**Example Algorithm for Steps in Solving Closed-Ended Problems**

**Statement**The elementary, liquid-phase, irreversible reaction

is to be carried out in a flow reactor. Two reactors are available, an 800 dm

^{3}PFR that can only be operated at 300 K and a 200 dm^{3}CSTR that can be operated at 350 K. The two feed streams to the reactor mix to form a single fee d stream that is equal molar in A and B, with a total volumetric flowrate of 10 dm^{3}/min. Which of the two reactors will give us the highest conversion?Additional Information: at 300 K, *k*= 0.07 dm^{3}/mol-min

E = 85000 J/mol-K

C_{A0B}= C_{B0B}= 2 mol/dm^{3}*v*_{A0}=*v*_{B0}= 0.5**v*_{0}= 5 dm^{3}/min**Real Problem**We have two choices, a PFR operated at 300 K and a CSTR operated at 350 K. Which one do we choose?

**Sketch**

**Identify and Name**- Relevant Theories and Equations
__Arrhenius Equation:__The higher the temperature, the faster the reaction rate.

__Rate Law:____Mole Balances:__ - Systems
Volume of CSTR

Volume of PFR - Dependent and Independent Variables
Independent: V, F

_{A0}, T

Dependent: X - Knowns and Unknowns
Knowns:

*k*_{0}, E, V, n_{0}, C_{A0B}, C_{B0B}

Unknowns: X - Inputs and Outputs
In: F

_{A0}= F_{B0}, so Q_{B}= 1

Out: F_{A}= F_{A0}(1-X), F_{B}= F_{A0}(1-X), F_{C}= F_{A0}X - What color should we paint the reactor?
Not an issue.

- Relevant Theories and Equations
**Assumptions**Isothermal, no pressure drop. The CSTR is well mixed. There are no radial variations in the PFR.

**Specifications**There is neither too much redundant information, nor is there too little information given. Therefore, the problem is neither over-specified, nor under-specified.

**Similar or Related Example Problems**This problem has a solution procedure in common with Examples 4-2 and 4-4 in the text.

**Algorithm****CSTR****PFR**

- Mole Balance
- Rate Law
- Stoichiometry
- liquid, v = v
_{o}; equal molar \ Q_{B}= 1C

_{A}= C_{A0}(1-X)C

_{B}= C_{A0}(1-X) - Combine

(eqn 1)

(eqn 2) - Evaluate

*v*_{A0}= 5 dm^{3}/min

Before mixing

C_{A0B}= 2 mol/dm^{3}

F_{A0}= C_{A0B}**v*_{A0}

F_{A0}= (5 dm^{3}/min)(2 mol/dm^{3}) = 10 mol/min

After mixing

*v*_{0}=*v*_{A0}+*v*_{B0}= 5 dm^{3}/min + 5 dm^{3}/min = 10 dm^{3}/min

C_{A0}= 1 mol/dm^{3}

at 350 K, *k*= 8.447 dm^{3}/mol-min

- Mole Balance
**Manipulate**- CSTR @ 350 K
the combined CSTR equation (eqn 1) can be arranged as

- PFR @ 300 K

Choose the CSTR, because it gives the highest conversion.

- CSTR @ 350 K
**Units Check**X is dimensionless

**Is it reasonable?**This is a reasonable conversion.

This the end of the PFR/CSTR example.
A sample registration exam problem
is also available.

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