Question

The magnitude of the liquid-phase diffusivity is much smaller than that of the gas-phase diffusivity -justify the steatment...

Answer 1

Solution:

Magnitude of the liquid-phase diffusivity is much smaller than that of the gas-phase diffusivity because,

In a gas phase, molecules possess a certain mean velocity depending on the temperature, but their motion is chaotic and in colliding, they change the direction of this motion. However, on the whole, the molecules of the substance migrate at a velocity much lower than the mean velocity of the molecular free motion. The higher the pressure, the denser is the molecule packing, the less is the free-path length, and the slower is the diffusion. The same occurs as molecule mass and size increase. Conversely, elevation of temperature causes an increase in the free-path length, a decrease in the number of collisions, and growth of free-motion velocity. These factors all lead to a speed-up of diffusion with increase in magnitude.

In liquids, molecular diffusion occurs by jumps of the molecules from one position to another; this arises when the energy of the molecule is high enough to rupture the bonds with the neighboring molecules allowing the molecule to move. On average, the jump does not exceed an intermolecular spacing, and since in a liquid this is much less than in a gas, the diffusion is substantially lower. Since a liquid is virtually incompressible, the diffusion rate is independent of pressure.

Hence, magnitude of the liquid-phase diffusivity is much smaller than that of the gas-phase diffusivity.