Understanding Reaction Mechanisms: Rate Law Interpretation

The rate law, or rate equation, is an expression that relates the rate of a chemical reaction to the concentrations of the reactants involved. The rate law for a reaction can be determined from the slowest elementary step, also known as the rate-determining step. This is because the overall reaction rate is limited by the slowest step. While intermediates are formed during the reaction mechanism, they do not appear in the final rate law expression. The rate law expression cannot be obtained from the balanced chemical equation as the partial orders of the reactants are not necessarily equal to the stoichiometric coefficients. However, the rate law can be proven from the rate law expression, which can be used to calculate the instantaneous rate of a reaction.

The rate law of a reaction can be determined from the slowest elementary step

The rate law of a reaction is an expression that provides a relationship between the rate of the reaction and the concentrations of the reactants. The rate law expression can be determined experimentally. The rate of a chemical reaction is determined by its slowest elementary step, also known as the rate-determining step.

A chemical reaction can occur in multiple elementary steps, and each of these steps has a rate constant. The slowest step in the mechanism is the rate-determining step. For example, if a reaction has two elementary steps with rate constants k1 and k2, and the first step is slower than the second, then k1 is the rate constant of the rate-determining step.

The rate equation is derived from the slowest step in the reaction. The rate equation is set up by writing that the rate is equal to the rate constant of the slowest step multiplied by the concentrations of the reactants. The rate law for the overall, macroscopic reaction can be determined by using the rate laws for each elementary reaction.

The rate law expression can be written in terms of the change in the concentration of reactants over a small interval of time. This is known as a differential rate equation and can be used to calculate the instantaneous rate of a reaction. Integrated rate equations express the concentration of reactants as a function of time and can be used to determine how long it would take for a given percentage of reactants to be consumed.

The rate law expression cannot be obtained from the balanced chemical equation

The stoichiometric coefficients of the reactants or products are represented by a, b, c, and d in the rate equation. The rate constant of the reaction is the proportionality constant 'k'. The sum of the partial orders of the reactants in the rate law expression gives the overall order of the reaction. For example, in the equation Rate = k [A]x[B]y, the overall order of the reaction (n) is x+y.

The order of the reaction provides insight into the change in the rate of the reaction that can be expected by increasing the concentration of the reactants. For instance, in a zero-order reaction, doubling the reactant concentration will not affect the reaction rate. In a first-order reaction, the reaction rate will double with the reactant concentration. In a second-order reaction, doubling the concentration of the reactants will result in a quadrupling of the overall reaction rate.

The rate law expression cannot be determined from the balanced chemical equation if there is a reverse reaction involved, it is an elementary reaction, it is a sequence of elementary reactions, or if any of the reactants are in excess.

The rate law can include the concentrations of intermediates

The rate law, or rate equation, for a chemical reaction expresses the relationship between the rate of the reaction and the concentrations of the reactants. The rate law for the overall, macroscopic reaction can be determined by using the rate laws for each elementary reaction in a mechanism by inspection. The rate law can be determined from the slowest elementary step, also known as the rate-determining step.

Intermediates are substances that are formed and consumed during the course of a reaction mechanism. They are not present in the overall chemical equation. However, their concentrations can be significant in specific steps of the reaction, particularly in the rate-determining step, which is the slowest step influencing the overall rate of the reaction. When a mechanism includes intermediates that play a role in determining the rate, their concentrations can appear in the rate law.

For example, consider a reaction mechanism where an intermediate A transforms into a product B. If step 2 includes intermediate A and is the rate-determining step, then the concentration of A could be significant to express how fast products are formed, and thus may appear in the rate law for that specific step. In this case, the reaction rate can be expressed as k [A], where k is the rate constant.

However, some sources argue that intermediates should not be included in the rate law because they are only produced and then used up during the reaction, so they do not appear in the final reaction. The only concentrations that can be controlled or observed clearly are those of the reactants and products. Therefore, the goal when writing rate laws is to match the expression for the rate law with the experimentally observed rate law.

The rate of the overall reaction is determined by the slowest step

The rate of a chemical reaction is determined by the slowest step in the reaction mechanism, known as the rate-determining step. This slowest step dictates the speed at which the overall reaction proceeds. It is comparable to the neck of a funnel, which limits the flow of water through it, regardless of how quickly water is poured in. Similarly, the slow step in a chemical reaction determines its rate.

Not all reactions have a rate-determining step; it is only applicable when one step is significantly slower than the others. Most chemical reactions occur in a series of elementary reactions or steps, and the overall reaction rate depends almost entirely on the rate of the slowest step. If the first step is the slowest, the entire reaction must wait for it, making it the rate-determining step.

The rate law, or rate equation, for a chemical reaction expresses the relationship between the rate of the reaction and the concentrations of the reactants. It is determined experimentally and cannot be obtained from a balanced chemical equation. The rate law for a reaction can be determined by writing rate equations for each elementary reaction in a mechanism by inspection. The rate law deduced from the mechanism must match the experimentally observed rate law.

For example, consider the reaction between carbon monoxide and nitrogen dioxide to form carbon dioxide and nitrogen oxide. The rate equation for a one-step reaction is usually written as 'r = k [NO2] [CO]', with the rate depending on the reaction of nitrogen dioxide and carbon monoxide. However, if the reaction is multistep, the rate equation becomes 'r = k [NO2]2', indicating that the reaction rate is determined by the step involving two NO2 molecules, while the CO molecule enters at a faster step.

The rate law for an elementary reaction depends on the product of the concentrations of the species that collide

The rate law, or rate equation, for a chemical reaction expresses the relationship between the rate of the reaction and the concentrations of the reactants. It is a mathematical expression that shows how the rate of product formation varies with the concentrations of the reactants. The rate law for an elementary reaction depends on the product of the concentrations of the species that collide. This is because the number of collisions between reactant particles increases as the product of the number of particles, not as the sum.

The rate law expression cannot be obtained from the balanced chemical equation. This is because the partial orders of the reactants are not necessarily equal to the stoichiometric coefficients. The rate law for an elementary reaction can be written by inspection, and the rate law for the overall reaction can be determined using these elementary rate laws. The rate law for an elementary reaction is straightforward to write because we know how many molecules must collide simultaneously for the reaction to occur. For example, a reaction with a single reactant molecule is unimolecular, while one with two reactant molecules is bimolecular.

The order of the reaction for an elementary reaction is the same as its molecularity, or the number of molecules that collide in that step. The order of the reaction provides insight into the change in the reaction rate that can be expected by increasing the concentration of the reactants. For instance, if the reaction is of the first order, doubling the reactant concentration will double the reaction rate.

The rate of the reaction is proportional to some rate constant, usually denoted by 'k'. The relationship may not be linear, so the exponent 'x' indicates that the rate will vary with reactant concentrations to some power. Differential rate equations can be used to calculate the instantaneous rate of a reaction, which is the reaction rate under a very small time interval.

Frequently asked questions