How do you identify a chemist?

One way is to pose the question 'What is a mole?'

A gardener will inform you that it is a small, seldom seen black furry creature which digs holes in the lawn. A doctor or nurse will inform you that it is a dark raised blemish on the skin where colour changes should be treated with caution as it can become cancerous. A Company Director will tell you that a mole is somebody engaged in industrial espionage. The chemist, however, will respond with a totally different kind of answer. It is the purpose of this entry to inform the layperson what the mole means to a chemist.

To cut a long story short, the mole is a fundamental unit devised for measuring out quantities; it is a quantity (of anything!) that is equivalent to the number of atoms present in 12g of carbon-12.

Practical chemistry has been likened to glorified cookery. That being the case, if you were baking a cake, you'd need to measure out the requisite quantities of ingredients. This is usually done by weighing. The chemist, on the other hand, often needs to synthesise new compounds. A compound is a substance consisting of two or more elements chemically united in definite proportions by mass; for example, sodium chloride (common salt) is a compound of sodium and chlorine. Water is a compound of hydrogen and oxygen, where one molecule contains two atoms of hydrogen and one of oxygen. In order to make a compound, the chemist will follow a recipe, very much like baking a cake, in order to ensure that the correct atoms are made available in the correct proportions.

The Concept of Relative Mass

The mass of any object, expressed in any unit, is measured relative to some standard. For example, the universal standard of mass is the standard kilogram, which is a block of platinum-iridium alloy kept at Sevres, near Paris (the more convenient unit of mass, most commonly used in the kitchen, is the gram; which is one-thousandth the mass of a kilogram).

If you purchase 5kg of potatoes, you are effectively purchasing five times the mass of the standard kilogram. This may be expressed in two ways:

1. The mass of the potatoes is 5kg
2. The relative mass of the potatoes on the kilogram scale is 5

This idea of relative masses can now be applied to atoms.

Relative Atomic Mass

When the chemist wishes to make a compound, he needs to mix together precisely the correct amounts of starting atoms (ingredients) according to the chemical equation. For example, consider the manufacture of water:

Hydrogen + oxygen -> water

2H + O -> H₂0

This tells us that two atoms of hydrogen react with one atom of oxygen to form one molecule of water. So we need to mix the reactants (ingredients) together in these proportions.

Now an atom of hydrogen (ie, one proton + one electron)) weighs 1.66 x10^-27 kg; so fairly obviously we can't weigh individual atoms! Fortunately, chemists of the past have worked out the relative masses of different atoms. This information is available in the form of a Table of Relative Atomic Masses (RAM); the same information can be obtained from the Periodic Table of the Elements.

From the table of Relative Atomic Masses, it can be ascertained that one oxygen atom is approximately 16 times heavier than one hydrogen atom (on the hydrogen scale). Now, as there are two hydrogen atoms in the molecule of water, we need to use eight times the mass of oxygen compared to hydrogen. As hydrogen is the simplest, lightest atom with RAM of 1 and the standard unit of mass was the gram, chemists originally calculated how many atoms there were in one gram of hydrogen. This number was given the name 'mole'. Furthermore, as the oxygen atom is 16 times heavier than the hydrogen atom, this same number of atoms would be present in 16g of oxygen.

Hence the mole originally came to be defined as the amount of substance that contains the same number of atoms as 1g of hydrogen. So, how many particles are present in one mole of a substance?

It is not feasible at present to accurately count the atoms contained in grams of a substance, hence the number is not known with absolute precision. The generally accepted number at present is 6.022 10²³ atoms. This figure is called the Avogadro Constant, N_A (sometimes called the Loschmidt Number,L after the Austrian chemist who first estimated its value). Therefore, returning to the example of the manufacture of water, the equation is really telling us that we need to mix 2 X (6.022 10²³) hydrogen atoms with 6.022 10²³ oxygen atoms.

Now, to avoid using numbers with such absurd exponents as 10²³, chemists decided to name the number of particles present in the relative atomic mass of an element when expressed in grams as the mole: ie,

One mole = 6.022 10²³ atoms.

This makes calculations in terms of number of atoms astonishingly easy. One mole is a conversion factor between atomic mass units, which are tabulated in the periodic table.

Relative Atomic Mass on the Oxygen Scale

Relative Atomic Mass on the Carbon Scale

In 1961 the International Union of Pure and Applied Chemistry (IUPAC) adopted a new standard based on the mass of the most abundant isotope of carbon, carbon-12.

The table below now shows the Relative Atomic Masses of selected elements on the hydrogen scale, the oxygen scale and the carbon scale.

In most GCE Advanced Level work (UK), RAMs are expressed to three Significant Figures and it can be seen that, to this level of precision, the oxygen scale and the carbon-12 scale are the same. However, the hydrogen scale is significantly different and is now no longer used.

How big is a mole?

There is the tale, perhaps apocryphal, concerning the teacher who asked a colleague for a pile of sand containing Avogadro's Constant of sand grains in it to show his pupils. The colleague replied that if he could find a merchant willing to supply it, then he would guarantee that the school would pay for it. Work out for yourself how many lorry loads would be required, assuming that each sand grain was a 0.1mm cube, and each lorry could carry 10m³ of sand. How long would this take to deliver, assuming that one lorryload could be carried every ten minutes for 24 hours/day?

Another calculation shows that if all the 6.022 x 10²³ atoms in 12g of carbon were turned into marbles, the marbles would cover Great Britain to a depth of 1500km.

Using the mole

Consider a neutralization reaction where:

Acid + Base -> Salt + Water

(see also Acidity and Basicity)²:

eg, NaOH + HCl -> NaCl + H₂O

Sodium hydroxide reacts with hydrochloric acid on a 1:1 ratio to form sodium chloride (table salt) and water in a ratio of 1:1. Any other ratio will leave an excess of hydroxide or acid, resulting in an alkaline or acidic product. To get the desired result, a neutral product with no excess of base or acid, the reactants have to be mixed together in the exact proportions molecule-wise³.

Consider mixing together 100g of NaOH with 100g of HCl. The problem here is that the NaOH and the HCl molecules have different molecular masses (6.6 10^-26kg and 6.0 10^-26kg respectively). So simply adding 100g of NaOH and 100 g of HCl will not lead to the desired result; there will be an excess of HCl 'molecules', as there are more HCl 'molecules' in 100g than NaOH. To correct this, chemists have to know how many molecules there are in a given mass, expressed in grams. In that way it is possible to achieve the ideal ratio by weighing the substances and mixing them together.

The calculation goes like this: The Relative Molecular Mass of NaOH is 40 in atomic units⁴. So 100g of NaOH correspond to (100/40) = 2.5 moles of NaOH (or 15.1 10²³ molecules). To carry out a neutralisation reaction with this amount of NaOH, 2.5 moles of HCl⁵ (Relative Molecular Mass is 36.5 atomic units) are needed, which correspond to (2.5 X 36.5) = 91.25g.

Summary