Chemistry 1215 Unit 1 Chapter 13: Chemical Kinetics

Conditions for a proposed reaction mechanism to be valid

1. The elementary steps in the mechanism must sum to the overall reaction. 2. The rate law predicted by the mechanism must be consistent with the experimentally observed rate law.

Speed

= (change in distance (x)) / (change in time (t))

Elementary Step

Each step in a reaction mechanism and they cannot be broken down into simpler steps . Unlike the overall reaction, elementary steps occur exactly as they are written. Elementary steps are characterized by their molecularity.

Termolecular

Elementary steps in which three reactant particles collide. They are very rare because the probability of three particles simultaneously colliding are small.

First-Order Reaction Half-Life

For a first order reaction, the half-life is constant and independent of concentration. Constant half-lives

Initial Rates

For a zero-order reaction, the initial rate is independent of the reactant concentration, the rate is the same at all measured initial concentrations. For a first-order reaction, the initial rate is directly proportional to the initial concentration. For a second order reaction, the initial rate quadruples for a doubling of the reactant concentration, the relationship between the concentration and rate is quadratic.

First-Order Integrated Rate Law

If our simple reaction is first order, the rate is directly proportional to the concentration. In this form, the rate law is also known as the *differential rate law*. The integrated rate law has the form of an equation for a straight line. For a first order reaction, a plot of the natural logarithm of the reactant concentration as a function of time yields a straight line with a slope -k and a y-intercept of ln[A]. Note that the slope is negative but that the rate constant is always positive.

Second-Order Integrated Rate Law

If our simple reaction is second order, the rate is proportional to the square of the concentration of A. The second order integrated rate law is also in the form of an equation for a straight line. However, you must now plot the inverse of the concentration of the reactant as a function of time. The plot yields a straight line with the slope of k and an intercept of 1/[A].

Zero-Order Integrated Rate Law

If our simple reaction is zero order, the rate is proportional to a constant. The zero order integrated rate law is in the form of an equation for a straight line. A plot of the concentration of the reactant as a function of time yields a straight line with a slope of -k and an intercept of [A].

First-Order Reaction

In a first order reaction, the rate of the reaction is *directly proportional* to the concentration of the reactant. For a first order reaction the rate slows down as the reaction proceeds because the concentration of the reactant decreases. The slope of the curve (the rate) becomes less steep (slower) with time. There is a *linear relationship* as the rate is directly proportional to the concentration.

Second-Order Reaction

In a second order reaction, the rate of the reaction is *proportional to the square of the concentration* of the reactant. The rate is even more sensitive to the reactant concentration. The slope of the curve (the rate) flattens out more quickly than it does for a first order reaction. There is a *quadratic relationship* as the rate is proportional to the square of the concentration.

The Spectrometer

In a spectrometer, light of a specific wavelength is based through a sample and the intensity of the transmitted light, which depends on how much light is absorbed by the sample, is measured and recorded.

Zero-Order Reaction

In a zero order reaction, the rate of the reaction is independent of the concentration of the reactant. The concentration of the reactant decreases linearly with time. The slope of the line is constant, indicating a constant rate. The rate is constant because the reaction does not slow down as the concentration os A decreases. Zero-order reactions occur under conditions where the amount of reactant actually available for the reaction is unaffected by changes in the overall quantity of the reactant. For example, *sublimation* is normally zero order because only molecules at the surface can sublime, and their concentration does not change when the amount of subliming substance decreases.

Arrhenius Analysis

In an Arrhenius analysis, the pre-exponential factor (A) is assumed to be independent of temperature. Although the pre-exponential factor does not depend on temperature to some degree, its temperature dependence is much less than that of the exponential factor and is often ignored.

Rate-Determining Step

In most chemical reactions, one of the elementary steps, the rate-determining step, is much slower than others. The rate-determining step in chemical reactions analogous to the narrowest section on a freeway. If a section of the freeway narrows from four lanes to two lanes, for even a short distance, the rate at which cars travel along the freeway is limited by the rate at which they can travel through the narrow section. Similarity, the rate-determining step in a reaction mechanism limits the overall rate of the reaction, even though the other steps occur much faster and therefore *determines the rate law for the overall reaction*.

Measuring Reaction Rates

In order to study the kinetics of a reaction, we must have an experimental way to measure the concentration of at least one of the reactants or products as a function of time. The most common way to study the kinetics of a reaction is through spectroscopy. Because light travels so fast and current experimental techniques can produce very short pulses of light, spectroscopy can be used to measure reactions that happen on time scales as short as several femtoseconds. Reactions in which the number of moles of gaseous reactants and products change as the reaction proceeds can be readily monitored by measuring changes in pressure. As the reaction proceeds and the amount of gas increases, the pressure steadily rises. The rise in pressure can be used to determine the relative concentrations of reactants and products as a function of time. By taking aliquots regular time intervals, the relative amounts of reactants and products can be determined as a function of time.

The Collision Model

In the collision model, the chemical reaction occurs after a sufficiently energetic collision between two reactant molecules. In collusion there, therefore, each approach to the activation barrier is a collision between the reactant molecules. Consequently, the value of the frequency factor should simple be the number of collisions that occur per second. However, the frequency factors of most (though not all) gas-phase chemical reactions tend to be smaller than the number of collisions that occur per second.

Polarized Light

Light with an electric field oriented alone one plane.

Determining Reaction Mechanisms

Measuring rates of reaction is not only practically important (allowing us to keep the rate of a particular reaction) but is also theoretically important because it can help us determine the mechanism of the reaction. Details of reaction mechanism allow chemists to better manipulate chemical reactions. By doing experiments under different conditions, such as changing pressures or temperatures, we can propose a reaction mechanism that is consistent with the observations from these experiments.

Reaction Mechanisms of Chemical Reactions

Most chemical reactions do not occur in a single step, but through several steps. When we write a chemical equation to represent a chemical reaction, we usually represent the overall reaction, not the series of individual steps by which the reaction occurs. The overall equation simply shows the substances at the beginning of the reaction and the substances formed by the reaction. It does not show how the reaction occurs (the intermediate steps that may be involved).

The Average Rate of Reaction

The average rate decreases as the reaction progresses (the reaction slows down as the reaction proceeds). For most reactions, the rate depends on the concentrations of the reactants. As the reactions transform to products, their concentrations decrease, as the reaction slows down.

Heterogeneous Catalysis

The catalyst exists in a different phase than the reactants. The solid catalysts used in car converters are examples of heterogeneous catalysts: they are solids while the reactants are gases. The use of solid catalysts with gas phase or solution phase reactants is the most common type of heterogenous catalysis.

Homogenous Catalysis

The catalyst exists in the same phase, or state, as the reactants. The catalytic destruction of the ozone by Cl is an example of a homogeneous catalysis: the chlorine exists in the gas phase with the gas phase reactants.

The catalytic converter

The catalytic converter contains solid catalysts, such as platinum, rhodium, or palladium, dispersed on an underlying high-surface-area ceramic structure. These catalysts convert exhaust pollutants such s nitrogen monoxide and carbon monoxide into less harmful substances. The catalytic converter also promoted the complete combustion of any fuel fragments present in the exhaust. Fuel fragments in exhaust are harmful because they lead to the formation of ozone. Although the ozone is the natural part of our upper atmosphere that protects us from excessive exposure to UV light, it is a pollutant in the lower atmosphere, inferring with cardiovascular function and acting as an eye and lung irritant. The use of catalytic converters in motor vehicles has resulted in lower levels of these pollutants.

The Rate of a Chemical Reaction (13.2)

The rate of a chemical reaction is a measure of how fast the reaction occurs. If a chemical reaction has a slow rate, only a relatively small fraction of molecules react to form products in a given period of time. If a chemical reaction has a fast rate, a large fraction of molecules react to form products in a given period of time. The rate of a chemical reaction is measured as a change in the amounts of reactants or products (usually in concentration units) divided by change in time.

The Effect of Concentration on Reaction Rate

The rate of a reaction often depends on the concentration on one or more of the reactants. As long as the rate of the reverse reaction (in which products return to reactants) is negligibly slow, we can write a relationship, called the *rate law*, between the rate of the reaction and the concentration.

The Effect of Temperature on Reaction Rate

The rates of chemical reactions are, in general, highly sensitive to temperature. The temperature dependance of the reaction rate is contained in the rate constant, k, which is actually only constant when temperature remains constant. An increase in temperature usually results in an increase in k, which results in a faster rate.

Change in Reactant and Product Concentrations

The reactant concentration decreases with time because reactants are consumed in a reaction. The product concentration increases with time because products are formed in a reaction.

Absorption

The reactants are absorbed onto a metal surface.

Diffusion

The reactants diffuse on the surface until they approach each other.

Reaction

The reactants react to form products.

The Activated Complex

The reaction pathway includes a transition state (the activated complex) that has a higher energy than either the reactant or the product. Each wag is an approach to the activation barrier.

Reaction Rate

The reaction rate is defined as the negative of the change in concentration of a reactant divided by the change in time. The negative sign is part of the definition when the reaction rate is defined in terms of a reactant because reactant concentrations decrease as the reaction proceeds; therefore *the change in the concentration of a reactant is negative*. The negative sign thus makes the overall *rate positive* (By convention, reaction rates are reported as positive quantities). The rate can also be defined with respect to the product of the reaction. Because product concentrations increase as the reaction proceeds, the change in concentration of a product us positive. Therefore, when the rate is defined with respect to a product, we do not include a negative sign in the definition as the rate is naturally positive. In order to have a single rate for the entire reaction, the definition of the rate with respect to each reactant and product must reflect the stoichiometric coefficients of the reaction.

The Overall Order

The sum of the exponents (m+n).

The Rate Law

The value n (usually an integer) reflects how the rate depends on the concentration of the reactant. - If the *rate is independent of the concentration* of A, the reaction is *zero order* and n=0. - If the *rate is directly proportional to the concentration* of A, the reaction is *first order* and n=1. - If the *rate is proportional to the square of the concentration* of A, the reaction is *second order* and n=2. Although other orders are possible, including noninteger (or fractional) orders, these three are the most common.

Thermal Energy and Chemical Kinetics

Thermal energy produces constant molecular motion, causing molecules to readily collide with one another. In a tiny fraction of these collisions, the electrons on one molecule or atom are attracted to the nuclei of another. Some bonds weaken and new bonds form, a chemical reaction occurs. Chemical Kinetics is the study of how these kinds of changes occur in time.

Collisions of Reactive Gases

We can picture a sample of reactive gases as a frenzy of collisions between the reacting atoms or molecules. At normal temperatures, the vast majority of these collisions do not have sufficient energy to overcome the activation barrier and the atoms or molecules simply bounce off one another. Of the collisions having sufficient energy to overcome the activation barrier, most do not have the proper orientation for the reaction to occur (for the majority of common reactions). When two molecules with sufficient energy and the correct orientation collide, something unique happens. The electrons on one of the atoms or molecules are attracted to the nuclei of the other; some bonds begin to weaken while other bonds begin to form and, if all goes well, the reactant go through the transitions state and are transformed into products. This is how a chemical reaction occurs.

The Integrated Rate Law: The Dependance of Concentration on Time

We often want to know the relationship between the concentration of a reactant and time. *The integrated rate law* for a chemical reaction is a relationship between the concentrations of the reactants and time.

Sublimation

When a layer of particles sublimes, another identical layer is just below it. Consequently, the number of particles available to sublime at any one time does not change with the total number of particles in the sample, and the process is *zero order*.

Zero-Order Reaction Half-Life

When the concentration is half its original and depends on the initial concentration but as the reaction proceeds, the half life decreases because the concentration decreases.

Measuring Rate

When we measure how fast something occurs, or more specifically the rate at which it occurs, we usually express the measurement as a change in some quantity per unit of time. We report rates that represent the change in what we are measuring (distance or weight) divided by change in time.

Determining the Order of a Reaction

*The order of a reaction can be determined only by experiment*. A common way to determine reaction order is by the *method of initial rates*. In this method, the initial rate (the rate for a short period of time at the beginning of the reaction) is measured by running the reaction over several times with different initial reactant concentrations to determine to effect of the concentration on the rate. We can determine the value of the rate constant k, by solving the rate law for k and substituting the concentration and the initial rate from any one of the measurements.

Temperature and Reaction Rate

- The frequency factor is the number of times that the reactants approach the activation barrier per unit time. - The exponential factor is the fraction of approaches that are successful in surmounting the activation barrier forming products. - The exponential factor increases with increasing temperature, but a large activation energy results in a small exponential factor.

Summarizing Basic Kinetic Relationships

- The reaction order and rate law must be determined experientially. - The rate law relates the rate of the reaction and the concentration pf the reactants. - The integrated rate law (which is mathematically derived from the rate law) relates the concentration of the reactants to time. - The half-life is the time it takes for the concentration of a reactant to fall to one half of its initial value. - The half-life, lifetime, and decay time of a first order reaction are independent of the initial concentration. - The half-lives and decay times of zero order and second order reactions depend on the initial concentration.

Activation Energy and Temperature

A low activation energy and a high temperature make the exponential factory exponent small, so that the exponential factor approaches one. A large activation energy and a low temperature make the exponent a very large negative number, so that the exponential factor become exponentially small. As the temperature increases, the number of molecules having enough thermal energy to surmount the activation barrier increases. At any given temperature, a sample of molecules will have a distribution of energies. Under common circumstances, only a small number of molecules will have enough energy to make it over the activation barrier. Because of the shape of the energy distribution curve, however, a small change in temperature results in a large difference in the number of molecules having enough energy to surmount the activation barrier. This explains the sensitivity of reaction rates to temperature.

Reaction Mechanism

A reaction mechanism is a series of individual chemical steps by which an overall chemical reaction occurs. One of the requirements for a valid reaction mechanism is that the individual steps add to the overall reaction.

Hydrogenation

A second type of heterogenous catalysis involves hydrogenation of double bonds with alkenes. The large activation energy of the hydrogenation reaction, due primarily to the strength of hydrogen-hydrogen bonds in H2, is greatly lowered when reactants absorb onto the surface.

Orientation Factor (p)

A small orientation factor indicates that the original requirements for the reaction are very stringent (the molecules must be aligned in a very specific way for the reaction to occur). Reactions between individual atoms usually have orientation factors of approximately one, because atoms are spherically symmetrical and thus any orientation can lead to the formation of products. A few reactions have orientation factors greater than one.

Polarimetry

A technique of measuring the degree of polarization of light passing through a reacting solution.

A valid reaction mechanism

A valid mechanism is not a proven mechanism. We can say they the given mechanism is consistent with the kinetic observations and therefore possible. Other types of data, such as experimental evidence for a proposed intermediate, can further strengthen the validity of a proposed mechanism.

Enzymatic Catalysts and Rate Law

According to all three expressions for the rate law, the rate is expected to increase with increasing enzyme concentration. By allowing otherwise slow reactions to occur at reasonable rates, enzymes give living organisms tremendous control over which reactions occur, and when they occur. Enzymes are extremely specific as each enzyme will catalyze only one reaction or one type of reaction and efficient, speeding up reaction rates by factors as much as a billion. If a living organism wants to turn a particular reaction on, it produces or activated the correct enzyme to catalyze the reaction. Because organisms are so dependant on the reactions enzymes catalyze, many substances that inhibit the action of enzymes are highly toxic.

Rate Laws for Elementary Steps

Although the rate law for an overall chemical reaction cannot be deduced from the balanced equation, the rate law for an elementary step can be. Since we know that an elementary step occurs through the collision of the reactant particles, the rate law is proportional to the product of the concentrations of those particles.

Activation Energy (Ea)

An energy barrier that must be surmounted for the reactants to be transformed into products. It shows the energy of the molecule as the reaction proceeds. The x-axis represents the progress of the reaction from the left (reactant) to right (product). To get the reactant to the product, the molecule must go through a high energy intermediate state called the activated complex or transition state. The energy required to reach the activated complex is the activation energy. The higher the activation energy, the slower the reaction rate (at a given temperature).

Sucrase

An enzyme that catalyses the breaking up of sucrose into glucose as fructose within the body. At body temperature, sucrose does not break into glucose and fructose because the activation energy is high, resulting in a slow reaction rate. However, when a sucrose molecule binds to an active site within sucrase, the bond between the glucose and fructose weakens because glucose is forced into a geometry that stresses the bond. Weakening of this bond lowers the activation energy of this reaction, increasing the reaction rate. The reaction can then proceed towards equilibrium, which favours the products, at a much lower temperature.

Reaction Intermediates

An intermediate is not found in the balanced equation for the overall reaction, but plays a key role in the mechanism. The mechanism specifies the individual collisions that result in the overall reaction. Knowledge of the overall reaction mechanism could allow chemists to make modifications to reaction conditions in order to make a reaction more efficient.

Reaction Order for Multiple Reactants

As long as the reverse reaction is negligibly slow, the rate law is proportional to the concentration of [A] raised to the multiple m multiplied by the concentration of [B] raised to the n. The rate law for any reaction must always be determined by experiment, often by the method of initial rates. There is no simple way to merely look at a chemical equation and determine the rate law for the reaction. When there are two or more reactants, the concentration of each reactant is usually varied independently of the others to determine the dependance of the rate on the concentration of that reactant.

Second-Order Reaction Half-Life

At a time when the initial concentration of reactant decreases to a 1/n of its initial value. For a second order reaction the decay time depends on the initial concentration. The half life and decay time continue to get longer for a second order reaction as the reaction proceeds and the concentration of the reactant decreases.

Thermal Energy Distribution

At any given temperature, the atoms or molecules in a gas sample will have a range of energies. The higher the temperature, the wider the energy distribution and the greater the average energy. The fraction of molecules with enough energy to surmount the activation barrier and react increases sharply as the temperature rises.

Ectotherms

Body temperature is regulated by the environment.

Reaction Rates

Chemists must always consider reaction rates when synthesizing compounds. No matter how stable a compound might be, its synthesis is impossible if the rate at which it forms is too slow. The knowledge of reaction rates gives us the ability to control how fast a reaction occurs. The rate of a reaction can tell us how much the reaction occurs on the molecular scale.

Enzymes

Most of the thousands of chemical reactions that must occur for an organism to survive are too slow at normal temperatures. So living organisms rely on enzymes, biological catalysts that increase the rates of biochemical reactions. Enzymes are usually large protein molecules with complex 3-D structures. Within that structure is a specific area called the *active site*. The properties and shapes of the active sites are just right to bind to reactive molecules, usually called a *substrate*. When the substrate binds to the enzymes active site, though intermolecular forces such as hydrogen bonding and dispersion forces, or even covalent bonds, the activation energy of the reaction is greatly lowered, allowing the reaction to occur at a much faster rate.

The Steady-State Approximation

Most often for a proposed reaction mechanism, the potential energy surface is not known. It is therefore difficult to determine whether the activation energy for a particular elementary step in a reactions faster than another. It is still possible, however, to obtain a rate law using a slightly different method. The first step in predicting the rate law by this mechanism is to determine a preliminary expression for the rate of the reaction. Typically, but not always, the rate of reaction is defined as the rate of change in the concentration of a product. In a steady state approximation, *the rate of formation of intermediate equals the rate of consumption of the intermediate*. Using elementary steps we can write expressions for the rate of production and consumption of the reaction intermediate.

Catalysts

Reaction rates can be increased by using a catalyst, a substance that increases the ratio of a chemical reaction but is not consumed by the reaction. A catalyst works by providing an alternative mechanism for the reaction, one in which the rate determining step has a lower activation energy.

The Frequency Factor

Represents the number of approaches to the activation barrier per unit of time. With each wag of the molecule, the molecule approaches the activation barrier. However, approaching the activation barrier is not equivalent to surmounting it. Most of the approaches do not have enough total energy to make it over the activation barrier.

The Exponential Factor

The exponential factor is a number between 0 and 1 that represents the fraction of molecules that have enough energy to make it over the activation barrier on a given approach. The exponential factor is the fraction of approaches that are energetic enough to be successful and result in the product. For a given wag only 1 in 10^7 molecules has sufficient energy to actually make it over the activation barrier. The exponential factor depends on temperature (T), which you can control, and the activation energy (Ea) of the reaction, which is a property of the reacting species, and which you cannot control.

Ludwig Wilhelmy

The first person to measure the rate of a chemical reaction carefully. In 1850, he measured how fast sucrose, upon treatment with acid, hydrolyzed into glucose and fructose. This reaction occurred over several hours, as Wilhelmy was able to show how the rate depended on the initial amount present (the greater the initial amount, the faster the initial rate).

Chemical Kinetics

The focus on understanding how the molecular world changes with time. The molecular world is anything but static.

Arrhenius Plots: Exponential Measurements of the Frequency and the Activation Energy

The frequency factor and the activation energy are important quantities of understanding the kinetics of any reaction. A plot of a natural logarithm of the rate constant (ln (k)) versus the inverse of the temperature in kelvin (1/T) yields a straight line with the slope of -Ea/R and a y-intercept of ln(A). Such a plot is called the Arrhenius Plot and is commonly used in the analysis of kinetic data. In some cases when either the data are limited or plotting capabilities are absent, we can calculate the activation energy if we know the rate constant at just two different temperatures.

Half'-Life (t1/2)

The half-life of a reaction is the time required for the concentration of a reactant to fall to one-half of its initial value. Common for first order reactions because constant and changes for non first order reactions.

The Instantaneous Rate of Reaction

The instantaneous rate of reaction is the rate at any one point in time, and is represented by the slope of the curve at that point. We can determine the instantaneous rate from the slope of the tangent to the curve at the time of interest. The instantaneous rate is the same whether we use one of the reactant or the product for the calculation. From the definition, we can see that knowing the rate of change in concentration of any one reactant or product at a point in time allows us to determine the rate of change in the concentration of any other reactant or product at that point in time (from the balanced equation). *However, predicting the rate at some future time is not possible from just the balanced equation*.

Lifetime of a Reaction

The lifetime of a reaction is the time for a reactant concentration to decrease to 1/e of the starting concentration. The lifetime represents the average life expectancy of the chemical entity. Common for first order reaction because constant and changes for non first order reactions.

Arrhenius Equation

The modern form of the Arrhenius equation shows the relationship between the rate constant (k) and the temperature in Kelvin (T). In this equation, R is the gas constant, A is the frequency factor, and Ea is the activation energy.

Collision Frequency (z)

The number of collisions that occur per unit time, which can be calculated for a gas-phase reaction from the presence of pressure of the gases and the temperature of the reaction picture. Under typical conditions, a single molecule undergoes on the order of 10^9 collisions every second. Not all collisions with sufficient energy will lead to products because the reactant molecules must also be properly oriented. If two molecules are to react with each other, they must collide in such a way that allows the necessary bonds to break and form.

Molecularity

The number of reactant particles involved in the step. Th most common molecularities are unimolecular and bimolecular.

Desorption

The products desorb from the surface into the gas phase.

Rate Constant Units

The rate constants for zero and second order reactions have different units than for first order reactions. The rate constant for a zero order reaction has units of *mol/(L)(s)* and that for second order reaction has units of *L/(mol)(s)*. The rate constant for a first order reaction is *1/s*.