5.4: Reaction rates

Knowing whether a reaction is thermodynamically favorable and its equilibrium constant does not tell us much (or really anything) about whether the reaction actually occurs to any significant extent under the conditions with which we are concerned. To know the reaction’s rate we need to know the reaction kinetics for the specific system with which we are dealing. Reaction kinetics tells us the rate at which the reaction actually occurs under a particular set of conditions. For example, consider a wooden log, which is composed mainly of the carbohydrate polymer cellulose (CH2O)n. In the presence of molecular oxygen (O2) the reaction:

nO2 + wooden log ((CH2O)n) ⇆ nCO2 + nH2O + heat

is extremely favorable thermodynamically, that is, it has a negative ΔG and a large equilibrium constant, yet the log is stable - it does not burst into flames spontaneously. The question is, of course, why ever not? Or more generally why is the world so annoyingly complex?

The answer lies in the details of the reaction, how exactly the reactants are converted into the products. For simplicity let us consider another non-chemical but rather widespread type of reaction. In this reaction system, there is a barrier between two compartments, specifically the barrier membrane that separates the inside from the outside of a cell. At this point, we do not need to consider the exact details of the barrier’s structure (although we will in next chapter). In our particular example, outside the cell the concentration of molecule A is high while inside the cell its concentration is low. We can write out this reaction equation as Aoutside⇆Ainside (perhaps you make a prediction of the ΔG of this reaction and what it depends upon.) The reaction consists of moving A molecules across the barrier between the inside and the outside of the cell. In our example, the concentration of A outside the cell (written [Aoutside], with the square brackets indicating concentration) is much greater than [Ainside]. At any moment in time, the number of collisions between Aoutside and the barrier will be much greater than the number of collisions between Ainside and the barrier. Assuming that the probability of crossing the barrier is a function of the collision frequency, there will be net movement of Aoutside to Ainside. The real question is how large this net flux will be, which will depend on the amount of energy a molecule needs to cross the barrier. We can represent this energy as the highest peak in a reaction graph (here we assume a simple process with a single peak, in the real world it can involve a number of sub-reactions and look more like a roller-coaster than a simple hill). In such a graph, we begin with the free energy of the reactants along the Y-axis, and plot the changing free energies of the various intermediates along the X-axis, leading to the free energy of the products. In our simplified view of the subject, the difference between the intermediate with the highest free energy (ΔGtransition) and the free energy of the reactants (ΔGreactiants) corresponds roughly to the rate limiting step in the reaction and reflects the reaction’s activation energy.

For a reaction to move from reactants (Aoutside) to products (Ainside), the reactants must capture enough energy from their environment to traverse the barrier between outside and inside. In biological systems there are two major sources for this energy. The reactants can absorb electromagnetic energy, that is, light, or energy can be transferred to them from other molecules through collisions. In liquid water, molecules are moving; at room temperature they move on average at about 640 m/s. That is not to say that all molecules are moving with the same speed. If we were to look at the population of molecules, we would find a distribution of speeds known as a Boltzmann (or Maxwell-Boltzmann) distribution. As they collide with one another, they exchange kinetic energy, and one molecule can emerge from the collision with much more energy than it entered with. Since reactions occur at temperatures well above absolute zero, there is plenty of energy available in the form of the kinetic energy of molecules, and occasionally a molecule with extremely high energy will emerge. If such an energetic A molecule gains sufficient energy and collides with the boundary layer, it can cross the boundary layer, that is, move from outside to inside. If not, it will probably loose that energy to other molecules very quickly through collisions. It is this dynamic exchange of kinetic energy that drives the movement of molecules (as well as the breaking of bonds associated with chemical reactions).

The difference between the free energies of the reactants and products (ΔGreaction) determines the equilibrium constant for a particular reaction system. In the case of our barrier system, since the A molecules are the same whether inside or outside the cell, the difference in the free energies of the reactants and products reflects (primarily) the difference in their concentrations. Higher concentration correlates with higher free energy (remember, we are interested in the ΔG of the Aoutside ⇆ Ainside reaction). Clearly the more molecules of A are present, the higher the ΔG of A. One point is worth emphasizing, it is possible for a reaction to have a large ΔGreaction and either a large or small ΔGtransition. So assuming that there is enough energy in the system, and ΔGtransition is small enough for the reaction to proceed at a noticeable rate, you should be able to predict what happens to the system as it moves toward equilibrium. If the ΔGtransition is high enough, however the Aoutside ⇆Ainside reaction will not occur to any significant extent.

Contributors

• Michael W. Klymkowsky (University of Colorado Boulder) and Melanie M. Cooper (Michigan State University) with significant contributions by Emina Begovic & some editorial assistance of Rebecca Klymkowsky.