- #1

gfd43tg

Gold Member

- 950

- 50

## Homework Statement

A 400-liter CSTR and a 100-liter PFR are available to process 1.0 liter of feed per second. The feed contains 41% A, 41% B, and 18% inerts. The irreversible gas-phase reaction

[tex] A + B → C [/tex]

is to be carried out at 10 atm and 227 °C. The rate of reaction in mol/liter min is given below as a function of conversion

[tex]\begin{pmatrix}

-r_{A} & 0.2 & 0.0167 & 0.00488 & 0.00286 & 0.00204 \\

\hline

X & 0.0 & 0.1 & 0.4 & 0.7 & 0.9

\end{pmatrix}

[/tex]

(a) What is the maximum conversion that can be achieved with these two reactors connected in series (Ans. ##X_{C,P}## = 0.445, ##X_{P,C}## = 0.515.)

(b) What would be the overall conversion if two 400-liter CSTRs were connected in series for the same feed and operating conditions? (Ans: X = 0.595)

(c) What would be the overall conversion if two 400-liter CSTRs were connected in parallel with half of the feed going to each reactor? (Ans: X = 0.52)

(d) What is the volume of a single tubular reactor necessary to achieve 60% conversion if the molar feed rate is 2 mol A/min? (Ans: V = 180 liters.)

(e) If the total pressure were reduced by a factor of 10, would the conversion increase, decrease, or remain the same?

(f) Give a critique of the answers to this problem.

## Homework Equations

## The Attempt at a Solution

Right now I am working on part (a), and have some troubles. First off, is it fair to say that if I use a basis of one second, then the initial concentration of A, which I am using as my limiting reactant, is 0.41 mol/1 L, for 0.41 M?

In my attempt, I start off with a CSTR connected to a PFR to see the overall conversion, which I will then do a PFR connected to a CSTR and compare the overall conversion.

My material balance on the CSTR

[tex] \frac {dN_{A}}{dt} = F_{A0} - F_{A1} + r_{A1}V_{1}[/tex]

Knowing that ##F_{A1} = F_{A0} - F_{A0}X_{1}##, and assuming steady state, the mole balance simplifies to

[tex] 0 = F_{A0} - F_{A0} + F_{A0}X_{1} + r_{A1}V_{1}[/tex]

[tex]\frac {-F_{A0}X_{1}}{V_{1}} = r_{A1}[/tex]

[tex] \frac {-0.41X_{1}}{400} = r_{A1}[/tex]

Here I run into a problem. I don't know what the conversion of the CSTR is, hence I don't know what the reaction rate is, so I have two unknowns and only one equation.

I put the data into matlab, and here is my code

Code:

```
rA = [-0.2 -0.0167 -0.00488 -0.00286 -0.00204];
X = [0 0.1 0.4 0.7 0.9];
FA0 = 0.41;
plot(X,-FA0./(rA/60))
xlabel('X')
ylabel('-FA0/rA')
title('FA0/-rA vs. Conversion')
```

This reaction appears to be zero order, based on the nearly straight, which implies a zero order reaction. This may be a clue, but I'm not sure.

#### Attachments

Last edited: