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5.3: Thinking entropically (and thermodynamically)

We certainly are in no a position to teach you (rigorously) the basics of chemistry and chemical reactions (or physics for that matter), but we can provide a short refresher that focuses on the key points we will be using over and over again149. The first law of thermodynamics is that while forms of energy may change, that is, can be converted between distinct forms, the total amount of energy within a closed system remains constant. Again, we need to explicitly recognize the distinction between a particular system and the universe as a whole. The universe as a whole is itself (apparently) a closed system. If we take any isolated part of the system we must define a system boundary, the boundary and what is inside it is part of the system, the rest of the universe outside of the boundary layer is not. While we will consider the nature of the boundary in greater molecular detail in the next chapter, we can anticipate that one of the boundary’s key features is its selectivity in letting energy and/or matter to pass into and out of the system, and what constraints it applies to those movements.

Assuming that you have been introduced to chemistry, you might recognize the Gibb’s free energy equation: ΔG = ΔH - TΔS, where T is the temperature of the system150. From our particularly biological perspective, we can think of ΔH as the amount of heat released into (or absorbed from) the environment in the course of a reaction, and ΔS as the change in a system factor known as entropy. To place this equation in a context, let us think about a simple reaction:

oil mixed with water ⇄ oil + water (separate) ΔG is negative

While a typical reaction involves changes in the types and amounts of the molecules present, we can extend that view to all types of reactions, including those that involve changes in temperature of distinct parts of a system (the bar model above) and the separation of different types of molecules in a liquid (the oil-water example). Every reaction is characterized by its equilibrium constant, Keq, which is a function of both the reaction itself and the conditions under which the reaction is carried out. These conditions include parameters such as the initial state of the system, the concentrations of the reactants, and system temperature and pressure. In biological systems we generally ignore pressure, although pressure will be important for organisms that live on the sea floor (and perhaps mountain tops).

The equilibrium constant for a reaction is defined as the rate of the forward reaction kf (reactants to products) divided by the rate of the reverse reaction kr (products to reactants). At equilibrium (where nothing macroscopic is happening), kf times the concentrations of the reactants equals kr times the concentration of the products. For a thermodynamically favorable reaction, that is one that favors the products, kf will be greater than kr and Keq will be greater, often much greater than one. The larger Keq is, the more product and the less reactant there will be when the system is at equilibrium. If the equilibrium constant is less than 1, then at equilibrium, the concentration of reactants will be greater than the concentration of products.

\[K_{eq}={k_f}/{k_r}\]  \[K_f (reactants)=K_r (products)\]

While the concentration of reactants and products of a reaction at equilibrium remains constant it is a mistake to think that the system is static. If we were to peer into the system at the molecular level we would find that, at equilibrium, reactants are continuing to form products and products are rearranging to form reactants at similar rates151. That means that the net flux, the rate of product formation minus the rate of reactant formation, will be zero. If, at equilibrium, a reaction has gone almost to completion and Keq>> 1, there will be very little of the reactants left and lots of the products. The product of the forward rate constant times the small reactant concentrations will equal the product of the backward rate constant times the high product concentrations. Given that most reactions involve physical collisions between molecules, the changes in the frequency of productive collisions between reactants or products increases as their concentrations increase. Even improbable events can occur, albeit infrequently, if the rate of precursor events are high enough.

References

149 Of course, we recommend a chemistry course sequence based on Cooper & Klymkowsky, 2014. Chemistry, Life, the Universe and Everything: here: http://tinyurl.com/onapy7k (see http://virtuallaboratory.colorado.edu/CLUE-Chemistry/)

150 in the real world, the value of ΔG depends upon the concentrations of solute and solvent, but we will ignore that complexity for the moment.

151 This, of course, assumes that we have a closed system, that is, that neither the products or the reactants can leave the system, and that the volume of the system also remains constant. If the reactants can “leave the scene” of the reaction, then of course the back reaction, Products ⇆Reactants, will be much less likely to occur.

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.