Water containing \(0.1 \mathrm{M}\) benzoic acid flows at \(0.1 \mathrm{~cm} / \mathrm{s}\) through a \(1 \mathrm{~cm}\) diameter rigid tube of cellulose acetate. The walls of the tube are \(0.01 \mathrm{~cm}\) thick and are permeable to small electrolytes like the acid. Solutes within the tube wall diffuse as though moving through water. The tube is immersed in a large, well-stirred water bath containing negligible acid. After \(50 \mathrm{~cm}\) of tubing, what fraction of the \(0.1 \mathrm{M}\) benzoic acid solution has been removed? The diffusivity of benzoic acid in water is \(1 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}\).