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Energy and Chemical Kinetics

Chemical kinetics describes chemical reactions and the energetic forces that drive them. Central to this field of science is the idea of equilibrium between the reactants and products of a chemical reaction. Consider a hypothetical reaction in which reactants A and B react to form C and D. By convention, we write a chemical equation to represent the reaction:

where the coefficients j, k, l, m refer to the molar quantities of reactants A and B and products C and D, respectively.

In any chemical system, each side of the reaction will have a characteristic energy level. Usually, one side will have a higher energy level than the other. If a reaction proceeds from the high-energy side to the low-energy side, the reaction gives off energy and is said to be exergonic. The combustion of glucose is an example of an exergonic reaction. However, a reaction can also proceed from a state of low energy to high energy. In this case, energy must be fed into the reaction, which is then said to be endergonic. Any order-producing reaction is endergonic.

Usually, there is sufficient energy in a chemical system to drive both exergonic and endergonic reactions. What determines the net direction of the reaction is how fast each reaction proceeds relative to the other. The Second Law of Thermodynamics states there will always be a bias toward the exergonic reaction (producing an increase in entropy, or disorder). Consequently, reactions will always tend to run "downhill," from states of high energy to states of low energy. However, reaction speed in either direction is also determined by the molar concentrations of the reactants and products. Thus, even if a reaction were not energetically favored (if it required an input of energy, say), it could still proceed if the concentration of product was high enough to make the endergonic reactions more frequent than the exergonic reactions.

It follows that there will be some concentration of reactants and products that will drive the reaction toward products as fast as the reaction is driven toward reac-tants. At this point, the concentrations of reactants and products will experience no net change, and the reaction will be at equilibrium.

This condition is denoted with an equilibrium constant that relates the concentrations of the products and reac-tants:

Obviously, if Keq > 1, the products will be favored at equilibrium over the reactants, and the reaction is energetically disposed toward the right side of the equation. Conversely, if Keq < 1, the reactants are favored at equilibrium over products, and the reaction is energetically disposed toward the left side of the equation. The real value of the equilibrium constant, however, is that it provides a way of explicitly relating a chemical reaction's equilibrium to the energy driving it. Specifically, the change of free energy of a reaction (energy that is capable of doing work) is:

where AG is the net change of free energy in the reaction, R is the universal gas constant (8.31 J mol-1 K-1), Tis the absolute temperature (K) of the reaction, and ln Keq is the "natural" logarithm (logarithm to the base e) of the equilibrium constant. For purposes of comparison, the change of free energy is usually determined under an agreed-upon set of standard conditions (1 molar concentrations of product and reactant, 25°C, and pH = 7.0), which yields the net standard change of free energy, or AG°'.

Very useful to us is what energy is required to displace a reaction from equilibrium—a common problem for organisms that want to engineer or maintain a concentration inside their bodies different from that dictated by the standard change of free energy. In this case, we can simply look at the difference between the net change of free energy and the free energy of the reactants and products as they are in the animal. If we assume that the concentrations at equilibrium represent the minimum energies the system can attain, it follows that any displacement of the system from that equilibrium will require energy. If we assume that the actual concentrations of A, B, C, and D in an animal are a, 3, y and S, respectively, the energy, AE, required to force the system out of equilibrium will be:

Thus, adding or subtracting either reactants or products to a chemical system at equilibrium is the same as doing work on it and will force the reaction out of its equilibrium state. In the case of carbonate ion, adding or subtracting hydrogen ions is sufficient to drive the reaction to one or the other thermodynamically unfavorable state—high concentrations of either carbon dioxide or carbonate, rather than the favored form, bicarbonate.

as is just which ones, the corals or the zooxanthellae, are running the show, but the elements seem to be as follows. At the outside surface of the calciloblast, where the calcite will be deposited, there is an active transport protein that uses ATP (energy from sugar) to transport calcium ions from the cell's interior to the outside of the calciloblast (Fig 2.4). This interesting type of transport proton is known as an antiport because it transports two things in opposite directions across the membrane. In the calciloblast antiport, for every calcium ion moved out of the cell, two hydrogen ions are transported into the cell. Both transport processes work against their respective concentration gradients;that is, they are creating order, and so they require energy from ATP. In general, one ATP molecule is sufficient to turn the crank once, moving one calcium ion and two hydrogen ions in opposite directions across the calciloblast's membrane. The operation of the antiport does two things for the aqueous solution between the calciloblast and the cal-

Figure 2.4 The calcium-proton antiport in the calciloblast of a hermatypic coral.

cite base: it makes it rich in calcium ion, and it moves acidifying hydrogen ions away so that the carbonate may embrace calcium without the encumbrance of that last proton. And just as marriage follows love, cal-cite is finally produced.

On the other side of the calciloblast membrane, the hydrogen ions that are moved into the cell (at energetic cost) push bicarbonate toward carbon dioxide, which the zooxanthellae can then take up and combine with water to form sugar (Fig. 2.5). The sugar can then be used by the coral to make more ATP, which is then

Copyright © 2000 The President and Fellows of Harvard College

Zooxanthellae

Mitochondria

H2CO3

Calciloblastic ectoderm

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