Steady-state/ dynamic models of chemical reactors

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Hi everyone,

I'm trying to solve a problem concerning steady state and dynamic models of chemical reactor. I attached the problem statement for better understanding. Please disregard part (a). Here's what I have come up with so far:

For part (b) I have the following

From Mass Conservation
Component A: ρ*V*dx/dt = w*xi - w*x - V*k(T)*x or ρ*V*dx/dt = w(xi - x) - V*k(T)*x
Component B: ρ*V*dy/dt = -w*y - V*k(T)*yC

and from Energy Conservation (not sure about this one)
V*ρ*C*dT/dt = w*C*(Ti-T) + Q

For part (c) I think I should do the following

Set the derivatives equal to zero
Component A: 0 = w(xi - x) - V*k*x
Component B: 0 = -w*y - V*k*y

and then solve for x using the data given below part (c). However, I'm confused because the data already includes a value of x (x=0.05) so I think that I'm doing something wrong. Maybe I don't understand what the question is asking. Also, I'm a little confused about molecular weights, MA and MB. How am I supposed to use them? I did notice that when I was trying to solve for x (assuming my thinking is correct) I couldn't get the units to cancel out in this term V*k*x. V is in L and k is in mol/min and x is dimensionless. I'm pretty sure I'm not understanding something so if anyone could at least guide me in the right direction I would really appreciate it. Also please let me know whether my models are correct.
 

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