Chemical Equilibrium Constant computed
This is the screen after
a complete run of Statequ.exe. The four frames are explained below.
It shows the main ideas for calculating chemical
equilibrium constants from spectroscopic and other molecular data. Let's
assume an isomerization reaction A Û B.
A and B shall have the same properties except for a different formation
enthalpy at T = 0 K, and different frequency of one molecular vibration.
For A the formation enthalpy is taken as 0 (= reference), for B +400 cm-1
(= 4.77 kJ/mol, DE°). The vibrational frequency
in question is 475 and 150 cm-1, respectively. We start at a
temperature of 173 K in steps of 100 K and look on the screen shot at the
last temperature of 1773 K with a summary for the whole temperature range.
The first frame shows the equilibrium partition of the species
A and B, respectively, on their proper ladder of energy levels. This is
determined uniquely by the properties of each molecular species and the
total energy E of each ensemble. The length of the yellow and cyan bars
is proportional to the relative number of B or A molecules sitting on a
level in equilibrium at 1773 K.
Now we put both species into the same container in frame two.
They can freely exchange quanta while colliding, thus jumping around on
their respective ladder. If they are at the same temperature, defining
the same average energy per particle, as before, the same distribution
obtains as for each species alone.
third frame we add a catalyst to make the isomerization reaction
go. Now in addition to quanta also the identity of the species may be exchanged
in collisions: A particle on the A-ladder is an A, one on the B-ladder
is a B molecule. The chemical reaction makes them jump from one level system
to the other and back billions of times. This process induces two merged
ladders at the exact distance of the difference in formation enthalpy DE°.
This produces gains and losses from 50:50 starting populations - depicted
by different colors - such that a smooth equilibrium distribution over
the merged ladders is formed. For every temperature a different, but time
independent population ratio - an equilibrium constant -
is obtained as shown by the red and blue bars in the inset for every temperature,
and the numerical value of Kp = [B]/[A] given below the graph.
The bars correspond to the populations on the A- and B-levels.
In the last frame the usual plot of ln(Kp) versus
1000/T is shown with the calculated Kp values. As you might
recall - equation of van't Hoff -, the slope of the straight line allows
to compute the reaction enthalpy.
You can change interactively all parameters. Here,
we see that the reaction is enthalpy driven at low temperatures (the A
ladder is bottommost, A is more stable), at high temperature it is entropy
driven, since the finer spaced B ladder offers many more possibilities
to arrange particles, given a certain average energy defined by the temperature.
Therefore, the A species dominates at low, the B isomer at high temperature.
That's also a demonstration of the principle of Le Châtelier: At
higher temperature the equilibrium shifts towards the product, that consumes
heat. By changing the formation enthalpy (e.g. inverting its sign) and
the vibrational frequencies you can simulate any mix of enthalpy or entropy
driven reactions. You will also find out, that the straight line in the
4th frame does not stay 'straight' with all combinations of the parameters!
That is no surprise, however, because neither the van't Hoff equation produces
a straight line if the reaction enthalpy is changing in the temperature
range under observation.
Last modified May 3, 2005
This Web page created by ES.