How is the rate expression derived for a reaction?

The rate expression for a reaction is derived from the rate-determining step in the reaction mechanism.

The rate expression, also known as the rate equation, is a mathematical representation of the rate of a chemical reaction. It is derived from the rate-determining step, which is the slowest step in a reaction mechanism. The rate-determining step is crucial because it controls the overall rate of the reaction.

To derive the rate expression, we first need to understand the reaction mechanism, which is the sequence of elementary steps that make up a complex reaction. Each elementary step has its own rate, and the slowest of these rates is the rate-determining step. The rate expression is then derived from the stoichiometry of this slowest step.

The rate expression is usually of the form: rate = k[A]^m[B]^n, where 'rate' is the rate of reaction, 'k' is the rate constant, '[A]' and '[B]' are the concentrations of the reactants, and 'm' and 'n' are the orders of reaction with respect to the reactants. The orders of reaction 'm' and 'n' are usually equal to the stoichiometric coefficients of the reactants in the rate-determining step, but this is not always the case.

The rate constant 'k' is determined experimentally, as it depends on factors such as temperature and the presence of a catalyst. The orders of reaction 'm' and 'n' are also determined experimentally, usually by carrying out the reaction with different initial concentrations of the reactants and observing the effect on the rate of reaction.

In summary, the rate expression for a reaction is derived from the rate-determining step in the reaction mechanism. It is a mathematical representation of the rate of reaction, and its parameters are determined experimentally. Understanding the rate expression is crucial for predicting the rate of a reaction under different conditions.