9.21 Biochemical Reactions
395
the components of the angular momentum do not commute. One gets different
results in averaging a sequence of measurement of L x followed by L y than the
average measurements of L y followed by L x . But L 2 does commute with one of the
components, so one can measure L 2 = l(l + 1) ¯
h 2 followed by L z = m ¯
h in either
order without a subsequent change in the state of the system.
As stated above, the direction of a chemical change is determined not just by
the energetics for the process, but also by the entropy change. During the reaction,
δG = G products − G reactants =
μ J δN J is the energy which must be expended
to change the component numbers, i.e. to make the reaction proceed. If δG < 0,
the reaction will proceed spontaneously. We know that for constant temperature and
pressure, a macrosystem continues to change if the Gibbs free energy can be lowered
by spontaneous changes in concentration. But at constant temperature, δG = δH −
T δS. Thus, if the enthalpy is lowered or the internal entropy is increased (or some
combination of the two) by the reaction, with a resultant lowering of the Gibbs
free energy, the reaction will continue. The enthalpy change of a system during a
reaction at constant pressure is the negative of the heat energy that would be released
if the reaction proceeded by itself. Biological systems have come to use this kind of
reaction energy rather efficiently in a series of coupled reactions.
The entropy change term, −T δS, in the expression for δG comes from changes in
the disorder within the system, due to the reaction. Reactions can proceed without
any change in enthalpy simply by having the products more disordered that the
reactants. A model example: Suppose you filled a box with lots of balls, linked in
pairs by open hooks. If you shake the box for a while (‘thermal motion’), you would
find that most of the balls have unhooked. This is a more disordered state. The hooks
themselves did not store any energy, so no energy was released by shaking the box.
Thermodynamics can give us equilibrium conditions for chemical reactions. But
if we want to understand and utilize chemical reactions, we must also consider the
kinetics of a reaction, and what determines its speed. The oxidation of hydrogen to
produce water is a good example. If you wait long enough, a mixture of hydrogen
and oxygen will produce water, even at room temperature. But the time scale needed
for some reactions may be eons. (This may be a good thing: The diamond in a
diamond ring will eventually turn to graphite!)
The rate of a reaction is determined by the nature of the microscopic interactions,
the statistical probabilities that reactants and other participants encounter each
other, and the natural lifetimes of the various components. At given temperatures
and pressures, some reactions take microseconds to reach equilibrium; others take
billions of years. Using balls again as an example, suppose the balls in a box were
coupled together with open hooks, but now with springs pushing the balls apart. If
the springs and hooks are strong enough, shaking the box may not unhook any pair
of balls. However, if there were objects in the box to which the balls might attach
(such as balls and objects with Velcro surfaces) that make the balls get a little closer
together, the hooks might be more likely to unhook, and then the balls are propelled
by the spring to fly off the object. These objects act as a catalysis to the releasing of
the balls and the energy they carry.
395
the components of the angular momentum do not commute. One gets different
results in averaging a sequence of measurement of L x followed by L y than the
average measurements of L y followed by L x . But L 2 does commute with one of the
components, so one can measure L 2 = l(l + 1) ¯
h 2 followed by L z = m ¯
h in either
order without a subsequent change in the state of the system.
As stated above, the direction of a chemical change is determined not just by
the energetics for the process, but also by the entropy change. During the reaction,
δG = G products − G reactants =
μ J δN J is the energy which must be expended
to change the component numbers, i.e. to make the reaction proceed. If δG < 0,
the reaction will proceed spontaneously. We know that for constant temperature and
pressure, a macrosystem continues to change if the Gibbs free energy can be lowered
by spontaneous changes in concentration. But at constant temperature, δG = δH −
T δS. Thus, if the enthalpy is lowered or the internal entropy is increased (or some
combination of the two) by the reaction, with a resultant lowering of the Gibbs
free energy, the reaction will continue. The enthalpy change of a system during a
reaction at constant pressure is the negative of the heat energy that would be released
if the reaction proceeded by itself. Biological systems have come to use this kind of
reaction energy rather efficiently in a series of coupled reactions.
The entropy change term, −T δS, in the expression for δG comes from changes in
the disorder within the system, due to the reaction. Reactions can proceed without
any change in enthalpy simply by having the products more disordered that the
reactants. A model example: Suppose you filled a box with lots of balls, linked in
pairs by open hooks. If you shake the box for a while (‘thermal motion’), you would
find that most of the balls have unhooked. This is a more disordered state. The hooks
themselves did not store any energy, so no energy was released by shaking the box.
Thermodynamics can give us equilibrium conditions for chemical reactions. But
if we want to understand and utilize chemical reactions, we must also consider the
kinetics of a reaction, and what determines its speed. The oxidation of hydrogen to
produce water is a good example. If you wait long enough, a mixture of hydrogen
and oxygen will produce water, even at room temperature. But the time scale needed
for some reactions may be eons. (This may be a good thing: The diamond in a
diamond ring will eventually turn to graphite!)
The rate of a reaction is determined by the nature of the microscopic interactions,
the statistical probabilities that reactants and other participants encounter each
other, and the natural lifetimes of the various components. At given temperatures
and pressures, some reactions take microseconds to reach equilibrium; others take
billions of years. Using balls again as an example, suppose the balls in a box were
coupled together with open hooks, but now with springs pushing the balls apart. If
the springs and hooks are strong enough, shaking the box may not unhook any pair
of balls. However, if there were objects in the box to which the balls might attach
(such as balls and objects with Velcro surfaces) that make the balls get a little closer
together, the hooks might be more likely to unhook, and then the balls are propelled
by the spring to fly off the object. These objects act as a catalysis to the releasing of
the balls and the energy they carry.