You wish to extract aniline from an aqueous phase solution by contacting it with toluene in a counter-current solvent extraction process. The tower has 10 stages and is illustrated below. State any assumptions that you make. Extract Feed (W) 100 lb/h water 5 lb/h aniline 1 2 3 4 5 6 Recycled solvent (F) 13 lb/h toluene 0.003 lb-aniline/lb-toluene 7 8 9 10 Raffinate Solvent (S) 10 lb/h toluene i) By performing a material balance around each stage, derive a set of 10 simultaneous equations (with unknown X) that must be solved. Assume that toluene and water are completely immiscible. As a first approximation, assume that equilibrium is achieved at each stage and is described by the relationship, YA = 9 X; m = Where, Yi = mass of aniline / mass of toluene in the solvent-rich phase leaving stage i and, Xi = mass of aniline / mass of water in the aqueous phase leaving stage i ii) Solve the equations derived in (i) using in-built functions in python. iii) A better approximation of the equilibrium relationship is m = 9+20X;. Modify your equations and explain how you can recognize that the system is now non-linear. iv) Solve the system and compare your results to the linear approximation