5. physics insulated container problem: A thermally insulated container consists

Question

5. physics insulated container problem:

A thermally insulated container consists of two liquid solutions separated by a semi-permeable membrane. Both solutions consist of a charge neutral solvent C and two ion species A2+ and B-. A voltage is applied on the solutions. The electrical potential is uniform within each solution, but has two different values PhiI and PhiII in solution I and II. The membrane only allows ion A2+ to pass through. In addition, it is thermally conductive and can move freely to accommodate volume change of the liquid solutions. Generally for an open system containing charged species, its fundamental equation can be written as dU = TdS - PdV + i = 0 to J muidni + Phidq , where mui and ni(i=1... J) are the chemical i=0 potentials and molar numbers of all the species. q, the total charge of the system, can be expressed as q = eN0 i = 1 to J zini, where e= 1.602 Times10-19 coulomb is the electron charge, N0=6.02 Times 1023 is the Avogadro's number and zi is the charge number of the ions (zi = 2 for A2+, -1 for B- and 0 for C). Assume that C, A2+ and B- form ideal solution. At equilibrium, Solution I has a higher electrical potential than Solution II. Which one has a higher A2+ concentration? Briefly explain.

Explanation / Answer

At equillibrium, solution II will have higher A2+ ion concentration.

This is because the electrical potential of solution I is higher than solution II so electron flow will occur from solution II to solution. But according to the given condition only A2+ ions can pass through the membrane, A2+ ions will migrate from solution I to solution II in order to make the current flow from solution II to solution I.

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