



Lecture 2 Summary In today's class we discuss the free energy associated with an
electrochemical gradient, as well as that associated with redox reactions.
In the latter case, for each redox couple (an oxidant and its conjugate
reductant) we measure electrochemically a quantity called the standard
reduction potential and use a form of the Nernst
equation to calculate
standard free energy change (DG°')
from a difference in standard reduction potential, DE°'. 












Reduction potentials and free energy The electron transfer reactions that constitute the electron
transport chain are by definition oxidationreduction
("redox") reactions. We can distinguish the species oxidized
and the species reduced in redox reactions, and each reaction can
be thought of as being composed of two "halfreactions",
one a reduction in which electron(s) are a reactant, and the other
in which electron(s) are a product. These are not real reactions,
but they are useful in analysis of redox reactions. For a reduction
halfreaction, a standard reduction potential E^{o} can
be assigned, relative to a reference reaction, for reactants and
products under standard conditions. The more positive E^{o} is
for a given halfreaction, the greater the relative tendency toward
the reduced products. This suggests a relationship between reduction
potential and free energy. 









As with free energy, the important quantities connected
with reduction potentials are not absolute values, but differences.
By summing two halfreactions and taking the corresponding algebraic
sum of E^{o}s, we can say whether the resulting net
redox reaction can occur spontaneously. In the table, the halfreaction
with the most positive E^{o} value is the reduction
of O_{2} to H_{2}O. This means that in combination
with any of the other halfreactions, O_{2} will be the species
reduced, and the other halfreaction will occur in the reverse direction. 












As a particularly
pertinent example, we obtain the change in standard reduction potential, DE^{o}'
for the redox reaction representing the reduction of O_{2} by
NADH.
(In the table above, V represents volts, and  as for free energy
 the prime denotes a biochemical standard state where the pH =
7.0. The definition of the biochemical standard state can be found
here.) 

















A positive value for DE^{o}'
represents a reaction that can proceed spontaneously, i.e. DG^{o}'
< 0. In fact, there is a quantitative relationship between DE^{o}'
and DG^{o}', which can
be worked out from the Nernst equation: 


[ A review of redox chemistry, showing how the relation
between K'_{eq} and DE^{o}'
arises can be found here ]




This
equation states that the standard free energy change for a redox
reaction is equal to the negative of the product of the change in
standard reduction potential times n, the number
of electrons transferred in thereaction, times a constant F,
which is the Faraday. F is equal to 23.06 kcalmol^{1}V^{1}.
Thus, the free energy available under (biochemical) standard conditions
from the reduction of O_{2} by NADH is – (2)(23.06)(1.14)
= – 52.6 kcal/mol. 








Study questions
 Describe how biochemical standard state differs from physical
chemistry standard state.
 Use a table of halfreactions to write complete redox reactions
and use E'^{o} values to determine DE'° and
whether the products or reactants would be favored at equilibrium.
 The Nernst equation, its meaning and applications:
 Derive DG^{'o} and the
equilbrium constant K'_{eq} for a redox reaction
from its DE'° value.
 Calculate the biochemical reduction potential for a redox
reaction under arbitrary conditions
Page updated
010607
References
 Berg, Tymoczko, and Stryer. Biochemistry (BTS): 6th
edition (2007, Freeman) Ch.18, pp.506509.






