Tangential Velocity Homework: Calc Attractive Energy/Force & Find Min Velocity

[Priscilla]

Homework Statement

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

Homework Equations

N_A = 6.02*10^23 molecule/mol
E=fr
F_c = mv^2/r

The Attempt at a Solution

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?

 

[Priscilla]

Anyone know how to solve this?

 

[Quinzio]

Priscilla, 99,9% of posts in this section can be solved with the formula F=ma.

Your question is yet advanced, try posting it in Advanced Physic or Chemistry.
For myself, I am an electronic and I didn't even know that the attractive energy is measured in kJ/mol.

I'm going to read something about it because it looks interesting, and maybe let you know any idea.

What I find strange is that you divide an energy by a distance, and you get a force.
f = E/r = (6.03*10^-24 kJ/molecule) / 0.4*10^-9m = 1.51*10^-14 N/molecule of gel

Dimensionally, I don't know if it makes sense.
But, again, I'm pretty ignorant about.

Best things.

 

[Priscilla]

Thanks for your reply.
Our prof gives us some hints that, we could use F=fr which is derive from the intermolecular forces:
E(r) = 4e[ (s/r)^12 - (s/r)^6] s = lower case sigma
=> f = -dE/dr
=> E=fr

 

[luceprice]

You need to change kJ to Joules, since Joules is the SI Unit. The dimensionality will make sense then.