Bioenergetics

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Bioenergetics
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Learning Objectives
Calculate equilibrium constants, free-energy
changes, and standard free-energy changes. Define
enthalpy, entropy, and free-energy. Describe
equilibrium. Describe the difference between
standard free-energy and biochemical standard
free-energy. Describe the relationship between
free-energy and equilibrium constants and the
direction of a chemical reaction. Define the
terms exothermic and endothermic.
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Energy in biological systems is described in
terms of free energy.
Gibbs free energy, G, is the amount of energy
capable of doing work during a chemical reaction
at constant temperature and pressure.
Mathematical definition of free energy G H -
TS
where H is the enthalpy, an energy term
reflecting the number and kinds of chemical bonds
and non-covalent interactions broken and formed
in a chemical reaction S is the entropy, a
measure of the randomness in a chemical system
and T is the absolute temperature in degrees
Kelvin.
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Enthalpy, H, is the heat content of the reacting
system When a chemical reaction releases heat,
it is said to be exothermicthe heat content of
the products is less than that of the reactants,
and DH is, by convention, negative. When a
chemical reaction takes up heat from the
surroundings, it is said to be endothermic, and
DH is positive.
Entropy, S, is a measure of the randomness or
disorder in a system. When the products of a
reaction are less complex and more disordered
than the reactants, the reaction is said to
proceed with a gain in entropy. When entropy
increases, DS is, by convention, positive.
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Under the conditions existing in biological
systems (including constant temperature and
pressure), changes in free energy, enthalpy, and
entropy are related to each other by the
equation DG DH T DS
When entropy increases in a chemical reaction, DS
is positive. When a chemical reaction is
exothermic, DH is negative. Either of these
conditions, which are typical of favorable
processes, tend to make DG negative.
DG is always negative for a spontaneously
reacting system.
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Free energy change is directly related to the
equilibrium constant.
A mixture of chemical reactants and products
tends to change until equilibrium is
reached. When equilibrium is reached, reactants
and products are at their equilibrium
concentrations, and no further net change in the
concentrations of reactants or products occurs.
The concentrations of reactants and products at
equilibrium define the equilibrium constant, Keq.
aA bB
cC dD
Cc Dd
Keq
Aa Bb
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When a reacting system is not at equilibrium, the
tendency to move toward equilibrium represents a
driving force. The magnitude of this driving
force can be expressed as the free-energy change,
DG, for the reaction.
Under standard conditions 25oC concentrations
of reactants and products equal to 1 M
The force driving the system toward equilibrium
is defined as the standard free-energy change, DGo
For reactions that involve H, H 1 M or pH 0.
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The biochemical standard state 25oC concentr
ations of reactants and products equal
to 1 M pH 7
Constants based upon the biochemical standard
state are written with a prime DGo and Keq and
are called standard transformed constants.
By convention, when H2O, H, or Mg2 are
reactants or products, their concentrations are
not included in the expression for Keq, but are
incorporated into the constant.
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Relationship between free-energy and equilibrium
constant
DGo -RT ln Keq
The standard free-energy change of a chemical
reaction is simply an alternative mathematical
way of expressing its equilibrium constant.
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Remember this is only under standard conditions.
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There are two different quantities the
free-energy change, DG the standard free-energy
change, DGo
The standard free-energy change tells us in which
direction a given reaction must go to reach
equilibrium when the initial concentration of
each component is 1 M, the pH is 7, the
temperature is 25oC, and the pressure is 1
atm. The standard free-energy change is a
constant defined under very specific conditions.
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The actual free-energy change, DG, is a function
of reactant and product concentrations which will
not necessarily match the standard conditions. In
addition, DG will vary as the reaction proceeds
toward equilibrium. A reaction proceeding
spontaneously toward equilibrium has a negative
DG it becomes less negative as the reaction
proceeds and DG 0 at equilibrium, indicating
that no more work can be done.
A B
C D
actual concentrations not standard concentrations
C D
DG DGo RT ln
A B
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C D
DG DGo RT ln
A B
The concentrations terms in this equation express
the effects commonly called mass action, i.e. the
driving force toward equilibrium.
At equilibrium, DG 0, and
DGo -RT ln Keq
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The criteria for spontaneity is DG, not DGo
A reaction with a positive DGo can go in the
forward direction if DG is negative.
C D
DG DGo RT ln
A B
C D
This is possible if
RT ln
is negative and has a
A B
larger absolute value than DGo. The immediate
removal of products of a reaction can keep the
ratio of product/reactants well below 1, such
that this term has a large, negative value.
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Some reactions for which DGo is large and
negative, do not occur at measurable rates.
Free-energy terms are only concerned with the
direction a reaction will take in proceeding
toward equilibrium. They say nothing about how
fast this process will occur.