Derivation of Graham’s Law of Diffusion
According to Kinetic Molecular theory,
PV = mNc2 / 3
If we have 1 mole of gas then N = NA
PV = mNAc2 / 3
Where,
P = Pressure, V = Volume, m = Mass, NA = Avogadro’s number of molecule, c2 = Velocity
∴ PV = Mc2 / 3 …(mNA = M (Molar mass))
∴ c2 = 3PV/M
∴ c2 = 3P/d …(density (d) = M/V)
Take Square root on both side,
∴ √c2 = √(3P/d)
∴ √c2 = Rate of Diffusion
∴ Rate = 1/√d
Important Points to remember
- The gas goes from higher concentrations to lower concentrations during the phenomenon of diffusion, whereas during the process of effusion, the gas moves from lower to higher concentrations.
- A gas’s entrance system becomes significantly disorganized due to diffusion. Both solid and liquid gases have slower rates of action.
- The length of time a gas particle spends in the diffusion process is directly inversely proportional to its molecular weight.
- The molecular masses and vapor density of a gas molecule are calculated using Graham’s law of diffusion.
- Additionally, this is employed in the separation of isotopes from the same element as well as the separation of various gases from a mixture of gases.
Graham’s Law of Diffusion
Graham’s law of diffusion is the relationship between a gas’s rate of diffusion or effusion and its molecular weight. The law of diffusion’s basic tenet is that any gas’s rate of diffusion, at any given temperature and pressure, is inversely proportional to the square root of its density. The mechanism by which a gas can escape from the container is known as effusion, and the ability of a gas to spread and occupy all of the volumes that are available to it is known as diffusion.