CHEN 464 – Spring 2013 Homework #1 Due on Thursday 1/24/13 1. Given the following reaction N2O4(g) == 2 NO2(g) Determine the equilibrium composition at 25°C and 1 bar. Assume ideal gas behavior. Thermodynamic Information:

G°f,NO2 = 51.37 kJ/mol

G°f,N2O4 = 97.89 kJ/mol (20 pts)

2. Fogler P1-9 (10 pts) 3. Fogler P1-11 (10 pts) (Derive mole balances on the species at steady-state as well) 4. Fogler P1-15 (10 pts) 5. Fogler P1-17 (20 pts)

1. Given the following reaction

N2O4(g) == 2 NO2(g)

Determine the equilibrium composition at 25°C and 1 bar. Assume ideal gas behavior.

Thermodynamic Information:

G°f,NO2 = 51.37 kJ/mol

G°f,N2O4 = 97.89 kJ/mol

Solution:

o

ONf

o

NOf

o

if

n

i

iRXN GGGG 42,2,,

1

2

(1)

GRXN = 4.85 kJ/mol

Use value of GRXN in

RTG

K RXNa exp (2)

Ka = exp ( (-4.85 kJ/mol*1000J/kJ)/(8.314 Jmol-1

K-1

*298.15 K)) = 0.141

For reactions at chemical equilibrium we know that

42

2

2

11 ON

NOn

i

i

n

i

o

i

ia

y

yy

f

fK i

i

(3)

And we can reach the second step since we assume the mixture is an ideal gas and we are

operating at 1 bar (the reference state).

Now, we need to express the mole fractions yi as a function of the conversion. To do this we can

use a mole balance

Species Initial # moles Final # moles N2O4 1 1-X

NO2 0 2X_____

Total 1 1 +X

So yN2O4 = (1-X)/(1+X)

yNO2 = 2X/(1+X)

Problem # 1, (cont)

Substituting the yi’s into (3) gives

2

222

1

4

11

4

11

12

X

X

XX

X

XX

XX

K a

Rearranging this to solve for X

185.04

a

a

K

KX

which gives

yN2O4 = 0.688

yNO2 = 0.312

Since the cell is well-mixed, VrG pp

Therefore, dt

dNpFVr outpp ,

Likewise, for the corn steep liquor since there is no outflow,

dt

dNcVrF cinc ,

For RNA since there is neither inflow nor outflow

dt

dNVr RNA

RNA

At steady-state,

cp

outp

r

inFc

r

FV

,,, and no RNA is generated or destroyed.

The populations of rabbits and foxes are oscillating because of the fact that as the number of

rabbits increases so does the number of foxes and this will make the number of rabbits decrease,

thereby decreasing the number of foxes – Natural balance…