Question

State and explain Avogadro’s law.

Answer 1

Avogadro’s law is one of the Gas Laws based on the Kinetic Molecular Theory of Gases. Various gas laws can be explained based on the kinetic molecular theory of gases. Gas laws (Boyle’s law, Charles’s law, Dalton’s law of partial pressure, Avogadro’s Hypothesis) were based only on the practical observations.

Complete step by step answer:
The first step of the solution is the statement of Avogadro’s law. According to Avogadro’s law, “At constant temperature and pressure, an equal volume of gases have an equal number of moles.”
Now we will explain the statement of Avogadro’s law numerically under favorable considerations and conditions. Let us consider that two gases are having equal pressure and volume. The pressure of the two gases is represented by $P$ and the volume of the two gases is represented by $V$.
Now according to graham’s law of diffusion, the kinetic gas equation can be given as,
$PV = \dfrac{1}{3}mn{v^2}$ Where $mn = M$ represents the molecular mass. $P,V,v$ represents the pressure, volume, and velocity of the gas.
Now using graham’s law of diffusion for the two gases we can conclude that,
$PV = \dfrac{1}{3}{m_1}{n_1}v_1^2$ ,(first gas) $- \left( 1 \right)$
$PV = \dfrac{1}{3}{m_2}{n_2}v_2^2$, (second gas) $- \left( 2 \right)$
Now comparing equations $\left( 1 \right)$ and $\left( 2 \right)$ we get,
$\dfrac{1}{3}{m_1}{n_1}v_1^2 = \dfrac{1}{3}{m_2}{n_2}v_2^2$, as both equals to$PV$.
$\Rightarrow {m_1}{n_1}v_1^2 = {m_2}{n_2}v_2^2$ $- \left( 3 \right)$
Now the temperature for both gases is the same according to the statement of Avogadro’s law. So, the kinetic energy of the two gases will be the same. Because kinetic energy is directly proportional to absolute temperature.
$\dfrac{1}{2}{m_1}v_1^2 = \dfrac{1}{2}{m_2}v_2^2$
$\Rightarrow {m_1}v_1^2 = {m_2}v_2^2$ $- \left( 4 \right)$
Now we will divide equation $\left( 3 \right)$by equation$\left( 4 \right)$. We get,
$\dfrac{{{m_1}{n_1}v_1^2}}{{{m_1}v_1^2}} = \dfrac{{{m_2}{n_2}v_2^2}}{{{m_2}v_2^2}}$
$\Rightarrow {n_1} = {n_2}$
Hence, we have derived and explained that at similar temperature and pressure equal volume of gases has an equal number of moles.

Note:
Avogadro’s law is perfectly valid for ideal gases.
Avogadro’s law is approximately valid for the real gases at sufficiently low pressure and high temperatures.Lighter gas molecules for example hydrogen and helium obey Avogadro’s law perfectly as compared to heavy gases.