chemical kinetics: rates and mechanisms of chemical reactions general chemistry: an integrated...

Chemical Kinetics: Rates and Mechanisms of Chemical

Reactions

General Chemistry: An Integrated Approach

Hill, Petrucci, 4th Edition

Mark P. HeitzState University of New York at Brockport

© 2005, Prentice Hall, Inc.

Chapter 13: Chemical Kinetics 2

Chemical Kinetics: A PreviewChemical kinetics is the study of the rates of chemical reactions, the factors that affect these rates, and the reaction mechanisms by which reactions occur

Reaction rates vary greatly – some are very fast (e.g., burning) and some are very slow (e.g., disintegration of a plastic bottle in sunlight)

EOS

Catalysts are substances that speed up a reaction but emerge unchanged by the reaction. How catalysts work is covered later in the chapter


Predicting Reaction RatesVariables of control are:

Concentrations of reactants: Reaction rates generally increase as the concentrations of the reactants are increased

Temperature: Reaction rates generally increase rapidly as the temperature is increased

EOS

Surface area: For reactions that occur on a surface rather than in solution, the rate increases as the surface area is increased


Meaning of the Reaction RateThe rate of a reaction is the change in concentration of a species per unit of time Example: rate of formation of product A P

EOS

The rate of reaction has the units of moles per liter per (unit of) time, expressed as mol L–1 s–1

t

PRate

][

Appearance of product

Or …t

ARate

][

Disappearance of reactant


A Conceptual Example

EOS


Graphing Changes

EOS


General Reaction RateGeneral reaction rate: calculated by dividing rate expressions by stoichiometric coefficients

Consider: 2 H2O2 2 H2O + O2

t

O

t

OHRate

][][

2

1222

EOS

t

D

dt

C

ct

B

bt

A

aRate

][1][1][1][1

For aA + bB cC + dD,


Average Reaction RateRates of chemical reaction tends to slow down as time goes on in the reaction

EOS

At the beginning of the reaction, the rate is faster than the average and near the end of the reaction, the rate is slower than the average

The average rate of the reaction is calculated by dividing the change in concentration over the time interval of the reaction


Measuring Reaction RatesIn general, the greater the concentration of a reactant, the faster the reaction goes

EOS


Measuring Reaction RatesThe average rate of reaction during an experiment is the negative of the slope of the reaction rate

EOS

The instantaneous rate at the beginning of a reaction is called the initial rate of reaction


Rate Law ExpressionsThe rate law for a chemical reaction relates the rate of reaction to the concentrations of reactants

t

B

bt

A

aRate

][1][1For aA + bB cC + dD

The rate law is Rate = k[A]m[B]n

EOS

The exponents in a rate law must be determined by experiment. They are not derived from the stoichiometric coefficients in an overall chemical equation


Rate LawsThe values of the exponents in a rate law establish the order of a reaction

Rate = k[A]m[B]n

For reactant A, if m = 1, reaction is first order in A if m = 2, reaction is second order in A

EOS

The proportionality constant, k, is the rate constant and its value depends on the reaction, the temperature, and the presence or absence of a catalyst


Distinctions between Rate and the Rate Constant, k

The rate constant remains constant throughout a reaction, regardless of the initial concentrations of the reactants

For reaction orders other than zero, the rate and rate constant are numerically equal only when the concentrations of all reactants are 1 M, units are different EOS

The rate and the rate constant have the same values and units only in zero-order reactions

Rate = k[A]0


Method of Initial Rates

The method of initial rates involves a series of experiments in which the initial concentrations of some reactants are held constant and others are varied in convenient multiples in order to determine the rate law for that reaction

EOS

Rate = k[NO]2[Cl2]


Reaction Order and Concentration

The effects of doubling one initial concentration:

For zero-order reactions, no effect on rate

For first-order reactions, the rate doubles

For second-order reactions, the rate quadruples

EOS

For third-order reactions, the rate increases eightfold


First-Order ReactionsA first-order reaction is a reaction in which a single reactant yields products. Rate = k[A]1 = k[A]

The integrated rate law is an equation that describes the concentration of a reactant as a function of time

ln{[A]t/[A]0} = ln[A]t – ln[A]0 = –kt

EOS

ln[A]t = –kt + ln[A]0

y = mx + b


First Order Example

EOS


Half-life of a Reaction

The half-life (t½) of a reaction is the time in which one-half of the reactant originally present is consumed

ln[A]t – ln[A]0

= ln½[A]0 – ln[A]0 = –kt½

ln(½) = –kt½

EOS

t½ = –ln(½)/k = –(–0.693)/k = 0.693/k


Half-life of a ReactionFor a first-order reaction, the half-life is a constant; it depends only on the rate constant, k, and not on the concentration of reactant

If k is known, t½ can be calculated, and if t½ is known, k can be calculated

EOS

Common application is in half-life of radioactive isotopes – e.g., medicine, nuclear energy, etc.


Zero-Order Reactions

The rate of reaction remains constant throughout and is equal to the rate constant k and to the negative of the slope

EOS


Zero-Order ReactionsRate has the same value at all points, and is independent of initial reactant concentration

EOS

The half-life is proportional to the initial reactant concentration


Second-Order ReactionsA second-order reaction has a rate law with a sum of the exponents equal to 2

Rate = k[A][B] m + n = 2Rate = k[A]2 m = 2

The integrated rate law which expresses [A] as a function of time has the following form

1/[A]t = kt + 1/[A]o

EOS

Second-order half life is t½ = 1/k[A]o


Second Order Illustrated

EOS

Bimolecular Reaction


Summary of Kinetic Data

EOS


Collision TheoryBefore atoms, molecules, or ions can react, they must first come together, or collide

EOS

An effective collision between two molecules puts enough energy into key bonds to break them


Collision TheoryThe activation energy (Ea) is the minimum energy that must be supplied by collisions for a reaction to occur

EOS

The spatial orientations of the colliding species also affect the reaction rate


Transition State TheoryThe configuration of the atoms at the time of the collision is called the transition state

The transitory species having this configuration is called the activated complex

EOS

Heat of Reaction (H)

Activation Energy


Effect of Temperature on Rates

In 1889, Svante Arrhenius proposed the following mathematical expression for the effect of temperature on the rate constant, k

k = Ae–Ea/RT

EOS

ln k = –Ea/RT + ln A


The Arrhenius EquationThe constant A, called the frequency factor, is the product of the collision frequency and a probability factor that takes into account the orientation required for effective molecular collisions

EOS

The expression e–Ea/RT represents the fraction of molecular collisions sufficiently energetic to produce a reaction


Reaction MechanismsA reaction mechanism is a series of simple steps that ultimately lead from the initial reactants to the final products of a reaction

An elementary reaction represents a single stage in the progress of the overall reaction

EOS

The mechanism must account for the experimentally determined rate law


Elementary ReactionsThe molecularity of an elementary reaction refers to the number of free atoms, ions, or molecules that enter into the reaction

EOS


Elementary ReactionsThe rate-determining step is the slowest step in establishing the rate of the overall reaction

Slow – ratedetermining

EOS

Fast step


Effect of Catalyst on Reaction

Enhances reaction rate by reducing the activation energy

EOS


Homogeneous Catalysis

Reaction profile for the uncatalyzed and catalyzed decomposition of ozone

EOS


Heterogeneous Catalysis

Many reactions are catalyzed by the surfaces of appropriate solids

EOS


Enzyme Catalysis

Enzymes are high-molecular-mass proteins that usually catalyze one specific reaction—or a set of quite similar reactions—but no others

EOS


Concentrations and Rates

EOS

[Enzyme] = const [Substrate] = const


Summary of Concepts• Rates of reactions are based on the rate of

disappearance of a reactant or formation of a product

• An integrated rate law relates concentration and time

• The half-life of a reaction is the time in which one-half of the reactant initially present is consumed

EOS

• Chemical reactions occur when sufficiently energetic molecules collide in the proper orientation


Summary of Concepts• Reactions generally go faster at higher

temperatures or in the presence of a catalyst

EOS

• Reaction mechanisms provide a plausible explanation of how a reaction proceeds

chemical kinetics: rates and mechanisms of chemical reactions general chemistry: an integrated...

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