Applications of Avogadro’s Law
Avogadro’s law has been found very useful in
chemistry. The usefulness of the Avogadro’s law lies in the fact that it
differentiates between an atom and a molecule.
Some important applications of the Avogadro’s
law are described below.
1. Explaining Gay-Lussac’s Law of Combining
Volumes
Consider this reaction,
a A + b
B ® c C + d
D
Let, a
molecules of A react with b molecules
of B, and there be n molecules per
unit volume of A.
Under similar conditions of temperature and
pressure, B should also have n
molecules per unit volume.
Then,
Volume
of A involved in the reaction = 1 / n
× a units
and, Volume
of B involved in the reaction = 1 / n
× b units
Therefore, the ratio of volumes of the
reacting gases A and B is, a/n : b/n or a : b
Since a
and b are whole numbers (molecules cannot be in fractions), hence the
volumes of the reacting gases bear a simple whole number ratio to each other.
This is the Gay-Lussac’s law of combining
volumes.
2. Determining the
atomicity of an elementary gas
To illustrate the determination of the
atomicity of an elementary gas, let us consider the reaction between hydrogen
and chlorine to form hydrogen chloride.
It has been observed experimentally that
hydrogen and chlorine react in equal volumes. Then, one can write,
Atomicity of hydrogen and chlorine
Hydrogen + Chlorine ® Hydrogen chloride
1 vol 1 vol 2 vol
n molecules n molecules 2n
molecules (Avogadro’s law)
1/2 molecule 1/2
molecule 1 molecule
Since one molecule of hydrogen chloride
contains one atom of hydrogen and one atom of chlorine, hence,
1/2
molecule of hydrogen = 1 atom of hydrogen
or, 1 molecule of hydrogen = 2 atoms of hydrogen
Therefore, Atomicity of hydrogen = 2
Similarly, 1/2 molecule of chlorine = 1 atom of chlorine
or, 1
molecule of chlorine = 2 atoms of chlorine
Therefore, Atomicity of chlorine = 2
Thus, the atomicity of both hydrogen and
chlorine is two.
Atomicity of nitrogen and oxygen
Similarly, we can determine the atomicity of
nitrogen and oxygen.
Nitrogen + Oxygen ® Nitric oxide
1 vol 1 vol 2 vol
n molecules n molecules 2n molecules (Avogadro’s law)
1/2 molecule 1/2
molecule 1 molecule
1 atom 1 atom 1 molecule
Thus, 1/2 molecule of nitrogen = 1 atom of
nitrogen
1 molecule of nitrogen = 2 atoms of nitrogen
Therefore, Atomicity of nitrogen = 2
Also, 1/2 molecule of oxygen = 1 atom of oxygen
1 molecule of oxygen = 2 atoms of
oxygen
Therefore, Atomicity of oxygen = 2
3. Relationship
between molecular mass & vapour density
The vapour density (V.D.) of a gas is defined
as the ratio between the mass of a certain volume of gas, to the mass of the
same volume of hydrogen gas under similar condition of temperature and
pressure. Thus,
According to the Avogadro’s law equal volumes
of gases under similar conditions should contain equal number of molecules. So,
if V mL of any gas contain n molecules, then
Since, one molecule of hydrogen contains 2
atoms, hence
As per definition
Hence,
Molecular mass of the substance = 2 × V.D. of
the substance
In general, therefore,
Molecular mass = 2 × Vapour density
4. Determining
the molecular formula of a gaseous compound
The Avogadro’s law can also be used for
determining the molecular formula of a gaseous compound, if the volumes of the
reactants and products are known. This is illustrated by taking example of the
reaction between nitrogen and hydrogen gases to form ammonia. Experimentally,
it is found that one volume of nitrogen reacts with three volumes of hydrogen
to form two volumes of ammonia. Then, one can write,
Nitrogen +
Hydrogen ® Ammonia
1 vol 3 vol 2 vol
n
molecules 3n molecules 2n molecules (Avogadro’s law)
1/2
molecule 1/2 molecule 1 molecule
or 1 atom 3
atom 1 molecule (atomicity of nitrogen
and hydrogen = 2)
Thus, one molecule of ammonia contains one
atom of nitrogen and three atoms of hydrogen.
Therefore, the molecular formula of ammonia is NH3.
