The following elementary first-order reactions occur at constant density:
k1 k2
A --> B --> C
k1 = 5 hr-1
k2 = 4 hr-1
CA0 = 1 mol/lit
CB0 = CC0 = 0
v0 = 20 m^2/min
Find the maximum production rate of B in moles per minute and the optimum � for
(a) a plug flow reactor
(b) a mixed flow reactor
Find the production rate of B in moles per minute for
(c) a mixed flow reactor with V = 100 m3
(d) two mixed flow reactors in series, each 50 m3
To find the maximum production rate of B in moles per minute and the optimum θ for different types of reactors, we need to use the rate equation for each reaction and consider the different reactor configurations.
The rate equation for a first-order reaction is given by:
Rate = k * CA
where Rate is the reaction rate, k is the rate constant, and CA is the concentration of reactant A.
(a) Plug Flow Reactor:
In a plug flow reactor, the volume is constant, and the reaction proceeds as the reactant flows through the reactor without mixing. The production rate of B can be found by considering the rate equation for the first reaction (A -> B).
Rate of B production = k1 * CA
The maximum production rate of B will occur when CA is maximized. At the entrance of the reactor, CA0 is known to be 1 mol/lit. Therefore, the maximum production rate of B can be calculated as:
Maximum production rate of B = k1 * CA0
(b) Mixed Flow Reactor:
In a mixed flow reactor, there is continuous mixing of the reactants, and the volume can change. The production rate of B can be found by considering the rate equation for both reactions (A -> B and B -> C).
We need to calculate the concentration profiles of A, B, and C at steady-state. The equation for the concentration of A at any point (x) in the reactor is given by:
CA = CA0 * e^(-k1 * x)
The concentration of B can be obtained by integrating the rate of change of B with respect to volume (V):
CB = (k1 * CA0 / (k1 - k2)) * (e^(-k2 * x) - e^(-k1 * x))
The production rate of B can then be calculated as:
Production rate of B = V * dCB/dt
Optimum θ is the reactor volume (V) divided by the volumetric flow rate (v0):
θ = V / v0
(c) For a mixed flow reactor with V = 100 m3:
Using the concentration profile equations and the given values, we can calculate the production rate of B at steady-state.
(d) For two mixed flow reactors in series, each 50 m3:
In this case, we will calculate the concentration profiles for each reactor individually using the equations provided. Then we will determine the production rate of B for each reactor, considering the outlet concentration of the previous reactor as the inlet concentration for the next reactor. We can sum up the production rates from both reactors to obtain the total production rate of B.
Please provide the values for the volumetric flow rate (v0) and any other relevant information to proceed with the calculations.