Two different concentrations of a solution are separated by a membrane through which the solute can diffuse. The rate at which the solute diffuses is proportional to the difference in concentrations between two solutions. The differential equations governing the process are: dC1 dt= −k V1(C1−C2) dC2 dt= k V2(C1−C2) where C1 and C2 are the two concentrations, V1 and V2 are the volumes of the respective compartments, and k is a constant of proportionality. If V1 = 20liters,V2 = 5liters, and k = 0.2 liters/min and if initially C1 = 3moles/liter and C2 = 0, find C1 and C2 as functions of time.

Two different concentrations of a solution are separated by a membrane through which the solute can diffuse. The rate at which the solute diffuses is proportional to the difference in concentrations between two solutions. The differential equations governing the process are: dC1 dt= −k V1(C1−C2) dC2 dt= k V2(C1−C2) where C1 and C2 are the two concentrations, V1 and V2 are the volumes of the respective compartments, and k is a constant of proportionality. If V1 = 20liters,V2 = 5liters, and k = 0.2 liters/min and if initially C1 = 3moles/liter and C2 = 0, find C1 and C2 as functions of time.