3.1.2 Amount of Substance - The mole and the Avogadro constant (L)

Specification

Students should:
  • understand the concept of a mole as applied to electrons, atoms, molecules, ions, formulae and equations
  • understand the concept of the Avogadro constant. (Calculation not required)

The hydrogen standard

Hydrogen is the smallest atom and it was originally used as the standard by which all the other atoms were compared. It was assigned a value of 1 unit and other atoms masses calculated compared to hydrogen atoms.

The 1H isotope has a mass assigned a value of exactly 1 atomic mass unit. This was the original reference.

The 1H isotope The carbon 12 isotope standard 12C

Nowadays the 12C isotope is used as a reference for comparison of relative atomic masses. This isotope has the assigned mass of 12.00000, all other atoms are measured relative to 12C.


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The 12C isotope

Measured on this scale hydrogen atoms (on average) have a relative mass of 1.00797.

Carbon atoms have a relative mass of 12.01111 on average. Although this may seem strange at first sight, it is because carbon is made up of several isotopes 12C, 13C, and 14C. The relative mass of carbon is given as the weighted average of all of the isotopes in a naturally occuring sample. Clearly the average mass must be greater than 12.0000.

Most tables use the relative atomic masses rounded up to one or two decimal places.

A carbon atom has a mass approximately 12 times that of a hydrogen atom, therefore they have a RELATIVE mass of 12 (there are no units as it is a comparison - see relative measures)

Provided the number of carbon atoms is equal to the number of hydrogen atoms, the mass of carbon is always 12 times the mass of hydrogen.

Clearly, there will be a specific number of hydrogen atoms that when weighed have a mass of 1g and that the same number of carbon atoms MUST have a mass of 12g. This number, named after its discoverer is called:

Avogadro's constant (L) = 6.02 x 1023


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Avogadro's number

Avogadro's number, or constant, is the number to which the mass of an atom must be multiplied to give a mass in grams numerically equal to its relative atomic mass. That sounds like a mouthful, but it just means that an Avogadro number of carbon atoms has a mass of 12g, because the relative mass of carbon = 12.

Example: Hydrogen has a relative atomic mass of 1 therefore 6.02 x 1023 hydrogen atoms have a mass of 1g

Carbon has a relative mass of 12 therefore 6.02 x 1023 carbon atoms have a mass of 12g

Magnesium has a relative atomic mass of 24 therefore 6.02 x 1023 magnesium atoms have a mass of 24g

This gives rise to two important definitions

Example: 1 mole of magnesium contains 6.02 x 1023 magnesium atoms

1 mole of magnesium has a mass of 24g

12g of magnesium is equivalent to 1/2 moles = 0.5 moles of magnesium

12g of magnesium contains 1/2 moles of magnesium atoms = 0.5 x 6.02 x 1023 = 3.01x 1023 magnesium atoms

The relationship between moles, mass and number of particles can be expressed by simple formulae:

no. of particles = moles x Avogadro's constant

and

mass in grams = moles x relative mass

These formulae can be used to find any quantity when the other two quantities are known.


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