(20 point) A countercurrent extraction cascade with n equilibrium stages can be described like the scheme shown below. 1 Y2 yn ys Extracts 1- S Extraction solvent 1 2 n-1 n Feed F Xf X1 F Raffinate xn 2 xn-1 Prove the following relationship using a material balance on the solute for the (n 1) th stage, where E is an extraction factor. Assume that the partition coefficient is constant. Xn-2 = (E? + E + 1)xn = (20 point) A countercurrent extraction cascade with n equilibrium stages can be described like the scheme shown below. 1 Y2 yn ys Extracts 1- S Extraction solvent 1 2 n-1 n Feed F Xf X1 F Raffinate xn 2 xn-1 Prove the following relationship using a material balance on the solute for the (n 1) th stage, where E is an extraction factor. Assume that the partition coefficient is constant. Xn-2 = (E? + E + 1)xn =