ECHE 311/Fall 08
Problem Set #11
Chemical Reaction Equilibrium
Due Tuesday, December 2nd
1. A system initially containing 2 mole C2H4 and 3 mole of O2 undergoes the following
reactions:
C2 H 4 ( g )  1 / 2O2 ( g )  (CH 2 ) 2 )O( g )
C2 H 4 ( g )  3O2 ( g )  2CO2 ( g )  2 H 2O( g )
Develop expressions for the mole fractions of the reacting species as function of reaction
coordinate for the two reactions.
2. Consider the water-gas shift reaction:
H 2 ( g )  CO2 ( g )  H 2O( g )  CO( g )
A high temperatures and low to moderate pressures the reacting species form an idealgas mixture. Application of the summability relation to Equation
_ ig
G i  Giig  RT ln xi
yields
G   yiGi  RT  yi ln yi
i
i
If the Gibbs energies of the elements in their standard states are set equal to zero,
Gi  G of i for each species, and then
G   yi G ofi  RT  yi ln yi
(A)
i
i
With the understanding that T and P are constant, we may write the equilibrium
t
criterion of Eq. (dG )T , P  0 for this reaction system as
dGt  d (nG)  ndG  Gdn  0
1
or
n
dG
dn
G
0
d
d
For the water-gas –shift reaction,
becomes
dn / d  0 . The equilibrium criterion therefore
dG
0
d
Once the
(B)
yi are eliminated in favor of  , Eq (A) relates to  .

a) Determine the equilibrium value of e by application of Eq.(B) at 1,000; 1200 and
1500 K.
b) Plot G vs , indicating the location of the equilibrium value of e determined in
(a). Discuss the results.


Hint:
G of / Jmol 1

Data got

example of your textbook (SVNA)
For a temperature of 1,000; 1200 and 1500 K (the reaction is unaffected by P)
and for a feed of 1 mole H2 and 1 mol CO2.

Find

By Eq. 13.5 calculate

By Eq (A) and data from Example 13.3 at above temperatures write
expressions for G ( ) =

Guess value for

Given


and
for the compounds of interest are given in the
n0
yH 2 = yCO2
and
yH 2O  yCO
 e  0.5
d
G ( e )  0 find  e
d e
Plot G ( ) vs 
for   0.3,0.31..0.6
3. For the ammonia synthesis reaction written
1
3
N 2 ( g )  H 2 ( g )  NH 3 ( g )
2
2
2
with 0.5 mol N2 and 1.5 mol as the initial amounts of reactants and with the assumption
that the equilibrium mixture is an ideal gas, show that
 e  1  (1  1.299 K
P 1 / 2
)
Po
4. I asked Daniel Pittman , Punyawudho Conlayutt and Lee Zachary,
members of our thermodynamic class to find equilibrium composition at a particular T
and P and for given initial amounts of reactants for the following gas-phase reaction:
5
2 NH 3  3 NO  3H 2O  N 2
2
(A)
Each solves the problem correctly in a different way. Daniel bases his solution on
reaction (A) as written. PC who usually likes “well rounded things” prefers whole
numbers and multiplies reaction (A) by 2.
4 NH3  6 NO  6H 2O  5N2
LZ, who usually does things backward, deals with reaction:
5
3H 2O  N 2  2 NH 3  3 NO
2
Write the chemical-equilibrium equations for the three reactions, indicate how the
equilibrium constants are related, and show why, D, P and L all obtain the same results.
5. The following reaction reaches equilibrium at 500oC and 2 bar:
4HCl ( g )  O2 ( g )  2H 2O( g )  2Cl2 ( g )
If the system initially is an equimolar mixture of nitrogen and acetlylene, what is the
composition of the system at equilibrium? Assume ideal gases.
Hint: Use the routine outlined in Example 5.
3