WOLFRAM NOTEBOOK

Effect of Pressure on Chemical Equilibrium

​
dissociation
ammonia synthesis
equilibrium constant and pressure (Δν = 1)
equilibrium constant and pressure (Δν = -1)
p
6
show/hide
K
6
1
This Demonstration shows the displacement of a chemical equilibrium following pressure variation, a consequence of Le Chatelier's principle. In order for this shift to take place it is necessary that
Δν≠0
[1], namely that the sums of the stoichiometric coefficients for the products and for the reactants are not equal.
Two specific reactions were considered, the synthesis of ammonia, with
Δν=-2
, and the dissociation of phosphorus pentachloride, with
Δν=1
.
Ammonia synthesis takes place at 450 °C (in the Haber–Bosch process), associated with
K
c
=2.74×
-1
10
-2
M
[2]. The equilibrium was studied starting from initial concentrations
[
H
2
]
0
and
[
N
2
]
0
equal to
0.825M
; the same initial value was used for
[
PCl
5
]
0
in the dissociation reaction, at the temperature of 811.15 °C. Under these experimental conditions for the dissociation reaction
K
p
=3.20
.
The various equilibrium constants are related by[1]:
Δν
K
c
(RT)
=
K
p
=
K
x
Δν
P
.
Plots for the dissociation and synthesis are shown with varying the moles of the reactants and products in equilibrium at various pressures. In the diagram below, the numbers of moles inside a piston are schematized, neglecting thermal agitation. Although the displacement of the equilibrium in the two cases is opposite (shifting toward the side of reactants →
Δν=1
; shifting toward the side of products →
Δν=-1
), the general trend is the same: the decrease in the number of molecules inside the piston as the pressure increases. This can be visualized using "show/hide," which represents the molecules in both reactions as indistinguishable particles.
In "equilibrium constant and pressure," the trend of the molar fractions
X
A
and
X
B
is represented in a generic dimerization
2A⇄B(Δν=-1)
and in a generic dissociation
A⇄2B(Δν=1)
as functions of pressure, according to the different values of
K
p
[3].
The different values of
K
p
can be selected with the
"
K
p
". In the dissociation reaction, these coincide with the values shown on the button; for the dimerization reaction, these vary instead with an appropriate scale factor (
-2
10
) and are shown alongside the plot.

Details

Snapshot 1: dissociation of
PCl
5
(Δν=1)
: As required by the Le Chatelier principle, the increase in pressure produces a decrease in the total moles inside the reactor for this specific reaction. In this case, this tendency occurs by shifting toward the side of reactants.
Snapshot 2: generic dissociation reaction
(Δν=1)
: Shifting toward the side of reactants is also influenced by the value of
K
p
; the increase in
K
p
and pressure act in the opposite way. With the shift of the equilibrium to the left, the mole fraction of
B
(
X
B
)
decreases.
Snapshot 3: generic dimerization reaction
(Δν=-1)
: Both the value of
K
p
and the pressure shift the chemical equilibrium toward the side of products; in this way the molar fraction of
A
(
X
A
)
grows.
Snapshot 4: synthesis of ammonia in the Haber–Bosch process
(Δν=-2)
: As required by the Le Chatelier principle, the increase in pressure produces a decrease in the total moles inside the reactor. The trend can be easily visualized by representing the different molecules as indistinguishable particles and is achieved by shifting the reaction toward the side of products.

References

[1] P. M. Lausarot and G. A. Vaglio, Stechiometria per la Chimica generale, Padova, Italy: Piccin Nuova Libraria S.p.A., 2005.
[3] P. Atkins and J. de Paula, Atkins' Physical Chemistry, 8th ed., New York: Oxford University Press, 2006.

External Links

Permanent Citation

D. Meliga, L. Lavagnino, S. Z. Lavagnino, G. Follo
​
​"Effect of Pressure on Chemical Equilibrium"​
​http://demonstrations.wolfram.com/EffectOfPressureOnChemicalEquilibrium/​
​Wolfram Demonstrations Project​
​Published: September 8, 2020
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