Treatment of industrial wastewater using bacteria. Often the waters of industrial waste contains some organic contaminants that can be processed by bacteria. However, sometimes the degree of acidity of the water does not allow the bacteria live. A novel method to treat such waters consists of separating the bacteria and the waters through a membrane in which the organic compounds are dissolved, but which does not allow the passage of water and acid. Once dissolved, organic compounds diffuse inside the membrane, until you reach the other side of it, where the bacteria are attached. Organic contaminants "redissolve" in the bacterial phase, diffuse within it and at the same time are processed with a speed that is proportional to the concentration of pollutants, that is, RC=kRCCb. The process is outlined as continuation

The distribution coefficient of the contaminant compound between the water and the membrane is Hm, while between the membrane and the bacterial phase it is Hb. The diffusion coefficient of the contaminant in the membrane is Dm and in the bacterial phase is Db. At the end of the movie bacterial contaminant concentration is zero. Develop an expression that allows know the amount of contaminant that can be processed in this system