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# Avogadro's Law

Amedeo Avogadro introduced the term "molecule" and distinguished it from 'atom'. According to Avogadro, particles in the gaseous state do not exist as atoms but as molecules.

In 1811 he proposed his famous hypothesis, now known as 'Avogadro's Law'. As it was found that even a fraction of an atom was involved in certain chemical reactions Avogadro's Law helped in correcting Dalton's atomic theory on indivisible atoms.

Therefore, Avogadro postulated the existence of molecules along with atoms as two kinds of ultimate particles. The term molecule was introduced by Amedeo Avogadro and he distinguished the atoms and the molecules. He suggested that in the gaseous phase most of the particles exist as molecules.

It is known that in gases the rare gases or the noble gases exist as the atoms where as other elements like nitrogen, hydrogen, chlorine and fluorine exist as diatomic molecules. The molecules are the smallest part of the element which has an independent existence.

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## Avogadro’s Law Equation

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In the year 1811 Amedeo Avogadro put forward his famous law called as the Avogadro law.
The Law states that "Equal volume of all the gases at same temperature and pressure, contains equal number of molecules."
This law basically means that if you have two samples of Chlorine and oxygen, consider that there are two vessels, each of two liter capacity. In the first tank Chlorine gas is filled to 2atm pressure and in the second tank oxygen is filled to 2atm capacity.

If the temperature of both the tanks is same, then according to Avogadro’s Law, both the tanks contain equal number of molecules. The number of molecules in the chlorine tank is the same as the number of molecules in the oxygen tank.

Standard temperature and pressure is called as STP. For gases, the term STP is often used. STP means the temperature of the gas is 273K and the pressure of the gas is 1 atm. Avogadro said that 1 mole of any gas at STP occupies 22.4L of volume.

This means if you have 1 mole of Nitrogen gas at STP, it occupies 22.4 Liter and also the 1 mole of Hydrogen gas which occupies the same volume that is 22.4 Liter. The number of moles can be determined by using the above law, for example if a gas occupies 2.24L at STP, then we know that 1 mole of the gas will occupy 22.4L

So we have got x moles occupying 2.24L
So x = 2.24L x 1mole/22.4L = 0.1 mole
The ideal gas equation is given by
PV = nRT
Where
• P is the pressure of the gas
• V is the volume occupied by the gas
• n is the number of moles
• R is the universal constant
• T is the temperature in Kelvin
From this equation, we can also find find the number of moles or the volume occupied. For example, let us consider 1 mole of the gas at STP.

PV = nRT is the ideal gas equation

Here P= 1atm, V =?, n=1mole R is 0.0821atmL/(mole*K) T =273K
Substituting the values in PV = nRT
V = nRT/P
V = 1 mole * 0.0821 atmL/(mole*K) *298K/1atm

V = 22.4L

Avogadro also expressed the number of atoms present in the mole of a gas. He stated that 6.022 x 1023 particles are present in the 1 mole of a gas. This means if there is 1 mole of He atom, then there are 6.022 x 1023 atoms of Helium. If there is 1 mole of oxygen molecule, then there are 6.022 x 1023 molecule of oxygen atoms. If there is 1 mole of sodium chloride, then it means that there would be one mole of Na+ and one mole of Cl- ion in the solid.

Avogadro’s Law can be stated in other words as well. At standard temperature and pressure, 1 mole of the gas will occupy 22.4L and will contain 6.022 x 1023 particles of the matter.

“At STP 6.022 x 1023 particles of any gas will occupy 22.4L”

From this, we can find the number of particles when the volume at STP is given. For example, If we have 2.24L of oxygen gas at STP, then we can conclude that the volume would contain one tenth of the mole of oxygen gas. That is, total number of 6.022 x 1022 molecules of oxygen will be present.

## Kinetic Molecular Theory of Gas

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Kinetic molecular theory of gases depends on certain postulates, some of those postulates are given below:
1. Gases, as already seen, are made up of ideal particles; the particles may be atoms or molecules. For example, oxygen has molecules where as helium has atoms.
2. The particles of a gas move in a straight line. The particles such as atoms and molecules move in random direction. More precisely the particles in a gas move randomly in a straight line.
3. While in motion they collide with each other and with walls of the container.
4. The collision is perfectly elastic. That is, neither energy nor the momentum is changed.
5. The collision with the walls of the container produces the pressure of the gas. The Gas collision on the walls of the container is the reason for the pressure of the gas.
6. The average kinetic energy depends upon the temperature of the gas. Higher the temperature, more would be the kinetic energy.
7. All molecules do not have the same kinetic energy. The kinetic energy is taken for the average energy of all the molecules.
The kinetic gas equation of the system of gas is given by,

PV = $\frac{1}{3}$mnc2

Where P is the pressure, V is the volume, m is the mass, n is the number of moles and c is the velocity. For any two gases the kinetic gas equation may be written as
P1V1 = $\frac{1}{2}$ m1n1c12
And
P2V2 = $\frac{1}{2}$ m2n2c22

When pressures and volumes of two gases are same P1 = P2 and V1 = V2 then it follows.

$\frac{1}{2}$ m1n1c12 = $\frac{1}{2}$ m2n2c22

If the gases are also at the same temperature, for example, at 273K that is at STP, the average kinetic energies of these molecules will also

$\frac{1}{2}$ m1c12 = * $\frac{1}{2}$ m2c22
be equal,

Therefore, from the above equation, we get

n1 = n2

So we can see that at the same temperature, pressure and volume the number of moles are equal. The gases have same number of moles or molecules at the same temperature and pressure.

## Kinetic Molecular Interpretation

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Equal volumes of all the gases contain the same number of molecules, under the same conditions of temperature and pressure.

If we assume that 1 litre of hydrogen at STP contains 'n' molecules of hydrogen, then according to Avogadro's Law:
• 1 litre of oxygen at STP contains 'n' molecules of oxygen.
• 1 litre of ammonia at STP contains 'n' molecules of ammonia.
• 1 litre of any gas at STP contains 'n' molecules of that gas.

## Kinetic Theory Interpretation

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The kinetic gas equation is For any two gases the kinetic gas equation may be written as When pressures and volumes of two gases are same P1 = P2 and V1 = V2 then it follows. If the gases are also at the same temperature, the average kinetic energies of these molecules will also be equal, Therefore, from the above equation, we get
n1 = n2

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