Please solve the following question in detail!!!

II.22 Develop the state model for an ideal binary batch distillation column with N ideal plates (Figure PII.12). At t=0, the composition of the initial mixture is cA and cB (molar fractions), and its total mass is M (moles). (a) List all assumptions that you make for modeling the system. (b) Identify the relevant balance equations. (c) In addition to the balance equations, what other relationships do you need to complete the state model? (d) Show how you can find the time when the composition of the overhead product has reached a composition yA (molar fraction). (e) How many degrees of freedom does the system possess? (f) How many control objectives can you specify? Additional questions: (g) Does the vapor flow rate remain constant if the heat input Q remains constant with time? (h) What about FR; does it remain constant? Under what conditions would you change it