Chapter 6: Isothermal Reactor Design: Molar Flow Rates

Gas Phase PFR

 

Problem:

The elementary irreversible gas phase reaction 2A -> B is carried out isothermally with no pressure drop in a PFR.

Given:

Use measures other than conversion to plot molar flow rates of A and B down the reactor.

Hint 1: What are the mole balances on A and B and the rate law?

mole balances on A ?

(a) $\frac{dF_{A}}{dV} = 2r_{A}$

(b) $\frac{dF_{A}}{dV} = -2r_{A}$

(c) $\frac{dF_{A}}{dV} = -r_{A}$

(d) $\frac{dF_{A}}{dV} = r_{A}$

mole balances on B ?

(a) $\frac{dF_{B}}{dV} = r_{A}$

(b) $\frac{dF_{B}}{dV} = -2r_{A}$

(c) $\frac{dF_{B}}{dV} = \frac{-r_{A}}{2}$

(d) $\frac{dF_{B}}{dV} = \frac{r_{A}}{2}$

rate law ?

(a) $r_{A} = -k{C_{A}}^2$

(b) $r_{A} = k{C_{A}}^2$

(c) $r_{A} = kC_{A}$

Hint 2: What are the concentrations of A and B?

(a) $C_{A} = C_{T0}\frac{F_{A}}{F_{B}}p\frac{T_{0}}{T}$

(b) $C_{A} = C_{T0}\frac{F_{A}}{F_{A}+F_{B}}p\frac{T_{0}}{T}$

Hint 3: What is the rate of formation of B?

(a) $r_{B} = \frac{1}{2}C_{T0}\frac{F_{B}}{F_{T}}p\frac{T_{0}}{T}$

(b) $r_{B} = -2C_{T0}\frac{F_{B}}{F_{T}}p\frac{T_{0}}{T}$

(c) $r_{B} = -\frac{1}{2}C_{T0}\frac{F_{B}}{F_{T}}p\frac{T_{0}}{T}$

Hint 4: What are the combined mole balance, rate law and stoichiometry?

(a) $\frac{dF_{A}}{dV} = k_{A}C_{T0}\frac{F_{A}}{F_{A}+F_{B}}$

(b) $\frac{dF_{A}}{dV} = -k_{A}C_{T0}\frac{F_{A}}{F_{A}+F_{B}}$

Hint 5: What is the polymath program?

Full Solution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hint 1 - Mole Balances and Rate Law

           Mole Balances

            Rate Law

Back to Hints

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Hint 2 - Concentrations

            Stoichiometry

            For Isothermal and No DP

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Hint 3 - Rate of Formation of B

$$ \textrm{For } A + \frac{b}{a}B \rightarrow \frac{c}{a}C + \frac{d}{a}D $$

$$ \frac{r_{A}}{-a} = \frac{r_{B}}{-b} = \frac{r_{C}}{c} = \frac{r_{D}}{d} $$

$$ \textrm{For } 2A \rightarrow B $$

$$ \frac{r_{A}}{(-2)} = \frac{r_{B}}{(1)} $$

$$ r_{B} = \frac{1}{2}(-r_{A}) = \frac{k_{A}}{2}{C_{A}}^2 $$

Back to Hints

Back to Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hint 4 - Combined Mole Balances, Rate Law and Stoichiometry

            Combine 

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Hint 5 - Polymath Code

[Note: To=227C=500K]

            Use Polymath to solve

            One can back calculate X

See the Polymath Solution Below

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Back to Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Full Solution

           Mole Balances

            Rate Law

 

            Stoichiometry

          

            For 2A->B

           

            For Isothermal and No DP

            Combine 

[Note: To=227C=500K]

            Use Polymath to solve

            One can back calculate X

See the Polymath Solution Below

Back to Chapter 6