12.1 Reaction Rates

• Chemical kinetics deals with the speed at which these changes occur

• The speed, or rate, of a process, is defined as the change in a given quantity over a specific period of time

• Reaction rate: The change in concentration of a reactant or product per unit time

• The value of the rate at a particular time (the instantaneous rate) can be obtained by computing the slope of a line tangent to the curve at that point

• The rate of a reaction is not constant, but it changes with time. This is so because the concentrations change with time

• Be very specific when describing a rate for a chemical reaction

12.2 Rate Laws: An Introduction

• When forward and reverse reaction rates are equal, there will be no changes in the concentrations of reactants or products

• The proportionality constant k, called the rate constant, and n, called the order of the reactant, must both be determined by experiment

• The concentrations of the products do not appear in the rate law because the reaction rate is being studied under conditions where the reverse reaction does not contribute to the overall rate

• The value of the exponent n must be determined by experiment; it cannot be written from the balanced equation.

• Knowing the rate law for a reaction is important mainly because we can usually infer the individual steps involved in the reaction from the specific form of the rate law

• Differential rate law: A rate law that expresses how the rate depends on the concentration

• The integrated rate law expresses how the concentrations depend on the time

  • Because the differential and integrated rate laws for a given reaction are related in a well-defined way, the experimental determination of either of the rate laws is sufficient

  • If we can conveniently measure how the rate changes as the concentrations are changed, we can readily determine the differential rate law

  • If it is more convenient to measure the concentration as a function of time, we can determine the form of the integrated rate law

• Experimental convenience usually dictates which type of rate law is determined experimentally

12.3 Determining the Form of the Rate Law

• The order of a particular reactant must be obtained by observing how the reaction rate depends on the concentration of that reactant

• The value of the initial rate is determined for each experiment at the same value

• The idea is to determine the instantaneous rate before the initial concentrations of reactants have changed significantly.

• Overall reaction order is the sum of the orders for the various reactants

• k is the rate constant is the order; not related to the coefficients in the balanced equation

• The value of k can be determined from the plot of the appropriate function of [A] versus t

12.4 The Integrated Rate Law

• Since the rate of this reaction depends on the concentration of N2O5 to the first power, it is a first-order reaction

• This rate law can be put into a different form using a calculus operation known as integration

• An integrated rate law relates concentration to reaction time.

• For a first-order reaction, a plot of ln [A] versus t is always a straight line.

  • For a first-order reaction, t1/2 is independent of the initial concentration.

• The time required for a reactant to reach half its original concentration is called the half-life of a reactant

• When two identical molecules combine, the resulting molecule is called a dimer

• A zero-order reaction has a constant rate

• Zero-order reactions are most often encountered when a substance such as a metal surface or an enzyme is required for the reaction to occur

• The kinetics of complicated reactions can be studied by observing the behavior of one reactant at a time

12.5 Rate Laws: A Summary

• To simplify the rate laws for reactions, we have always assumed that the rate is being studied under conditions where only the forward reaction is important

• This produces rate laws that contain only reactant concentrations

• Whether we determine the differential rate law or the integrated rate law depends on the type of data that can be collected conveniently and accurately

• Once we have experimentally determined either type of rate law, we can write the other for a given reaction.

• To experimentally determine the integrated rate law for a reaction, concentrations are measured at various values of t as the reaction proceed

• Once the correct straight-line plot is found, the correct integrated rate law can be chosen and the value of k obtained from the slope

12.6 Reaction Mechanisms

• To understand a reaction, we must know its mechanism, and one of the main purposes for studying kinetics is to learn as much as possible about the steps involved in a reaction

• A balanced equation does not tell us how the reactants become products

• An intermediate is formed in one step and used up in a subsequent step and so is never seen as a product

• The prefix uni- means one, bi- means two, and ter- means three

• Unimolecular step: A reaction involving one molecule

• Bimolecular and termolecular: Reactions involving the collision of two and three species

• A unimolecular elementary step is always first order, a bimolecular step is always second-order, and so on

• Reaction mechanism, a series of elementary steps that must satisfy two requirements: The sum of the elementary steps must give the overall balanced equation for the reaction

  • The mechanism must agree with the experimentally determined rate law

• A reaction is only as fast as its slowest step

• A mechanism can never be proved absolutely

  • We can only say that a mechanism that satisfies the two requirements is possibly correct.

• Elementary step: rate law for the step can be written from the molecularity of the reaction

12.7 A Model for Chemical Kinetics

• The kinetic molecular theory of gases predicts that an increase in temperature raises molecular velocities and so increases the frequency of collisions between molecules

  • This idea agrees with the observation that reaction rates are greater at higher temperatures.

• The higher the activation energy, the slower the reaction at a given temperature

• Experiments show that the observed reaction rate is considerably smaller than the rate of collisions with enough energy to surmount the barrier.

• The answer lies in the molecular orientations during collisions

  • Two requirements must be satisfied for reactants to collide successfully: The collision must involve enough energy to produce the reaction; that is, the collision energy must equal or exceed the activation energy

  • The relative orientation of the reactants must allow the formation of any new bonds necessary to produce products

• A depends on the collision frequency and relative orientation of the molecules

• The value of Ea can be found by obtaining the values of k at several temperatures

12.8 Catalysis

• The catalyst allows the reaction to occur with lower activation energy, a much larger fraction of collisions is effective at a given temperature, and the reaction rate is increased

• It works by providing a lower-energy pathway for the reaction

• Catalysts can be classified as homogeneous or heterogeneous homogeneous: They exist in the same phase as the reactants

• Heterogeneous: They exist in a different phase than the reactants

  • An important example of heterogeneous catalysis occurs in the hydrogenation of unsaturated hydrocarbons, compounds composed mainly of carbon and hydrogen with some carbon-carbon double bonds

  • Heterogeneous catalysis also occurs in the oxidation of gaseous sulfur dioxide to gaseous sulfur trioxide

  • This process is especially interesting because it illustrates both positive and negative consequences of chemical catalysis

• The most effective catalytic materials are transition metal oxides and noble metals such as palladium and platinum