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A Reaction Coordinate Diagram for a One-Step Process. (a) reactants. (b) transition state. (c) products. (d) AG˚ Gibbs standard free energy change.
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progress of the reaction fr e e e n e rg y (a) (b) (c) (e) (d) A Reaction Coordinate Diagram for a One-Step Process (a) reactants (b) transition state (c) products (d) ΔG˚ Gibbs standard free energy change (e) ΔG≠^ free energy of activation We have already encountered a useful tool that allows us to track energy changes along a complex reaction pathway – the tool was the reaction coordinate diagram used to describe the ring flipping process of cyclohexane. Although cyclohexane’s “reaction” did not involve electron reconfiguration, the minimum energy pathway (MEP) correlated energy and progress of change for a complex set of conformations. Not only does the reaction coordinate diagram and its MEP serve as a way to track energy changes for conformational processes, but it also is a tool for tracking energy of reactions that involve electron reconfiguration. We are interested only in the minima and maxima on reaction coordinate diagrams. By knowing the energy at these positions, either qualitatively or quantitatively, we will be able to judge the equilibrium position of the reaction, and how fast each step of the reaction takes place. The essential components of a reaction coordinate diagram for a one-step reaction are shown above. Most important is the MEP on this diagram. The particular MEP on the above diagram might, for example, apply to the proton transfer from phenol to hydroxide. The reactants (a) are higher in energy than the products (c), so there is a favorable driving force (d) to promote the change. This driving force is the Gibbs standard free energy and it’s directly related to the equilibrium constant (Keq) by ΔG˚ = -RT ln Keq where T is the temperature in Kelvin and R is the gas constant. The transition state (b) is a transient structure caught in the act of undergoing electron reconfiguration. The symbol TS≠^ represents the transition state structure. Notice that the energy associated with TS≠^ is higher than the reactants. This maximum on the energy profile represents a barrier that resists the transformation of reactants to products_. The higher the barrier is, the slower the rate of the reaction._ The coefficient, k, is proportional to the reaction rate (k and ΔG≠ are related by k = 2.084x10^10 ·T·e-(ΔG≠/1.986T)). MEP on a 1-step reaction coordinate diagram
Getting from reactants to products requires energy, e.g., energy to surmount a transition state barrier or energy to become an unstable intermediate on the MEP. Where does this energy come from? In order to surmount barriers on the MEP, reactants must somehow acquire energy from their surroundings. This energy might come from heat, light, electrical potential, or mechanical force. The barrier is thus only a temporary one, because as soon as the reactants acquire sufficient energy from their surroundings, electron reconfiguration can take place. In the case of proton transfer, the barrier is not very high and is easily surmounted by the thermal energy (i.e., random, Brownian motion) available to the reactants at room temperature. The energy transduction network (diagram at the right) reminds us that potential energy of one form (e.g., electrical potential) can be converted into another form (e.g., chemical potential). When molecules acquire energy from their surroundings, they can surmount the barriers on an MEP and reactions will proceed. This is the basic idea behind the activated-rate theory which describes how fast reactants transform into products. The theory says that reactants must become activated to their transition state structures by acquiring energy from their surroundings.