The rate of the Diels-Alder addition between cycloocta tetraene and tetracyanoethylene is proportional to the tetracyanoethylene concentration \(\left[\mathrm{C}_{2}(\mathrm{CN})_{4}\right]\) at low concentrations of the addends but becomes independent of \(\left[\mathrm{C}_{2}(\mathrm{CN})_{4}\right]\) at high concentrations. Write a mechanism which accounts for this behavior.

The Diels-Alder reaction is a [4+2] cycloaddition reaction, where a diene (4 π-electron system) reacts with a dienophile (2 π-electron system) to form a six-membered ring. In this case, cyclooctatetraene is the diene and tetracyanoethylene is the dienophile. The mechanism is a single, concerted step in which the diene and dienophile react to form a six-membered ring with the new single bonds being formed simultaneously.

As the Diels-Alder reaction is a concerted process, the rate-determining step is the single step that forms the six-membered ring. This means that the rate of the reaction depends on both the concentration of the diene and the dienophile, which can be expressed as: \[rate = k[\text{diene}][\text{dienophile}]\]

At low concentrations, the rate of the reaction is directly proportional to the concentration of tetracyanoethylene. This implies that the concentration of cyclooctatetraene is in excess and does not significantly affect the rate of the reaction. This proportional relationship between the rate and the tetracyanoethylene concentration is consistent with the rate law derived in Step 2.

At high concentrations, the reaction rate becomes independent of the tetracyanoethylene concentration. This can be explained by a saturation effect, where the concentration of tetracyanoethylene is so high that the reactive sites on the diene (cyclooctatetraene) are saturated, meaning that further increases in tetracyanoethylene concentration do not result in a significant increase in the reaction rate. This saturation means that the reaction essentially becomes first-order with respect to the diene only, as the reaction rate is limited by the diene concentration. In conclusion, the observed behavior in the rate of the Diels-Alder addition between cyclooctatetraene and tetracyanoethylene could be explained by a saturation effect, where at high concentrations of tetracyanoethylene, the reactive sites of the diene are fully occupied, making the reaction rate independent of the tetracyanoethylene concentration.