I need help with Question 2.

Question 1. Consider the reaction sequence 2A$B>20 361 where each reaction obeys mass action kinetics. The reaction begins with A and B at concentrations a0 M and be M, respectively, and no G present. Let a = [A], b = [B] and c = [C]. In assignment 7, we found a system of ODEs, a conservation law and the equilibrium for this reaction scheme. You may refer to the solutions to assignment 7 on Canvas LMS for these. In this assignment we will continue our analysis of the reaction. For the reaction above: (a) Find equations for the vertical and horizontal nullclines in the ob plane (with a on the horizontal axis, 6 on the vertical axis). (b) Draw by hand a phase plane diagram. Include and label 0 the equilibria the nullclines the ow eld in each region of the plane some plausible trajectories, assuming that initially there is no B present I O I 0 some plausible trajectories, assuming that initially there is no A present Give a mathematical justication for the direction of the ow eld. (c) Sketch plausible graphs of a, b and 0 versus 35 for each of the initial conditions l.CLU=1M,bO=0,CU=0 ll. a0=0,bo=1M,Co=0 Include and label any asymptotes and axis intercepts. Question 2. For the reaction above, suppose that 191 = 100 M'1 31, k_1 = 100 81 and k2 = 1 31. Let the initial conditions be 0.0 = 4 M, bg = Cg = U. (a) Use an equilibrium approximation to derive an (approximate) equation for g in terms of a. (b) Use the answer from (a) to estimate 3: at a time when half the initial quantity of A has been used up. (c) According to the equilibrium approximation, does the overall reaction (of A being converted to C) have saturating behaviour? (d) Comment (in 12 lines) on whether or not an equilibrium approximation is reasonable