[Aiyume]

A carbohydrate gel is being centrifuged to remove excess physisorbed water. Assume that the magnitude of the attractive energy between the water molecules and the gel is given by 3.63 kJ/mol of molecules of water, with the water molecules being separated from the surface of the gel molecules by 0.4 nm.
a)Calculate the attractive energy per molecule of water, and the attractive force between one molecule of water and one gel molecule.
b)Assuming that the gel in the centrifuge has a radius of curvature of 0.5 m when the centrifuge rotates, find the minimum tangential velocity with which the centrifuge needs to rotate in order for water molecules to just begin to separate from the gel molecules, at a separation of 0.4 nm

The attractive energy per molecule of water
E = 3.63kJ/mol of molecules of water
E = 3.63kJ/mol / 6.02*10^23 molecule/mol = 6.03*10^-24 kJ/molecule of H2O

The attractive force between one molecule of water and one gel molecule
E = fr
f = E/r = (6.03*10^-24 kJ/molecule) / 0.4*10^-9m = 1.51*10^-14 N/molecule of gel

The minimum tangential velocity
F_c = mv^2/r
F = 1.51*10^-14 N r = 0.5m
I know I can use this equation to find the velocity, but I don't know the mass. How can I find the mass?

[ebaines]

You need to know the difference in mass between the gel molecue and the water molecule. This is because it's the difference in centripetal force that the two molecules experience that will pull them apart. Hence



Finding the mass of a molecule of water is easy, since you know its makeup (H20). But unless you're told what the mass of a gel molecule is, you can't complete this question.