Please answer all the questions correctly providing necessary formulae, equations, expressions, diagrams, charts, graphs, plots and tables.

3. i) Derive Rayleigh equation for binary mixture in batch distillation. [10] ii) Derive an expression relating crystal growth rate and overall mass transfer resistance for crystallization operation. [5] iii) The feed to a continuous crystallizer that can be simulated with the MSMPR model is 5,000kg/h of 40 wt\% sodium acetate in water. Monoclinic crystals of the trihydrate are formed. The pressure in the crystallizer and the heat-transfer rate in the associated heat exchanger are such that 20% of the water in the feed is evaporated at a crystallizer temperature of 40C. The crystal growth rate, G, is 0.0002m/h and a predominant crystal size, Lpr, of 20 mesh is desired (opening is 0.833mm ). Determine the: (a) kg/h of crystals in the exiting magma; (b) kg/h of mother liquor in the exiting magma; and (c) volume in m3 of magma in the crystallizer If density of the crystals =1.45g/cm3 and density of the mother liquor =1.20g/cm3. [10]