(2) Dimerization Reactor Separator 2A A (3) (4) (1) Pure A 111. In the process presented above, pure A is fed into a dimerization reactor at a rate of F1 (Kg/s), where it is converted into A2 at a conversion rate XA (mol/s). The outlet stream (2) contains a mixture of Az and unreacted A which is then sent to a separation unit. The separation unit outputs two streams: (4) rich in A2, and (3) rich in A. In order to monitor the process, you are provided two concentration sensors, which are able to measure the molar fraction of A in the streams (2), x) and (4), xA(), as well as a mass flow controller that monitors the mass flow rate (Kg/s) of stream (3), F3. i. (10 points) Write a system of equations that allows you calculate the molar flow rates of species A and Az in all the stream as a function of the input parameters: F1, F3, XA XA(4) ii. (5 points) Express this system of equation in matrix form (1.e. A*v=b). (10 points) Write a Matlab function that takes as input F1, F3, x4(2), 4(4) and outputs the molar flowrates (mol/s) of each species for all the streams. Your output should be a vector with the following structure: [m4; ma;MA;m&(4); mazl2); m42%); m424]. Evaluate your function and report the output vector for Fi= 10 Kg/s, F3=1 Kg/s, XA2=0.2, x 4) =0.05. Does a unique solution exist? Explain your reasoning. (10 points) Plot the conversion of A %) in the reactor against the flow rate of stream (3), while keeping F1, XA, XA(4) constant at the values provided in (111). Plot at least 100 points from 0 to 100 Kg/s. (5 points) The flow controller for stream (3) stopped functioning, and the plant operator decided to install a new one in stream (4). Re-write your system of equations for the new situation. Does a unique solution exist for the new system? Explain your reasoning. Physical parameters: Molecular Weight of A = 53.06 g/mol (2) iv. (2) V