5. In equilibrium sedimentation, a centrifuge is used to generate a concentration gradient in a test tube. Consider a test tube that contains an aqueous solution, which is spun at an effective gravitational field G (typically, G is on the order of 104105g ). The potential energy E(z) of a solute molecule in this field is meffGz, where meff is an effective mass (which includes the effect of buoyancy) and z is the height of the molecule relative to the bottom of the test tube (set at z=0 ). A) Find the chemical potential of the solute at the height z. To simplify the problem, model the solute molecules as a non-ideal gas of spheres with molecular volume v0, but neglect any attractive interaction energies and the presence of the solvent. Write your answer so that the dependence of the chemical potential on the local concentration c is clear. B) Starting with the idea that chemical equilibrium requires the chemical potential to be the same everywhere, show that the concentration profile obeys the following equation: c(1cv0)2kT(zc)T=meffG C) Find the normalized concentration profile c(z)/c(0) for the ideal case of v0=0. Why is this result expected