In what situation might the stoichiometric coefficients in a chemical equation differ from the rate law expressed for that reaction?

The concept of stoichiometric coefficients and their relationship to rate laws is fundamental in chemical kinetics. In nonelementary reactions, the stoichiometric coefficients derived from the balanced chemical equation do not necessarily reflect the order of the reaction in the rate law. This is primarily because nonelementary reactions can involve complex mechanisms that include multiple steps or intermediate species.

In contrast, for elementary reactions, the rate law can often be directly derived from the stoichiometric coefficients, as each step is a simple molecular event occurring in a single stage. When all reactants are solids, the reaction may not progress in a manner resembling their stoichiometric coefficients, but this isn't a general reason for deviation from the stoichiometric relationships in rate laws. Similarly, at equilibrium, the forward and reverse reactions may still honor the initial stoichiometric relationships, as they pertain to concentrations of products and reactants but do not specifically pertain to the rate law expression.

Thus, nonelementary reactions represent the scenario where there can be a divergence between stoichiometric coefficients and the rate law due to the complexities of their mechanisms.