# Gay Lussac and Avogadro Law

So this is the volume in which the gas molecules
are enclosed. So as they are in a state of motion, in 9 seconds you get 9 hits, that
means 1 hit per second. Now, if the volume of the container is reduced to half, so you
observe that in 9 seconds again there are 18 hits. As the volume of the container is
reduced to half, the number of it’s per seconds increases or doubles. So initially
we had a volume, so we got one hit per second. Now, when we reduced the volume of the container
to half, we got 18 hits in 9 seconds. That means we got 2 hits per second. So, on reducing
the volume of the container to half, the number of hits per second doubles. So we saw, that
in 9 seconds, we got 9 hits. So, there is 1 hit per second. Now, when the volume of
this vessel was reduced to half in the same time, i.e. in 9 seconds, there were 18 hits
in 9 seconds. So n reducing the volume to half, the number of hits per second doubled.
So what do we observe? We observe that as the volume decreases, the pressure increases.
Why is this so? This is because as the volume decreases, there is lesser space for the same
number of molecules to travel so they hit the walls of the container more. As the number
of hits per unit time increases, the pressure increases. So this law was given by Boyle,
which is known as the Boyle’s Law. He said that the volume of the gas is inversely proportional
to its pressure, provided the temperature remains constant. So we see that we get the
volume equal to constant by pressure. So to remove the proportionality sign, we introduce
a constant. So we get that pressure into volume is equal to constant. So if we have a particular
temperature and a particular pressure, there is a fixed volume of a gas. So for a particular
pressure and temperature, there is a fixed volume.
So how do we read this equation? O₂ + 2H₂ ―› 2H₂O
So far we have seen that whenever we are given ay chemical equation we read it as-
See, in this case there is no coefficient. So this means there is 1 molecule. So we read
it as- 1 molecule of oxygen reacts with 2 molecules of hydrogen to give us 2 molecules
of water. But years back it was not easy to count the
number of molecules. The scientists did not have sophisticated instruments to measure
the number of molecules of the substances. So what they did, they measured the substances
in terms of their volumes. The first scientist to do this was Gay-Lussac. He observed that,
for the same equation, when oxygen reacts with hydrogen, 1 volume of oxygen reacts with
2 volumes of hydrogen to give 2 volumes of water. This means, say that 1 liter of oxygen
reacts with 2 liters of hydrogen to give 2 liters of water or 2 liters of oxygen reacts
with 4 liters of hydrogen to give 4 liters of water. So, what is observed here is that
the substances or gases in this case, they react in volumes and if you observe in this
case, 1 volume of oxygen reacts with 2 volumes of hydrogen. So what is the ratio of hydrogen
is to oxygen? We get, 1:2. So there’s 1 liter reacting with 2 liters, again the ratio
is 1:2 or if there are 2 liters of oxygen reacting with 4 liters of hydrogen, again
we get 1:2. So this is the ratio in which oxygen combines with hydrogen. Now, say if
you look at the ratio of oxygen is to water, in this case, water is formed in the form
of steam. So this is also in the gaseous state. So if we take oxygen is to steam, or oxygen
it to water vapor, we get 1 volume of oxygen gives 2 volumes of steam. So again the ratio
of oxygen is to steam remains 1:2. Gay-Lussac observed some other gases. So for
this reaction- N₂ + 3H₂ ―› 2NH₃
Nitrogen reacts with hydrogen to form ammonia gas. So in this case, he observed that 1 volume
of nitrogen reacts with 3 volumes of hydrogen to give 2 volumes of ammonia. That means,
nitrogen reacts with hydrogen in 1:3 ratio and nitrogen forms ammonia in the ratio 1:2,
i.e. 1 volume of nitrogen is required to form 2 volumes of ammonia. If you look in terms
of hydrogen and ammonia, so we see that 3 volumes of hydrogen give 2 volumes of ammonia.
So 3:2 is the ratio of hydrogen is to ammonia. Let’s take another example-
2CO + O₂ ―› 2CO₂ In this case, carbon monoxide reacts with
oxide to form carbon dioxide. Again, 2 volumes of carbon monoxide react with 1 volume of
oxygen to give 2 volumes of carbon dioxide. So if you observe the ratio of carbon monoxide
to oxygen, we get 2:1, and if you observe the ratio of carbon monoxide that gives carbon
dioxide, we get 1:1. So based on all these observations, Gay-Lussac
gave his law which is known as “Gay-Lussac’s Law of Combining Volumes”. Since he had
observed that gases react in volumes, so he gave his law of combining volumes, which states
that- whenever gases react, they do so in volumes and this bears a simple whole number
ratio. As we have seen before, whenever they react in volumes, they bear a simple whole
number ratio to each other and to the volume of the product which is formed. But one important
condition remains, that is all the volumes are measured at the same temperature and pressure.
Provided all the measurements, for a particular equation are taking place at the same temperature
and pressure, the Gay-Lussac’s law of combining volumes holds, i.e. whenever gases react,
they do so in volumes and it bears a simple whole number ratio to each other and to the
product which is formed. The volumes of solids and liquids are taken
to be ZERO. This is because, if there is some amount of heat given, the change in the volume
of gases is remarkable. Even a little heat supplied to gases changes its volume to a
large extent. But a little heat does not change the volume of solids or liquids. So the change
in solids and liquids is quite negligible. That is why the volumes of solids and liquids
are considered to be zero and we always take into account the volumes of gases.
There’s an industry, Fischer Pharma Industry. The industry manufactures a medicinal drug
comprising of Nitric Oxide (NO), which is used as an energy booster. NO, i.e. Nitric
Oxide is produced by a reaction involving the oxidation of ammonia. If 100L of ammonia
is used, what is the amount of nitric oxide produced?
4NH₃ + 5O₂ ―› 4NO +6H₂O (l) This reaction is used to make or produce Nitrogen
Oxide. So by Gay-Lussac’s law of combining volumes, we know that whenever gases react,
they react in volumes. So we are given, 100L of ammonia is used. If we take the ratio of
ammonia, which is used to form Nitric Oxide, we see that 4 volumes of ammonia is used to
form 4 volumes o nitric oxide, i.e. 1:1 ratio of ammonia to nitric oxide is present. 4 volumes
of ammonia produce 4 volumes of nitric oxide. So 100L of ammonia produces 100L of nitric
oxide. So whenever gases react, they react in volumes that bear a simple whole number
ratio. So if you see the ratio of ammonia to oxygen, it’s 4:5 and ammonia to nitric
oxide, it’s 1:1. Keep in mind, the water formed in this case, the subscript ‘l’
shows that it is in the liquid state, so the volume of water is zero. So in this case we
get, 4 volumes of ammonia giving 4 volumes of nitric oxide. So 100L of ammonia used in
this reaction produces 100L of nitric oxide. Now, you all must’ve seen a balloon. You
all must’ve inflated a balloon. What happens? As you pass air in the balloon, a deflated
balloon increases in volume. So let’s see what happens. Now, as you pass more and more
air into the balloon, the volume starts increasing. This is because, now when you are passing
more air, you are passing more number of molecules in the balloon. So as more air is passed,
the number of molecules of air, which are now passed in the balloon, increases. As the
number of molecules of air increases, the balloon starts expanding in volume. And whenever
you deflate it, i.e. you allow the air to be expelled out, so the number of air molecules
is decreasing, so the volume of balloon also starts decreasing. So in this case, i.e. in
your day-to-day life, you have observed a relationship between the number of molecules
and the volume. Something like this was observed by a scientist
in 1811. In 1811, there was a scientist who observed that if there are two gases at the
same temperature and pressure, equal volumes of the gases contain equal number of molecules.
This scientist was Lorenzo Romano Amedeo Carlo Avogadro. So Avogadro observed that for any
two gases, if they are at the same temperature and same pressure, so equal volumes; so we
know that at the same temperature and same pressure, a gas occupies a fixed volume. So
for the same temperature and same pressure, equal volumes of any two gases contain the
equal number of molecules. So based on this observation, Avogadro gave his law which is
known as Avogadro’s Law. It states that equal volumes of all the gases, under similar
conditions of temperature and pressure, they contain the same number of molecules. So this
holds for all gases. If we have equal volumes of all the gases at the same temperature and
pressure, they all contain the same number of molecules. So if you have the same temperature
and pressure, we are given two gases- oxygen and hydrogen. They contain the same number
of molecules, i.e. oxygen contains 50 molecules and there are 50 molecules of hydrogen. So
when there is same number of molecules that means that they occupy the same volume. So
Avogadro states that equal volumes of all gases under the same temperature and pressure,
contains equal number of molecules and vice versa. If we have two gases containing the
same number of molecules, this means that the two gases occupy the same volume.
Avogadro when presented his work initially, his work was rejected. Nobody was ready to
accept that gasses react in molecules. But later experiments were performed and it was
So again we have the same industry i.e. Fischer Pharma Ltd which produces a drug that uses
nitric oxide. In this case we have the industry producing the drug using nitric oxide. Under
the same conditions of temperature and pressure, which of the following species contain the
maximum number of molecules? 4NH₃ + 5O₂ ―› 4NO +6H₂O (l)
Now, first of all we observe that water is in the liquid state. We know that the volume
of solids and liquids is considered to be zero so the volume of water, in this case
is considered to be zero. Now, if we observe that 4 molecules of ammonia react with 5 volumes
of oxygen to give 4 volumes of nitric oxide. By Gay-Lussac’s law, we know that gases
react in volumes. So by this we have ammonia reacts with oxygen in 4:5 ratio and ammonia
produces nitric oxide in 4:4, i.e. 1:1 ratio. Avogadro states that under the same conditions
of temperature and pressure, equal volumes of all gases contain the same number of molecules.
So if the volume of the gases is the same, they have the same number of molecules. This
means that the gas which has the greatest volume or the gas which occupies the greatest
volume has the greatest number of molecules. In this case we observe 4 volumes of ammonia,
5 volumes of oxygen and 4 volumes of nitric oxide. This means that ammonia and nitrogen
contain the same number of molecules. Since the volume of oxygen is the greatest, so oxygen
has the greatest number of molecules. So by Avogadro’s law, under the same conditions
of temperature and pressure, the gas which occupies the maximum volume contains the maximum
number or the greatest number of molecules.