Question

In what way is the rate law for a reaction related to the rate-determining step?

Short answer

The rate law for a reaction reflects the stoichiometry of reactants involved in the rate-determining step, being the slowest step, which controls the overall reaction rate.

Step-by-step solution

Understanding the Rate Law

The rate law is an equation that relates the rate of a chemical reaction to the concentration of reactants. It has the general form rate = k[A]^m[B]^n... where k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are the reaction orders with respect to each reactant.

Understanding the Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism. It has the highest activation energy barrier to overcome and thus determines the overall rate of the reaction because the entire reaction cannot proceed faster than this slowest step.

Relating Rate Law to the Rate-Determining Step

The rate law for a reaction is directly determined by the rate-determining step. The exponents in the rate law (the reaction orders) correspond to the stoichiometry of the reactants involved in the rate-determining step, not necessarily the overall reaction stoichiometry. Hence, the rate law provides insight into the mechanism of the reaction, especially the rate-determining step, through its order with respect to individual reactants.

Key concepts

Rate Law

The rate law is a fundamental concept in chemical kinetics, which is the study of the rates at which chemical reactions occur. It is an expression that delineates how the reaction rate is related to the concentration of the reactants involved. The typical form of a rate law is: \[\text{rate} = k[A]^m[B]^n...\]Here, \(k\) indicates the rate constant, which is specific to each reaction and can vary with temperature. The brackets, such as \([A]\) and \([B]\), represent the concentrations of reactants A and B, respectively. The exponents \(m\) and \(n\) are known as the 'order' of the reaction with respect to each reactant. They tell us how sensitive the reaction rate is to changes in the concentration of each reactant.
Understanding the rate law is crucial because it allows chemists to predict how changes in conditions will affect the speed of a reaction. For example, if the reaction order with respect to a reactant is two (second order), doubling the concentration of that reactant will quadruple the reaction rate. The rate law is determined experimentally and cannot be surmised solely from the chemical equation. It provides intimate details about the steps involved in the progression of the reaction, which is why it is especially useful when studying complex mechanisms.

Chemical Reaction Rate

The chemical reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. It is quantitatively expressed as the change in concentration of a reactant or product per unit time. Mathematically, it can be represented as: \[\text{rate} = -\frac{d[A]}{dt} = \frac{d[P]}{dt}\]where \( [A] \) is the concentration of a reactant and \( [P] \) is the concentration of a product. The negative sign indicates that the concentration of the reactants is decreasing over time. Reaction rates can be affected by various factors such as temperature, concentration of reactants, surface area of solid reactants, and the presence of a catalyst.
Understanding how these factors influence the reaction rate is important for controlling reactions in industrial processes, where it may be desirable to increase the efficiency of product formation or prevent the formation of undesirable by-products. The concept of reaction rate is also essential for the calculations of reaction kinetics and the formulation of the rate law.

Reaction Mechanism

A reaction mechanism is a detailed, step-by-step description of how a chemical reaction occurs at the molecular level. It includes the sequence of elementary steps that lead to the formation of products from reactants. Each elementary step involves a single molecular event, such as the breaking or forming of bonds, resulting in the creation of intermediate species or the rearrangement of atoms.
The rate-determining step is a critical concept within the reaction mechanism. It is the slowest step in the mechanism and acts as a bottleneck for the overall reaction, much like the narrowest part of an hourglass controls the flow of sand. The intrinsic properties of this step, such as its activation energy, heavily influence the rate at which the reaction progresses.
Deducing the reaction mechanism is a complex task that often requires experimental evidence and theoretical calculations. Scientists use clues provided by the rate law and the stoichiometry of the reaction to propose possible mechanisms. They then carry out experiments, such as measuring the rate of reaction at different concentrations of reactants, to verify these mechanisms. A correct mechanism will be consistent with the observed rate law, allowing the relationship between the mechanism and the rate law to be a powerful tool for understanding chemical reactions in depth.