Understanding reactions in depth requires developing an understanding of the energy changes that occur as we break old bonds and create new ones--or even change the shape of a molecule. You are aware of a couple mathematical relationships from General Chemistry:ΔG° = ΔH° - TΔS°This relates the enthalpy change ΔH°, mostly changes in bond strength, and the entropy change ΔS°, "disorder" (represented by the number of particles, symmetry, and rotational freedom) to an overall energy change called Gibbs free energy, ΔG°. This latter energy measure can be related to an observable quantity, the equilibrium constant Keq through the following equation: ΔG° = -RTlnKeqThe more negative ΔG°, the larger is Keq; the more positive ΔG°, the smaller is Keq. | ||
However, a stable molecule exists in a potential energy well--it costs energy to make a change in bonding. ΔG° reflects the net energy change for the reaction, but ignores energy changes as the bonds break and reform. We can illustrate this through a "potential energy diagram" (often called a reaction profile). A PE diagram for a simple one-step reaction is shown below. | ||
We can observe several things.
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The energy barrier is related to rate, but in an inverse fashion. The mathematic relationship is:
k = (𝓀T/h)e-ΔG/RTwhere k is the rate constant, 𝓀 and h are physical constants (Boltzmann's and Planck's, respectively), R is the gas constant, and T is temperature. This a small ΔG leads to a large rate; a big ΔG leads to a small rate. The rate constant increases with temperature, but in a complex fashion (T appears twice).We also have to be aware of the distinction between reaction rate and the rate constant. The expression for the rate depends on both the rate constant k and (potentially) the concentrations of any of the reactants: Rate = k[A]n[B]m...for the reaction nA + mB + ... → products. The rate is changed either by changing the rate constant or by changing the concentrations of reactants. When investigating a new reaction we normally hold the concentrations constant as we vary structure (to see the impact on ΔG) but often the dependence of the rate on reactant concentration is a major clue to the mechanism. | ||
Reactions may also involve one or more reactive intermediates. The diagram to the left indicates such a reaction, and how we illustrate that. |