Energy Profiles

Refer to the Zumdahl text discussion starting on page 718, and Figure 15.9 in particular, as you read this web page.

The connection between reaction thermochemistry and reaction kinetics is a subtle but important one, and the reaction activation energy provides the link.

Here we consider the simple, elementary unimolecular reaction

CH₃CN -> CH₃NC

in which methyl cyanide (CH₃CN) converts to methyl isocyanide (CH₃NC). This reaction is very endothermic; the energy of the isocyanide is about 100 kJ mol–¹ above the energy of the cyanide. This thermochemistry (dominated by energy effects because the two molecules have very similar entropies) tells us that the equilibrium constant for the reaction as written is very small, even at high temperatures:

K_eq = e–^DG/RT = e–^DE/RT = 3.6 x 10–¹¹ at T = 500 K

This would seem to suggest that, first, even at high T, a sample of the cyanide remains very pure with little isocyanide present, and, second, that the isocyanide might be impossible to isolate in pure form—it seems to be too unstable compared to the cyanide, and it should spontaneously turn into cyanide.

In fact, only the first statement is true. The isocyanide can be prepared and maintained in pure form for long periods of time, even at temperatures significantly above room temperature. The reason the isocyanide does not instantly convert to the much lower energy cyanide can be traced to the activation energy for the conversion.

Think about what the molecule does during reaction: the methyl group (CH₃) stays fixed while the CN atoms remain bonded to each other and simply rotate around into a new bonding configuration. (We will understand why this is so in a few weeks when we discuss chemical bonding in molecules like these.) During the rotation, the one old bond must be broken (this takes energy to do) before the new bond can be formed. The really unstable molecular species that exists in between reactant and product (a methyl group with a CN group next to it, but not strongly bonded to it) is an example of a transition state or activated complex of atoms. These terms are used fairly interchangeably to describe that fleeting, transient group of atoms that is no longer the reactant (or reactants—see Figure 15.9) but is not yet clearly the final product or products.

We can map out the energy change as the CN group rotates, taking that 180° rotation to be the reaction coordinate—a term for the collective motion of atoms moving from distinct reactants to distinct products. These energy changes are almost impossible to measure experimentally, but quantum mechanical chemical theories of bonding allow us to calculate the energy changes quite accurately.

The figure below shows the situation for our unimolecular reaction:

The molecular models show the changes in bonding along the reaction coordinate (and the subtle changes in bond lengths, too; note that the CN bond is quite a bit longer in the cyanide than in the isocyanide) while the red line shows the schematic energy change. Note first that the isocyanide energy is about 100 kJ mol–¹ above the cyanide energy (which is arbitrarily taken to represent zero energy). The transition state, however, is 261 kJ mol–¹ above the cyanide, or 161 kJ mol–¹ above the isocyanide. These numbers are, respectively, the forward activation energy and the reverse activation energy.

To keep it simple, Zumdahl's figure 15.9 illustrates only the forward activation energy. You should also notice that the difference between the forward and reverse activation energies equals the internal energy change for the reaction, which the figure above shows graphically. We can now understand why the isocyanide is stable: even though there is a large energy release as the isocyanide converts to the cyanide, a significantly larger energy input is required to reach the transition state, and at modest temperatures, very, very few collisions have enough energy to fuel that trip up the activation energy hill, even though once at the top (at the transition state), it's all downhill in energy to the cyanide. Similarly, while the small equilibrium constant we calculated earlier for the cyanide to isocyanide reaction assures that the cyanide will remain pure, the cyanide has another factor in its favor, the extremely high activation energy of 261 kJ mol–¹.

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