AMOUNT OF SUBSTANCE
Reacting masses and atom economy
Solutions and titrations
The ideal gas equation
Empirical and molecular formulae
Mill Hill County High School
Since atoms are so small, any sensible laboratory quantity of substance must contain a huge number of atoms: 1 litre of water contains 3.3 x 1025 molecules.
1 gram of magnesium contains 2.5 x 1022 atoms.
100 cm3 of oxygen contains 2.5 x 1021molecules.
Such numbers are not convenient to work with, so it is necessary to find a unit of "amount" which corresponds better to the sort of quantities of substance normally being measured. The unit chosen for this purpose is the mole. The number is chosen so that 1 mole of a substance corresponds to its relative atomic/molecular/formula mass measured in grams. A mole is thus defined as follows:
A mole of a substance is the amount of that substance that contains the same number of elementary particles as there are carbon atoms in 12.00000 grams of carbon-12.
One mole of carbon-12 has a mass of 12.0g.
One mole of hydrogen atoms has a mass of 1.0g.
One mole of hydrogen molecules has a mass of 2.0g.
One mole of sodium chloride has a mass of 58.5g.
The number of particles in one mole of a substance is 6.02 x 1023. This is known as Avogadro's number, L.
Thus when we need to know the number of particles of a substance, we usually count the number of moles. It is much easier than counting the number of particles.
The number of particles can be calculated by multiplying the number of moles by Avogadro’s number. The number of moles can be calculated by dividing the number of particles by Avogadro’s number.
(Number of particles) = (number of moles) x L
The mass of one mole of a substance is known as its molar mass, and has units of gmol-1. It must be distinguished from relative atomic/molecular/formula mass, which is a ratio and hence has no units, although both have the same numerical value.
The symbol for molar mass of compounds or molecular elements is mr. The symbol for molar mass of atoms is ar.
Mass (m), molar mass (mr or ar) and number of moles (n) are thus related by the following equation:
MASS = MOLAR MASS X NUMBER OF MOLES
or m = mr x n
Mass must be measured in grams and molar mass in gmol-1.
It is possible to use the relationship moles = mass/mr to deduce the masses of reactants and products that will react with each other.
When performing calculations involving reacting masses, there are two main points which must be taken into account:
The total combined mass of the reactants must be the same as the total combined mass of the products. This is known as the law of conservation of mass.
The ratio in which species react corresponds to the number of moles, and not their mass. Masses must therefore all be converted into moles, then compared to each other, then converted back.
i) reactions which go to completion
Eg What mass of aluminium will be needed to react with 10 g of CuO, and what mass of Al2O3 will be produced?
3CuO(s) + 2Al(s) Al2O3(s) + 3Cu(s)
= 0.126 moles of CuO
3:2 ratio with Al
so 2/3 x 0.126 = 0.0839 moles of Al, so mass of Al = 0.0839 x 27 = 2.3 g 3:1 ratio with Al2O3
so 1/3 x 0.126 = 0.0419 moles of Al2O3, so mass of Al2O3 = 0.0419 x 102 = 4.3 g
ii) reactions which do not go to completion
Many inorganic reactions go to completion. Reactions which go to completion are said to be quantitative. It is because the reactions go to completion that the substances can be analysed in this way.
Some reactions, however, particularly organic reactions, do not go to completion. It is possible to calculate the percentage yield of product by using the following equation:
% yield = amount of product formed x 100...
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