Steady-state/ dynamic models of chemical reactors

[koala]

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.

 

[Achy47]

Hi there,

It looks like you have made some good progress so far! Let's break down the problem and go through it step by step.

First, for part (b), you are correct in using the mass and energy conservation equations. However, for the energy conservation equation, you will need to also include the energy from the reaction, which is given by -ΔHr*x*w, where ΔHr is the enthalpy of the reaction and x is the extent of reaction. So your energy conservation equation will look like this:

V*ρ*C*dT/dt = w*C*(Ti-T) + Q - ΔHr*x*w

For part (c), you are on the right track. Setting the derivatives equal to zero will give you the steady state conditions. However, you will also need to include the equilibrium equations for each component, which are given by:

Kc = (y/x)^n

Where Kc is the equilibrium constant, y is the molar concentration of component B, x is the molar concentration of component A, and n is the stoichiometric coefficient. These equations will help you solve for the unknown variables.

As for the molecular weights, MA and MB, you will need to use them to convert between molar concentrations and mass concentrations. The molar concentration of a component is given by C = ρ/M, where ρ is the mass concentration and M is the molecular weight. So for example, for component A, the molar concentration will be given by:

CA = ρA/MA

I hope this helps guide you in the right direction. Let me know if you have any further questions or need clarification on anything. Best of luck!