OK. There are many counterexamples. Let me start with two of them.
1. Is the work done by a single ATP molecule concentration-dependent or
is it concentration-independent? In any biosynthesis the energy transfered
(e.g. to the peptide bond) is obviously concentration-independent. Also,
in studies of ATP driven muscle motion the ATP concentration is never
mentioned, i.e. the work done is a priori regarded as concentration-
independent. I have problems with finding literature, but it seems to me
that in all MOLECULAR studies of ATP work,dependence on the concentration
is not even assumed (if not, please give me references). If so, we can say
that all molecular studies represent strong experimental evidence that the
work done by a single ATP molecule is concentration-independent. Do you
agree? If yes, the conclusion that the second law is invalid follows
directly - I will show this.
2. Please consider the following equilibrium system:
10 mM KCl M pure water
where M is a membrane permeable only to K+. At equilibrium, a capacitor-
like double layer is established at the membrane, positive on the right
and negative on the left. Accordingly, a transmembrane potential
difference (Donnan potential) is established, positive on the right.
So far everybody agree. But do you know what the second law adds to this
picture? That the electrical potential in the right compartment increases
as we go away from the membrane and even approaches infinity with
distance! Simply because the K+ electrochemical potential should, according
to the second law, be uniform throughout the system. Can you imagine
an absurdity greater than that? Can you imagine a case more easily verifiable?
I have proposed the experiment to hundreds of people - nobody jumped up and
down, rather, everybody begged the question. Only one of them, John Wheeler
from UCSD, calculated the increase of the potential with distance, found
that it is logarithmic and therefore slow, and concluded that there is
no danger - the potential gets dangerous when the system gets longer than
the laboratory. After receiving this answer, I jumped up and down, but
not from joyous excitement.
The examples are many more, but I still don't believe that there will be
any interest. The group neglected an obvious theoretical evidence that
catalysts can shift the equilibrium, and experimental verification is
difficult, if at all possible. What does this mean?
Best regards,
Pentcho
