THE MOLE AND AVOGADRO'S NUMBER

1. Defining the mole:

The SI unit for an amount of matter is called the MOLE. In the same way that the amount of certain objects (such as apples or eggs) is often expressed in terms of multiples or fractions of a unit we call a DOZEN, the amounts of the building blocks of matter (such as protons, electrons, atoms or molecules) are expressed in terms of multiples or fractions of a unit we call mole, or just mol for short.

Thus, if you are familiar with expressions such as "two dozen eggs" or "half a dozen apples", you will easily see the similarity with expressions such as "3 mol sulphuric acid", "half a mol of copper atoms" and "0.001 mol photons".

2. Avogadro's number:

Of course, everyone knows that the unit we call "dozen" is associated with the number 12. What number is associated with the unit "mole"?

The mole is defined as the amount of matter which contains the same number of elementary particles of the matter in question as there are atoms in 0.012 kg of the carbon isotope 12C

The number involved is huge, and is a fundamental constant known as AVOGADRO'S NUMBER, NA.

3. Molar mass

If the relative atomic mass of an atom (or the relative molar mass of a molecule, or the relative formula mass of a salt, as the case may be) is expressed in grams, this gives rise to a quantity known as the MOLAR MASS, M of the substance in question. The units of molar mass are g·mol-1 ()

Equal numbers of moles of different substances always contain the same number of elementary particles. Just as half a dozen eggs is always 6 eggs and half a dozen onions is always 6 onions, half a mole of hydrogen gas is always equal to 3.011 x 1023 molecules of H2. Similarly, we know that half a mole of gold is always equal to 3.011 x 1023 atoms of Au.

To convert a given number of moles of a substance to the corresponding mass in grams, multiply the relative molar mass (or relative atomic mass for an monoatomic element) by the number of moles, and express the result in grams.

For example, calculate the mass of 0.25 moles of fluorine gas F2. (Ar for F = 19.00):

To convert a given mass of a substance to the corresponding amount in moles, divide the mass (which must be in grams) of that substance by the molar mass for the substance.

For example, let us calculate the number of moles of sodium chloride (NaCl) in 3.3 g NaCl (Ar for Na =22.99 and Ar for Cl = 35.45):

4. The molar volume

The volume occupied by one mole of a substance is called the MOLAR VOLUME for that substance. It may be easily calculated from the density of the substance:

Density = Mass/Volume

If one works in moles, this becomes

Density = Molar mass /Molar volume

The molar volume is of particular interest when dealing with gases. Since the density of a gas is greatly dependent on the temperature and pressure, the density should be measured at the standard temperature and pressure (STP), which is a temperature of 273.14 K (0 C) and pressure of 101.3 kPa.

It turns out that the molar volume (measured at STP) is nearly the same for all gases, and has the value of 22.4 dm3. To put it in another way, one mole of any gas at STP will occupy a volume of 22.4 dm3.

5. Avogadro's law

The constancy of the molar volume of gases is explained in terms of Avogadro's Law, formulated in by 1811 by Amedeo Avogadro.

Avogadro's Law
"Equal volumes of all gases, measured at the same temperature and pressure, will contain the same number of molecules."

This makes it very simple to calculate the amount (that is, the number of moles) of a gas, if its volume at STP is known:

How many moles of sulphur dioxide are there in 250 cm3 of this gas, assuming the volume was measured at STP?

22400 cm3 of the gas is 1.00 mole. Hence, 250 cm3 is 250 (cm3)/22400 (cm3·mol-1) = 0.0112 mol.


5. Additional questions