CHEMICAL KINETICSChapter 12

Chemical kinetics deals with the speed at which 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 – change in concentration of a reactant or product per unit time.

12.1 Reaction Rates

Note that a change can be positive (increase) or negative (decrease), thus leading to a positive or negative reaction rate by this definition. For convenience, we will always define the rate as a positive quantity.

A negative sign will appear in front of the equation when we are focusing on the reactants. The equation will look like this:

12.1 Reaction Rates

Instantaneous rate –the rate is not constant, but decreases with time, so rate can be measured for a given point in time.

Rate = -(slope of tangent line)

When examining products of a reaction, rates are proportional to the coefficients represented in a balanced chemical equation.

12.1 Reaction Rates

Chemical reactions are reversible.◦ After a period of time, enough products

accumulate so that the reverse reaction becomes important.

Concentration of the reactants depends on the difference in the rates of the forward and reverse reactions.◦ This tends to complicate matters, so we will focus

on the reaction soon after the reactants are mixed, before products have had time to build up to significant levels.

Choose conditions where the reverse reaction can be neglected.

12.2 Rate Laws: An Introduction

The reaction rate will depend only on the concentrations of the reactants

Rate = k[A]n

Where k is the proportionality constant, and n, the order of the reactant, must be determined by experiment. The order of a reactant can be an integer (including zero) or a fraction

Rate Law – The above expression shows how the rate depends on the concentration of the reactants.

12.2 Rate Laws: An Introduction

Note two important points about the Rate Law equation:

1. 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

2. The value of the exponent “n” MUST be determined by experiment. It can’t be written from the balanced equation.

12.2 Rate Laws: An Introduction

Differential Rate Law (Rate Law) – expresses how the rate depends on concentration

Integrated Rate Law – expresses how the concentration depends on time

Why do I need to know this? You can work backwards from the rate law to infer the steps by which the reaction occurs. Most chemical reactions do not take place in a single step but result from a series of sequential steps. To understand a chemical reaction, we must learn what these steps are.

See purple box on page 559

12.2 Rate Laws: An Introduction

The first step in understanding how a given chemical reaction occurs is to determine the form of the rate law. You need to determine experimentally the power to which each reactant concentration must be raised in the rate law.

Method of initial rates – common method for experimentally determining the form of the rate law for a reaction.

Initial Rate – instantaneous rate determined just after the reaction begins (just after t=0)

Overall reaction order – sum of all the exponents in the rate law.

12.3 Determining the Form of the Rate Law

The reaction between bromate ions and bromide ions in an acidic aqueous solution is given by the following equation:

BrO3- + 5Br- + 6H+ 3Br2 + 3H2O

Using the experimental data from the table below, determine the

1. orders for all three reactants2. overall reaction order3. value of the rate constant

EXP [BrO3- ] [Br- ] [H+ ] INITIAL RATE

1 0.10 0.10 0.10 8.0 X 10-4

2 0.20 0.10 0.10 1.6 X 10-3

3 0.20 0.20 0.10 3.2 X 10-3

4 0.10 0.10 0.20 3.2 X 10-3

Now we need to include time into the rate law.

First order rate laws – the rate of the reaction depends on the concentration to the first power

12.4 The Integrated Rate law

Integrated rate law – expresses the concentration of the reactant as a function of time. We take the above equation and do a calculus operation known as integration and we come up with the

Integrated first-order rate law:

12.4 The Integrated Rate law

Several important things to note about this equation:◦ The equation shows how the concentration of “A”

depends on time. If the initial concentration of “A” and the rate constant “k” are known, the concentration of “A” at any time can be calculated.

◦ The equation is of the form y = mx + b, where a plot of y vs x is a straight line with slope m and intercept b.y = ln[A] x = t m = -k b =

ln[A]o

◦ This integrated rate law for a first-order reaction can also be expressed in terms of a ratio of [A] and [A]o

12.4 The Integrated Rate law

Half-life of a reaction – the time required for a reactant to reach half its original concentration. ◦ For the half-life of a first order reaction the

equation is:

12.4 The Integrated Rate law

Second-order rate laws – doubling the concentration of “A” quadruples the reaction rate; tripling the concentration of “A” increases the rate by nine times. The equation would be as follows:

12.4 The Integrated Rate law

Integrated second-order rate law – if we integrate the above equation we come up with the following equation:

Characteristics of this equation:◦ A plot of 1/[A] versus “t” will produce a straight

line with a slope equal to “k”◦ This equation shows how [A] depends on time and

can be used to calculate [A] at any time “t”, provided “k” and [A]0 are known.

12.4 The Integrated Rate law

Half-life of a second-order reaction – each successive half-life is double the preceding one:

12.4 The Integrated Rate law

Zero-order rate law - rate law of a zero order reaction is a constant:

Integrated rate law for a zero-order reactionIn this case a plot of [A] versus “t” gives a straight line of slope –k

Half-life of a zero-order reaction -

12.4 The Integrated Rate law

Reaction mechanism – series of steps in which a chemical reaction occurs. A balanced equation does not tell us how the reactants become products.

Intermediate – a species that is neither a reactant nor a product but that is formed and consumed during the reaction sequence.

Elementary step – a reaction whose rate law can be written from it molecularity

Molecularity – the number of species that must collide to produce the reaction indicated by that step.

12.6 Reaction Mechanisms

Unimolecular step – a reaction involving one molecule

Bimolecular step – reaction involving the collision of two species

Termolecular step – reaction involving the collision of three species. These are quite rare, because the probability of three molecules colliding simultaneously is very small.

12.6 Reaction Mechanisms

Reaction Mechanism (the improved definition)◦ A series of elementary steps that must satisfy two

requirements:1. The sum of the elementary steps must give the overall

balanced equation for the reaction2. The mechanism must agree with the experimentally

determined rate law.

See table 12.7 page 574

A reaction mechanism can NEVER be proved absolutely. We can only say that the mechanism that satisfies the two requirements is possibly correct.

12.6 Reaction Mechanisms

Collision Model – this model is built around the central idea that molecules must collide to react

Activation Energy (Ea) – a threshold of energy that must be overcome to produce a chemical reaction.

Transition State – the arrangement of atoms found at the top of the energy hill. Transitional molecule forms the products or reform the reactants

12.7 A Model for Chemical Kinetics

Chemcial reactions can be sped up by using several techniques. Each of these allows for more collisions, increasing the number of collisions which produced more product.

• Stirring• Increase surface area• Increase temperature• Adding a catalyst

12.7 A Model for Chemical Kinetics Molecular orientations – When molecules

collide, they not only must have enough energy in the collision, but they must also collide at the correct orientation to each other in order for an effective collision.

Arrhenius equation – finds the rate constant by showing the fraction of collisions with effective orientations and represents the fraction of collisions with sufficient energy to produce a reaction.

Where “A”, called the frequency factor, is a combination of the collision frequency and reflects the fraction of collisions with effective orientations. e-Ea/RT represents the fraction of collisions with sufficient energy to produce collisions

12.7 A Model for Chemical Kinetics

If we take the natural log of Arrhenius equations we get the equation of a line:

12.7 A Model for Chemical Kinetics

Catalyst – a substance that speeds up a raction without being consumed itself. It lowers the activation energy and allows for a greater fraction of molecules to have effective collisions.

12.8 Catalysis

Homogeneous catalyst – is present in the same phase as the reacting molecules

Heterogeneous catalyst – exists in a different phase as the reaction molecules, usually as a solid

Adsorption – refers to the collection of one substance on the surface of another substance.

12.8 Catalysis

The typical heterogeneous catalysis involves four steps:

1. Adsorption and activation of the reactants2. Migration of the adsorbed reactants on the

surface3. Reaction of the adsorbed substances4. Escape, or desorption of the products

12.8 Catalysis