Problem 8: Mean Passage Time Through a Membrane The concentration profile inside a certain membrane of thickness d (0 d, and B is a so-called partition coefficient. (a) Sketch n(x) versus x. RC (b) Calculate the particle flux through the membrane. j (x) = - D- an = D- Bn , dx d (c) If the membrane has a cross-sectional area A, what is the net number of particles per second (call it I ) passing through the membrane? 1 = jA Bn Bn I =D--A = DA- d(CI) The function n(x) gives the number of particles per unit volume. What then is the number of particles in a volume of cross-sectional area, A, and thickness along x of dx in terms of n(x), A, and ox? (e) Using your answer to (d) write and carry out an integral to calculate the total number of particles in the membrane (call it N). (1') Use your answers to (c) and (e) to calculate the mean time (call it T ) that each particle spends inside the membrane