1. A batch rectification column shown in the figure below (N=5). Total Condenser V 5 L D=10 kmol/hr 4 3 2 1 Feed=100 kmol C3(20%) iC4(20%) nC4(20%) iC5(20%) nC5(20%) Q The K values are given by the equations shown below (T is in F): K_C3 = (0.00007*T*T) - (0.003*T) + 1.441 K_iC4 = (0.00005*T*T) - (0.002*T) + 0.531 . K_nC4 = (0.00005*T*T) - (0.006*T) + 0.745 . K_iC5 = (0.00003*T*T) - (0.004*T) + 0.438 . K_nC5 = (0.00003*T*T) - (0.004*T) + 0.327 a. Find the bubble point temperature of the feed mixture. (50 points) b. Using nC5 as the reference component, find the values of relative volatility for each component. If the distillation column is operated at total recycle at startup, find the distillate composition at the startup phase using the shortcut method. (50 points) C. Batch rectification operation is started at time t = 0. It is operated such that V = 110 kmol/hr and R = 10. To simulate the behavior of the distillation operation, take a time step of 0.5 hours. At this time point, calculate the composition of the bottom pot. Using this composition, calculate the new bubble point temperature of the bottom pot. (100 points) d. At this new temperature, calculate the new values of relative volatility for each component. Use the shortcut method to evaluate the expressions for the Gilliland equation and Underwood equation. Solve simultaneously to find the values of Nmin and Rmin. Find the new distillate composition. (200 points) e. At the next time step, calculate the new bottom pot composition and the new bubble point temperature. Using these values, repeat step (d) to find the new distillate composition. (100 points)