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?
>>Pentcho Valev
>State Commission of Varieties
>125 Tzarigradsko Chaussee, Block 1
>1113 Sofia, Bulgaria
>E-mail: rumym at bgearn.acad.bg>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.
Guy Brown
Dr Guy C. Brown
Department of Biochemistry,
University of Cambridge,
Tennis Court Road,
Cambridge CB2 1QW,
UK
Tel: +44 (0)1223 333342
Fax: +44 (0) 1223 333345
