Chapter 35 - Elementary Chemical Kinetics

What is a typical rate constant for a diffusion- controlled reaction in aqueous solution?

Rate constants for diffusion-controlled reactions in solution are on the order of 10¹⁰ M⁻¹ s⁻¹

What is a transition state? How is the concept of a transition state used in activated complex theory?

A transition state is a position of maximum energy along the reaction coordinate. This maximum corresponds to an unstable configuration of the reaction

What is meant by a diffusion-controlled reaction?

In a diffusion-controlled reaction, the species diffuse through solution until they are close enough for the chemical reaction to occur. The reaction rate is directly related to the diffusion coefficients of the reactants and potentially intermediate species.

What is the difference between a first-order reaction and a second-order reaction?

In a first-order reaction, the reaction rate depends linearly on the concentration of a single reactant species. In a second-order reaction, the reaction rate depends either on a product of the concentration of two different reactant species with each concentration to the first power, or on the square of the concentration of a single reactant concentration.

What is the steady-state approximation, and when is this approximation employed?

In the steady-state approximation, the assumption is made that the concentrations of one or more intermediate species undergo a negligible change with time. This approximation is generally valid when the elementary step that generates the intermediate is the rate-determining step, and the subsequent step resulting in the decay of intermediate is rapid, ensuring that the intermediate undergoes decay as soon as it is formed so that the intermediate concentration is modest at all times.

In a temperature-jump experiment, why does a change in temperature result in a corresponding change in equilibrium?

The T-jump method relies on the fact that the kinetics for many chemical reactions are temperature dependent. For example, for a reaction that demonstrates Arrhenius behavior, the rate constant is temperature dependent. When temperature changes, the rate constant changes as well and a new equilibrium will exist. The system will relax to establish this new equilibrium

In a parallel reaction in which two products can be formed from the same reactant, what determines the extent to which one product will be formed over another?

The extent to which a product will be formed, or reaction yield, for a parallel reaction depends on the reaction rate for the product channel of interest. The reaction yield is defined as the ratio of the rate constants for the given branches.

What is a half-life? Is the half-life for a first-order reaction dependent on concentration?

The half-life of a chemical reaction is the time it takes for the initial reactant concentration to be reduced by exactly one half. The half-life for a first-order reaction does not depend on initial reactant concentration.

What is the kinetic definition of equilibrium?

The kinetic definition of equilibrium is the state at which the concentrations of reactants and products do not vary appreciably with time. This will occur when the forward and back reaction rates are equivalent.

Why is the stoichiometry of a reaction generally not sufficient to determine reaction order?

The order of a rate equation for a chemical reaction indicates the concentration dependence of the rate. The order is dependent on the mechanism of the reaction, and not on the proportionality of the reaction.

What is the difference between the order of a reac- tion with respect to a given species and the overall order?

The overall order of a reaction is equal to the sum of orders for each species in the rate law.

What is the relationship between the parameters in the Arrhenius equation and in the Eyring equation?

The principal connection between the Arrhenius and Eyring equations is the relationship between the activation energy () E in the Arrhenius expression and the enthalpy difference between the reactants and transition state a (ΔH )

What is meant by the rate-determining step in a sequential reaction?

The rate-determining step in a sequential chemical reaction is the elementary reaction step with the smallest reaction rate. This step is called rate limiting because no matter how large the reaction rates are for the other elementary steps, the overall reaction rate is determined by the smallest rate.

What is a rate law expression, and how is it determined?

The reaction rate law expression is a mathematical equation that expresses the reaction rate in terms of reactant concentrations and the microscopic rate constant of the reaction. Reaction rate law expressions must be determined experimentally.

In a sequential reaction, what is an intermediate?

The simplest sequential reaction involves two elementary reaction steps in which the reactant decays to form an intermediate species in the first step, then the intermediate proceeds to form product in the second step. An intermediate is a chemical species that is both produced during the course of the reaction and subsequently decays, resulting in product formation.

What is the method of initial rates, and why is it used in chemical kinetics studies?

a chemical reaction is initiated using a specific set of reactant concentrations and the reaction rate is measured. Measurements are taken in which the concentration of the reactant of interest is changed, but all of the other concentrations are left the same. This process is repeated with varying initial concentrations of the reactant of interest while holding the other reactant concentrations constant. The variation in reaction rate with change in concentration of a single species can be used to determine the order of the reaction with respect to the species being changed.

What is the difference between chemical and physical methods for studying chemical kinetics?

a chemical reaction is used to quantify concentrations of species in the reaction mixture Physical methods involve measurement of some physical property of the system that changes as the reaction proceeds.

What is an elementary chemical step, and how is one used in kinetics?

An elementary reaction step is a chemical process that occurs in a single step. Elementary reaction steps are combined to construct complex reaction mechanisms.

What are the fastest timescales on which chemical reactions can be investigated? Describe three experimental techniques for investigation of chemical reactions.

Femtoseconds Other spectroscopic techniques, such as infrared absorption and NMR, can also be used in studies of chemical kinetics.