Indicate whether each statement is true or false. Rewrite each false statement to make it true. (a) The exponents in the rate law for a reaction that has a one-step mechanism can be determined from the balanced equation for the reaction. (b) A rate law can be used to prove that a proposed mechanism is correct. (c) The step \(\mathrm{A}+\mathrm{X}+\mathrm{Y} \rightarrow \mathrm{AX}+\mathrm{Y}\) in a reaction mechanism is plausible. (d) A reaction intermediate appears first as a reactant and then as a product in a reaction mechanism.

Understanding the rate law is crucial for studying chemical reactions. It provides a mathematical relationship between the rate of a reaction and the concentration of reactants. In simple terms, the rate law shows us how the speed of a chemical reaction changes as you vary the amount of starting materials.

For example, consider a reaction where the rate law is expressed as \( rate = k[\mathrm{A}]^m[\mathrm{B}]^n \), where \(k\) is the rate constant, \([\mathrm{A}]\) and \([\mathrm{B}]\) are the concentrations of the reactants, and \(m\) and \(n\) are the exponents that indicate the reaction order with respect to each reactant. These orders typically must be determined experimentally, except for elementary reactions (ones that occur in a single step), where they can often be deduced from the stoichiometry of the reaction.

The reaction order is a key concept in chemical kinetics that tells us how the rate is affected by the concentration of reactants. It is the exponent given to the concentration of a reactant in the rate law. For instance, if a reaction is first order with respect to reactant \(\mathrm{A}\), doubling the concentration of \(\mathrm{A}\) also doubles the rate of the reaction. On the other hand, if the reaction is second order with respect to \(\mathrm{A}\), then doubling \(\mathrm{A}\)'s concentration quadruples the reaction rate.

Reaction order can be zero, which means the rate of reaction is independent of the reactant's concentration, first, second, or even fractional — a concept that might seem strange but is important in understanding reactions that do not fit simple whole-number orders.

A reaction intermediate is like a behind-the-scenes actor in the world of chemical processes. It is a transient species that is formed during the reaction but does not appear in the overall balanced equation. It is produced in one step and consumed in another, acting as a bridge between reactants and products.

Understanding intermediates can be the key to unlocking the path a reaction takes from start to finish — the reaction mechanism. They can also provide clues on how to alter reaction conditions to improve yields or speed up industrial processes. However, identifying intermediates can be challenging, as they are often unstable and exist in very low concentrations.

Chemical kinetics is the study of rates of chemical processes and the factors that affect these rates. It includes not only the speed at which products are formed and reactants are consumed but also the pathway the reaction takes, known as the mechanism.

Various factors such as temperature, pressure, the presence of a catalyst, and the concentration of reactants can influence the kinetics of a reaction. Understanding these factors enables chemists to control reactions, whether to speed up the production of a desired pharmaceutical or to slow down the rusting of a car. Kinetics is a bridge between molecular-level interactions and the macroscopic world we observe.