Question

Problem (15 points) A complex reaction (A-> products) involving 2 enzymes occurs in an ideal steady state mixed flow reactor (constant flowrate, outlet concentration is the same as reactor concentration). Both reactions consume reactant A. See the diagram below. The reaction constants for the enzymes and reactor volume/flow are given below. If needed, enzymatic reaction rate model is, r= -Vm*C/(Km+C) Reactor volume, V=100 L flowrate, q = 5 L/hr CA.=100 mol/L Vml=3.3 mol/L-hr Kml=0.05 mol/L| (reaction 1) Vm2 = 5 mol/L-hr Km2 = 200 mol/L (reaction 2) 1. (5 points) Assuming C is the reactant concentration in the tank, write the mass balance for the reactor as the system. Check your units to make sure they are correct!

Answer 1

In an ideal mixed flow reactor we can write-
Using the mass conservation of A

Rate of mass coming in - rate of mass going out- rate of disappearance by the reaction = rate of accumulation of mass

Rate of mass coming in = flow rate coming in*concentration of the incoming reactant

=q*Cao
=5 L/he * 100 mole/L
=500 mole/hr
Assuming that the reactor is well mixed and thus the concentration in the reactor as well as in the outgoing steam is C.

Rate of mass going out = q*C
=5C mole/hr

Rate of disappearance due to the reaction=
Net rate of reaction*Volume of the reactor
(Vm1*C/km1+C )+ Vm2*C/km2+C

Values are given in the question-
Net rate of reaction
=3.3C/(0.05+C ) +5C/(200+C)

Rate of accumulation of mass = d(V*C)/dt

V= 100 L.

d(100*C)/dt

Keeping all the values in the conservation equation.

500-5C- 100*(3.3C/(0.05+C ) +5C/(200+C)=100dC/dt

This is the mass balance equation for the given case.

Hope this helps

Thanks