Question

I was wondering what would be the rate at which water would cross a semipermeable membrane that allows particles of size greater than 0.5 mm. Knowing that size of water molecules is 2.75 angstroms which is much smaller compared to the sieve, will the membrane allow water to pass through it without any effort? Or, I am missing some concepts involved?

Also without loss of generality, it can be assumed that on one side it is water containing some impurities whose size can be greater than 0.5 mm while the other side do not contain any impurities.

Additionally, what is the mathematical approach to finding the approximate rate involved?

Answer 1

Water will pass through the semipermeable membrane by osmosis because its molecular size is smaller than the membrane's pores. The osmotic rate is influenced by the membrane's permeability, area, and the osmotic pressure gradient.

Step-by-step explanation:

The concept at play here is osmosis, which is the diffusion of water through a semipermeable membrane from an area of low solute concentration to an area of high solute concentration. The size of the water molecule, at 2.75 angstroms, is much smaller than the 0.5 mm pore size of the membrane in question, so the membrane will indeed allow water to pass through it without any effort.

As for the mathematical approach to determine the rate of water movement, it involves understanding the osmotic gradient created by the difference in solute concentration on either side of the membrane. The rate can be estimated using equations that utilize variables such as the membrane's permeability to water (hydrated radius of solute particles and viscosity of the solution), the area of the membrane, and the osmotic pressure gradient.