Question

According to Avogadro’s law, why do the equal volumes of molecular hydrogen and nitrogen contain the same number of molecules when they are at the same temperature and pressure?

Answer 1

To solve this question we should know about:
Avogadro’s law: Avogadro's law states that equal volumes of different gases contain an equal number of molecules under the same conditions of temperature and pressure. The kinetic theory of gases can be used to determine this empirical relationship under the premise of a perfect (ideal) gas. For real gases with sufficiently low pressures and high temperatures, the law is approximately correct.
So, we will go with its basic definition and we will use a formula to correlate different quantities and get our desired output.

Complete answer:
This is a fascinating question.
When pressure and temperature are held constant, Avogadro Law explains the link between volume and quantity. Keep in mind that the amount is expressed in moles. Also, because one of the variables is volume, the container housing the gas must be flexible in some fashion, allowing it to expand and shrink. The volume of a container grows when the amount of gas in it is increased.
When the amount of gas in a container is reduced, the volume of the container drops.
Assume the sum is raised. This indicates that there are more gas molecules, which means that the number of hits on the container walls will grow. This indicates that the gas pressure inside the container will rise (for a brief moment), surpassing the pressure outside the walls. As a result, the walls begin to shift outward. As a result, the walls begin to shift outward. The volume of gas has increased as a result of this process.
Assume the amount is reduced. As a result, there will be fewer gas molecules, reducing the number of impacts on the container walls. This indicates that the gas pressure inside the container will drop (for a brief moment) and become less than the pressure outside the walls. The walls begin to move inward as a result of this. The volume of gas will decrease as a result of this procedure.
$\dfrac{V}{n} = k$ is the mathematical form of Avogadro's Law.
This indicates that if the pressure and temperature remain constant, the volume-amount fraction will always be the same.
Let ${V_1}$ and ${n_1}$ be a pair of volume-amount data at the start of an experiment. The volume will change to ${V_2}$ if the amount is increased to a new number named ${n_2}$ .
We know this: $\dfrac{{{V_1}}}{{\;{n_1}}}\; = k$
And we know this: $\dfrac{{{V_2}}}{{\;{n_2}}}\; = k$
Since $k = k$ , we can conclude that $\dfrac{{{V_1}}}{{\;{n_1}}}\; = \dfrac{{{V_2}}}{{\;{n_2}}}\;$
Assume we have a container with a volume of ${V_1}$ litres, which is filled with n moles of hydrogen gas, which has a temperature of T Kelvin and a pressure of P atmosphere.
We have a container with a volume of ${V_1}$ liters that are filled with x moles of hydrogen gas at T Kelvin temperature and P atmospheric pressure.
According to the law $\dfrac{{{V_1}}}{{\;{n_1}}}\; = \dfrac{{{V_2}}}{{\;{n_2}}}\;$
$\dfrac{{{V_1}}}{{\;n}}\; = \dfrac{{{V_1}}}{{\;x}}\;$
${V_1}n = {V_2}x$
On problem-solving, because $x = v$ the two gases must have a comparable number of moles if they take up the same volume and have the same pressure at the same temperature.

Note:
The following are some examples of Avogadro's law's applications:
It clarifies Gay Lussa’s volume combining law.
It determines the atomicity of gases.
It aids in the determination of a gas's molecular formula.
It aids in the discovery of a link between molecular mass and vapor density.