So far I have been trying to explain this in terms of rate constants, but
the proof is complicated so the discussion naturally shifted to more
interesting psychological matters. In fact there is a much more simple and
convincing proof - let me present it.
At equilibrium the rates of the forward and back reaction of A + B <-> C
are equal:
v+ = k+(A)(B) = k-(C) = v- /1/
On adding a catalyst, the rates may increase dramatically but the second law
requires that the equilibrium do not shift, i.e. the equilibrium concentrations
remain the same. No kinetic course of the catalysed forward and back reactions
guarantees this - on the contrary, any possible one shifts the equilibrium.
Let us assume that what the second law says is correct, that the equilibrium
concentrations have remained the same and that, for simplicity, the rate of
the catalyzed forward reaction is determined by the first step - bonding of
A to E. Then
V+ = K+(A)(E) = K-(C)(E) = V- /2/
In order for the equilibrium concentrations to remain the same, the two
rates must increase proportionally, i.e.
V+/v+ = V-/v- = K+(A)(E)/k+(A)(B) = K-(C)(E)/k-(C) /3/
This leads to
(B) = (k+)(K-)/(k-)(K+) /4/
what is an obvious absurdity.
I expect any criticism to be constructive, i.e. to show not so much how
incompetent I am but rather how a particular kinetic course of the catalyzed
reaction satisfies the requirements of the second law.
Also, if I am right, the property of catalysts to shift chemical equilibrium
would deserve extensive study. It may have incredible biological consequences.
Best regards,
Pentcho
