with every molecule of the other compound, then mixing the two gram molecular weights would allow this condition. The idea of a mole allows you to produce this kind of combination.

The concept of a mole is relatively simple even though the number of particles in a mole is unimaginably large. By using this idea we can get a better understanding for the combinations that occur in our glazes. We can know how many atoms of each constituent are involved in making our glaze and we can know the ratios between them. We can know how many flux atoms there are for each silica or alumina molecule and we can know when we alter the recipe to change that relationship what may happen to the glaze. We can use the idea to compare two glaze recipes that have no ingredients in common but do have atomic constituents in common. All from the idea of a MOLE. A big number and a big idea.

# Checking out The Mole

by chemical engineer Tom Buck

Potters tend to have trouble with the word "mole". They should know that they are by no means the only ones: many scientists will mis-use this term, which they encounter infrequently in their fields. For potters, the mole is an essential notion of glaze technology, a division of applied chemistry, or chemical engineering, ceramics branch. When scientists in a world congress wanted a term to stand for "amount of substance", they chose "mole" and defined it 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 kilograms of carbon 12."

This definition makes today's "mole" the same as the "gram-molecule" of Chemistry invented about 150 years ago, that is, the "amount of substance" in grams that is equal to its molecular weight. In this context, "substance" has a special meaning: namely, that the molecular "species" under consideration is "pure", that is, there are no contaminants. eg, a mole of sodium chloride, NaCl, common table salt, weighs 22.99 + 35.45 = 58.44 grams and exhibits this molar weight in its chemical behaviour (as in a solution or in a salt firing).

As so defined, the mole became a key unit (fundamental unit) of the International System of Weights and Measures (aka Metric System) adopted worldwide, including USA where it is legal although not popular. As a key unit of SI (Systeme International), the mole is technical unit used mainly by chemists, chemical engineers, ceramic engineers, and potters.

Also, the mole is the only SI unit based on the gram, and so departs from all other SI units that are linked to the kilogram as the accepted unit of mass (matter in the Universe).

The notion of the mole arose from work by an Italian naturalist, Avogadro (1776-1856), who discovered a key constant of Chemistry. His research showed that all gases held the same number, "N", of molecules when they were contained in a specific volume at a standard temperature and pressure, or STP for short. Today, STP is 20 degrees Celsius (aka centigrade) and 1 bar (aka 1 "atmosphere" or 101.3 kilopascals -- the old 760 mm of Hg is obsolete).

Avogadro discovered that a volume of 22.4 litres weighed one mole ("gram-molecule" in his day) when a pure substance was held in that container. He also calculated that this weight represented a vast number, N, of actual molecules of gas, ie, N molecules totaled 6.022 x 10 to the 23rd power (6 followed by 23 zeros). [Every so often IUPAC, the International Union of Pure & Applied Chemists, reports a re-evaluation of N, Avogadro's Number, and lately it offered 6.02252x10E23 which likely will be adjusted again in the coming decade].

The significance of N is that it helps us to grasp what is involved when dealing with fractions of a mole during glaze design work. Although "half a mole", 0.5 mol, seems small, in reality it represents an immense number of individual molecules, in this case, 3.011 x 10E23 molecules. But since these huge numbers are beyond easy manipulation; the mole is a workable substitute.

And if we wish to look at tiny factors of N for reasons of "purity", then we can make use of SI's prefixes. A micromole (one millionth of a mole) of a gaseous substance contains 6x10E17 molecules (23 zeros minus 6 zeros), which is still a huge number; a nanomole (1 billionth of a mole) contains 6x10E14 molecules, and a picomole (1 trillionth of a mole) still contains 6x10E11 molecules.

### Molar weights

What we are counting when we say "1 mole of alumina"? Since alumina at room conditions is a crystalline substance, we cannot distinguish single individual molecules of Al2O3. Our imagination, however, can take us to a Universe where alumina is a gas at STP. The "molar" volume (22.4 L) then would have a weight of 102 grams, or restating it, 102 grams is the weight of a mole of aluminum oxide.

Now, while N is strictly correct ONLY for gases at STP, one can make a mental stretch and "apply" it to solutions with a known amount of solute in a solvent. Molten glass (ie, glaze) represents a "solvent" in chemical terms, so trace amounts of a colourant, say copper(I) oxide (red), present as 0.1 mol (14.2 grams) in 1000 grams of glass, would represent the solute and consist of a vast number of molecules of Cu2O in the liquid ("liquidus") ... a ballpark figure might be (repeat, might be) 10E22 molecules of Cu2O in 18x10E23 "molecules" of molten glass. That is, even a tiny percentage of red copper oxide would have an effect on the molten glass (say, 1 molecule of Cu2O to 200 "molecules" of alumino-silicate glass).

So, in a Seger/Unity Formula, we now use the term "mole" to symbolize the number of molecules of a particular substance -- the old term "molecular equivalents" is both obsolete and misleading since there is an assumption that the amount in question is taking the place of 1 atomic weight of hydrogen, which never occurs as such in ceramics. The word mole has no such connotation.

Without the notion of "mole" and Avogadro's Number, the above insights into the makeup of a glaze would be denied to us potters.

Copyright (C) July 2002 by Tom Buck. All rights reserved, including any presentation in electronic form. The individual potter may make one copy for their own use. Please ask Tom Buck for permission to depart from this approval.

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