In reply to Guy Brown
On 24 May Pentcho Valev wrote:
>Dear Colleagues,
> I would like you to help me solve a few thermodynamic paradoxes. I have
>been trying to discuss them with people for many years, but as my claims
>question ultimately the validity of the second law... you can imagine what the
>reaction was.
> Ten days ago I posted some of them in the bio-info group, so you can see
>them there. Let me present here the briefest one.
> Let the ATP-ADP-Pi system do work on another system, e.g. driving the
>reaction M = N:
>> ATP + M = ADP + Pi + N /1/
>>Obviously the enthalpy of the reaction is equal to the sum of the enthalpies
>of ATP hydrolysis and M = N, and this relation is independent of both
>the concentrations and the distance from equilibrium:
>> delta H = delta H(ATP = ADP + Pi) + delta H(M = N) /2/
>>However note that delta H(M = N) is in fact the energy the second system
>receives, i.e. it can be conceived as work, W, done on it. Hence
>> W = delta H(M = N) = delta H - delta H(ATP = ADP + Pi) /3/
>>It follows that the work done on the second system is independent of both
>the concentrations and the distance from equilibrium, insofar as the
>enthalpies are, according to the first law, independent.
> On the other hand, if the reaction /1/ is close to equilibrium, the
>second law predicts that
>> W = -delta G(ATP =ADP + Pi) = -delta Go - RTln((ADP)(Pi)/(ATP)) /4/
>>i.e. W does depend on the concentrations.
> It seems to me that /3/ and /4/ are incompatible. What do you think?
Guy Brown wrote:
The>paradox arises directly from your>two definitions of "work": >
in /3/ you define work as the>enthalpy change of the driven reaction,
while in /4/ you define work as>the Gibbs free energy change of the>
driving reaction.> Obviously these are not equal. >
In general>work has been defined in many different ways: there is >
mechanical>work, electrical work, chemical work, osmotic work, >
etc, etc., but some of these definitions are in terms of energy changes
and>some in terms of Gibbs free energy changes. >
So>to avoid paradox it is neccessary>to use a consistent definition of>
work, and to produce>anything useful it is neccessary to use the >
definition>of work that is interesting in your problem. >
Personaly>I do not think that "work" is a useful concept in biochemical>
thermodynamics: does a>reaction really do "work"? I do not see how the >
concept>can be used to tell us anything useful or>important about an >
ATP driven>reaction or any reaction. >
You are right that the two different concepts of work can be used
independently, but only insofar as "work" in a standard chemical reaction
is something not very clear. However I do not believe that the idea of W.
Gibbs was something like "The negative of delta G will be named work, but this
work should not be juxtaposed with any other work". Rather, delta G was
originally meant to be traditional work, but just because it is incompatible
with the physical definition "force times distance", people have been trying
for many years to forget that any work is first "force times distance" and then
anything else. Moreover, there are cases in which the work is the same in any
sense, and these cases show the seriousness of the problem. Let me describe
one such case.
An ATPase transports H+ against a transmembrane electrical gradient, but
(for simplicity) in the absence of a transmembrane pH gradient. You can use
both concepts of work done by the ATP-ADP-Pi system, but here we will have to
chose one and reject the other, since they provide contradictory predictions.
I have dealt with the case in the bio-info group (the title is "The Second
Law Against the First Law"), so let me state only the two options:
1. If the reaction is close to equilibrium and ATP >> ADP = Pi,
free energy calculations predict that the reaction is STRONGLY ENDOTHERMIC.
2. Under the same conditions the enthalpy concept says that the reaction
is EXOTHERMIC - part of the energy stored in ATP is converted into electrical
potential, but as the process cannot be 100% efficient, the other part is
dissipated as heat.
As you can see, the problem has quite concrete dimensions. Let us solve it.
Pentcho
