# Gay Lussac and Avogadro Law

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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

found that, yes Avogadro was right. But unfortunately, that was after Avogadro was dead.

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.

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Rajesh KumarPost authorLorenzo Romano Amedeo Carlo Avogadro's law state that "equal volume of all gases under similar conditions of temperature and pressure contain the same number of molecules." but [ gases do not have fixed volume .then how he was able to calculate the volume of gases.]

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