Biophysics Equation for Cell Permeability: Alcohol Concentration Model

[charlielow]

Homework Statement

Consider a simple, physical model of a cell in which the cell is regarded as a spherical bag with radius r, bounded by a membrane permeable to alcohol with permeability, P=20μms^-1. Show the concentration of alcohol in the cell is governed by this equation.

Homework Equations

-d(Δc)/dt = (3P/r)Δc

The Attempt at a Solution

I don't really know what to do with this, I don't really know where to start. The second bit of the question asks to solve the equation which I guess you can do by bringing dt over to the other side and dividing by Δc and integrating both sides, but I have no idea how to get the equation really.

 

[Ygggdrasil]

Have you learned any equations to find the flux of molecules across a membrane? Or, have you learned Fick's laws of diffusion? Either one could serve as a starting point for the derivation. (If not, here's a website with some explanations)