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The mole and the Avogadro constant

The unit for the amount of a substance is the mole. It is defined as the amount of a substance that contains the same number of particles (atoms or molecules) as the number of atoms in 12 g of the isotope carbon-12. This number is known as the Avogadro constant (NA or L) and is 6.02 x 1023 particles per mole.

The ratio of the mass of one mole of the substance to one twelfth of the mass of one mole of carbon-12 is called the relative molecular mass of the substance - it is 32 for oxygen, 2 for hydrogen and so on.

A knowledge of the Avogadro constant enables us to calculate the number of molecules in any mass of a substance and therefore to get an idea of the size of one molecule.
For example, a drop of water of volume 1.0 cm3 has a mass of 1 g. The relative molecular mass of water is 18, and therefore this drop of water must contain 6.02x1023/18 = 3.34x1022 molecules.

Avogadro's constant is the number of particles in a mole of the substance. This number is always the same.
So in:
1 mole of hydrogen (2 g) there are 6.02x1023 molecules (hydrogen exists as H2)
1 mole of oxygen (32 g) there are 6.02x1023 molecules (oxygen exists as O2)
1 mole of copper (63 g) there are 6.02x1023 atoms
1 mole of uranium 235 (235 g) there are 6.02x1023 atoms

For example if we have 2 kg of uranium in a fuel rod we have 2000/235 = 8.51 moles and this contains 8.51x6.02x1023 = 5.12x1024 atoms and so 5.12x1024 uranium nuclei.

The average volume of a water molecule must therefore be 2.99x10- 23 cm3, and if we assume the molecules to be spherical the diameter of a water molecule is about 2x10-8 cm or 2x10-10 m, a result confirmed by X-ray diffraction.

Molar mass and molecular mass

As has been mentioned the molar mass of a substance is the mass of one mole of the substance - 6.02x1023 molecules. The molecular mass is the mass of one molecule of the substance.

The molecular mass is the molar mass divided by the Avogadro constant


For example the molecular mass of hydrogen is [2/6.02x1023] gm = 3.32x10-24 gm = 3.32x10-27 kg, and for oxygen [16/6.02x1023] gm = 2.66x10-24 gm = 2.66x10-26 kg.

Example problem
A sample of 2 mg of polonium is found to emit 2.90x1018 alpha-particles during one half-life. If the relative atomic mass of polonium is 210, calculate a value for the Avogadro constant.

During a half-life one half of the polonium atoms will have decayed. Therefore 2 mg of polonium would emit 5.80 x 108 alpha-particles before it decayed completely.

Therefore: Number of moles in 2 mg =2x10-3/210 = 9.52x10-6
Therefore one mole contains [5.80 x 1018]/[9.52x10-6] = 6.09 x 1023 particles
a good approximation to the Avogadro constant.
 

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© Keith Gibbs