ECHE 311/SPRING 2015
Problem Set #11
Chemical Reaction Equilibrium
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
ideal- gas 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
t
equilibrium criterion of Eq. (dG )T , P  0 for this reaction system as
1
dGt  d (nG)  ndG  Gdn  0
or
n
dG
dn
G
0
d
d
For the water-gas –shift reaction,
therefore becomes
dn / d  0 . The equilibrium criterion
dG
0
d
Once the
(B)
yi are eliminated in favor of  , Eq (A) relates to  .
a) Determine the equilibrium value of
and 1500 K.
 e by application of Eq.(B) at 1,000; 1200

b) Plot G vs , indicating the location of the equilibrium value of
determined in (a). Discuss the results.
Hint:
G of / Jmol 1
e

Data got

the 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

and
for the compounds of interest are given in
n0
yH 2 = yCO2
and
yH 2O  yCO
G ( ) =
Guess value for  e  0.5
d
G ( e )  0 find  e
Given
d e
Plot G ( ) vs 
for   0.3,0.31..0.6
expressions for



3. The following reactions reaches equilibrium at 650oC and atmospheric pressure
N2(g) + C2H2 (g) =2HCN (g)
2
If the system initially is an equilibrium mixture of nitrogen and acetylene, what
is the composition of the system at equilibrium? What would be the effect of
doubling the pressure? Assume ideal gases
4. For the following three reactions find the chemical equilibrium composition at a
particular T and P and for given initial amount of reactants:
5
2 NH 3  3 NO  3H 2O  N 2
2
(A)
4 NH3  6 NO  6H 2O  5N2
(B)
If one multiplies reaction (A) by 2 results in reaction (B)
If one writes reaction (A) backward obtains reaction )C)
5
3H 2O  N 2  2 NH 3  3 NO
2
(C)
Write the chemical-equilibrium equations for the three reactions, indicate how
the equilibrium constants are related, and show why one obtains the same result.
5. The following reaction reaches equilibrium at 500oC and 2 bar:
4HCl ( g )  O2 ( g )  2H 2O( g )  2Cl2 ( g )
If the system initially contains 5 mole of HCl for each mole of oxygen, what is the
composition of the system at equilibrium? Assume ideal gases.
3