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#### The Volume-Amount Relationship: Avogadro’s Law

The work of the Italian scientist Amedeo Avogadro complemented the studies of Boyle, Charles, and Gay-Lussac.

❒ In 1811 Avogadro published a hypothesis stating that at the same temperature and pressure, equal volumes of different gases contain the same number of molecules (or atoms if the gas is monatomic). It follows that the volume of any given gas must be proportional to the number of moles of molecules present; that is,

where n represents the number of moles and k is the proportionality constant.

❒ The  following  Equation is the mathematical expression of Avogadro’s law:

"At constant pressure and temperature, the volume of a gas is directly proportional to the number of moles of the gas present".

From the following Figure we see that:

k =  RT/P.

❒ According to Avogadro’s law we see that when two gases react with each other, their  reacting volumes have a simple ratio to each other. If the product is a gas, its volume is related to the volume of the reactants by a simple ratio (a fact demonstrated earlier by Gay-Lussac).

For example, consider the synthesis of ammonia from molecular hydrogen and molecular nitrogen:

Because, at the same temperature and pressure, the volumes of gases are directly proportional to the number of moles of the gases present, we can now write:

The volume ratio of molecular hydrogen to molecular nitrogen is 3:1, and that of ammonia (the product) to the sum of the volumes of molecular hydrogen and mole cular nitrogen (the reactants) is 2:4 or 1:2

Reference:Chemistry / Raymond Chang ,Williams College /(10th edition).