AP Chem, Kinetics, Chapter Fifteen

1 UNIT FOUR: THE CONTROL OF CHEMICAL REACTIONS Chapter 15: Principles of Reactivity, Chemical Ch emical Kinetics (Text from Barron’s AP Chemistry and Chemistry, by Kotz, Treichel, and Weaver)

Principles of Reactivity: Chemical Kinetics (Chapter Fifteen) 15.1 Rates of Chemical Reactions The rate of a chemical reaction refers to the change in concentration of a substance per unit of time. ܴܽ‫= ݊݋݅ݐܿܽ݁ݎ ݂݋ ݁ݐ‬

ܿℎܽ݊݃݁ ݅݊ ܿ‫݊݋݅ݐܽݎݐ݊݁ܿ݊݋‬ ܿℎܽ݊݃݁ ݅݊ ‫݁݉݅ݐ‬

Since concentration can either be measured in terms of the rate of formation of products or the rate of disappearance of reactants, a positive sign is used to indicate increasing concentration while a negative sign indicates decreasing concentration. Pay attention to the language of the question—for example, if a question asks for the rate a substance is disappearing, it is unnecessary to include a negative sign in the answer. 15.2 Reaction Conditions and Rates Factors that affect reaction rates include:





Concentration – increasing the concentration/pressure of reactant substsances will always increase the reaction rate, provided the substance is part of the rate law Temperature – increasing the temperature always increases the reaction rate and vice versa Ability of Reactants to Meet – reactants in gas phase or solution react most rapidly because individual ions can react; solids will react more rapidly if their surface areas are increased Catalyst Presence – catalysts increase the reaction rate, offering an alternate reaction path with a lower activation energy

15.3 Effect of Concentration on Reaction Rate The rate law (rate rate equation) equation is an equation expressing the relationship between reactant concentration and reactant rate. In general, for a reaction ܽ ‫ ܣ‬+ ܾ ‫ܺ ݔ → ܤ‬, the rate equation has the form ‫݇ = ݁ݐܽݎ‬ሾ‫ܣ‬ሿ௠ ሾ‫ܤ‬ሿ௡ . The order of a reaction with respect to a reactant is the exponent of its concentration term (such as ݉ or ݊). The overall reaction order is the sum of the exponents. ݇ is the rate constant—it relates the rate and concentration at a given temperature. ܽ and ܾ are stoichiometric coefficients for the substances ‫ ܣ‬and ‫ܤ‬. A rate equation must be determined experimentally, for there is no theoretical way to predict the exponents of a rate law. By looking at a chart of how the rate of a reaction is affected by changing the concentration of reactants, it is possible to determine the order of a reaction with respect to a certain reactant and the overall reaction order.

2 UNIT FOUR: THE CONTROL OF CHEMICAL REACTIONS Chapter 15: Principles of Reactivity, Chemical Ch emical Kinetics (Text from Barron’s AP Chemistry and Chemistry, by Kotz, Treichel, and Weaver)

Principles of Reactivity: Chemical Kinetics (Chapter Fifteen) For example, if one reactant concentration is held constant, and another is doubled, with the reaction rate also doubling, then the reaction is first-order with respect to the manipulated reactant. Remember that these are exponents—a reaction will be second order if when one reactant concentration is held constant, another is doubled, and the reaction rate quadruples. The unit of the rate constant can be useful for determining the overall reaction order. Units of ݇ are

௅೙షభ , where ௠௢௟ ೙షభ ∙ ௧௜௠௘

݊ is the overall order.

Thus, second-order reactions have ݇ in units of

௅ , first-order ௠௢௟ ∙ ௧௜௠௘

ଵ

reactions have ݇ in units of ௦ , and

zero-order reactions (these are reactions with a constant rate, unaffected by concentration) have ݇ in units of

௠௢௟ . ௅ ∙ ௧௜௠௘

15.4 Concentration-Time Relationships: Integrated Rate Laws ሾோሿ

In the first-order integrated rate law, the ratio of concentrations, ሾோሿ೟ , is the fraction of reactant that remains బ

after a given time has elapsed. ሾܴሿ௧ is the reactant concentration at some time ‫ݐ‬, while ሾܴሿ଴ is the initial concentration of the reactant. Integrated rate laws can be rearranged into the form of a linear equation (‫ ݔ݉ = ݕ‬+ ܾ). Order 0

Rate Equation ݇ሾܴሿ଴

1

݇ሾܴሿଵ

2

݇ሾܴሿଶ

Integrated Rate Equation ሾܴሿ଴ − ሾܴሿ௧ = ݇‫ݐ‬ ሾܴሿ௧ ln = −݇‫ݐ‬ ሾܴሿ଴ 1 1 − = ݇‫ݐ‬ ሾܴሿ௧ ሾܴሿ଴

Linear Form −ሾܴሿ௧ = ݇‫ ݐ‬− ሾܴሿ଴

lnሾܴሿ௧ = −݇‫ ݐ‬+ lnሾܴሿ଴ 1 1 = ݇‫ ݐ‬+ ሾܴሿ௧ ሾܴሿ଴

By plugging experimental data into the above equations to find which one results in a straight line, it is possible to determine the reaction order and the rate constant. The halfhalf-life of a reaction is the time required for the concentration of a reactant to decrease to one-half its initial value. First-Order: ln

଴.ହሾ஺ሿబ ሾ஺ሿబ ଵ

= −݇‫ݐ‬ଵൗ , which leads to ‫ݐ‬1ൗ = ଶ

ଵ

2

0.693 ݇ ଵ

Second-Order: ଴.ହሾ஺ሿ − ሾ஺ሿ = ݇‫ݐ‬ଵൗ , which leads to ‫ݐ‬ଵൗ = ௞ሾ஺ሿ ೟

బ

ଶ

ଶ

బ

3 UNIT FOUR: THE CONTROL OF CHEMICAL REACTIONS Chapter 15: Principles of Reactivity, Chemical Ch emical Kinetics (Text from Barron’s AP Chemistry and Chemistry, by Kotz, Treichel, and Weaver)

Principles of Reactivity: Chemical Kinetics (Chapter Fifteen) 15.5 A Microscopic View of Reaction Rates The collision theory states that three conditions must be met in order for an equation to occur: 1. Reacting molecules must collide with one another. 2. Reacting molecules must collide with sufficient energy to break bonds. 3. Reacting molecules must collide in the proper orientation that leads to rearrangement of atoms.

The Effect of Concentration The number of collisions between reactant molecules is directly proportional to the concentration of each reactant. Since molecules must collide with each other to react, and increasing concentration increases the number of collisions, the rate of a reaction is primarily related to the concentration of reactants.

The Effect of Heat In any sample of gas or liquid, some molecules have very low energies, others have very high energies, but most have some intermediate energy. As the temperature increases, energy of the molecules increases. The minimum energy requirement for molecules to react is the energy of activation (EA). When molecules are heated, more molecules will be able to surmount the EA barrier and react.

The Effect of Orientation The lower the probability of achieving the proper orientation, the slower the reaction will occur. Complex molecules are less likely to collide in exactly the right orientation required. The Arrhenius equation summarizes the dependence of reaction rates on the above three factors. ݇ = ‫݁ܣ‬

ିாಲൗ ோ் ,

where ݁

ିாಲൗ ோ்

is the fraction of molecules having the minimum energy required to react ln ݇ = ln ‫ ܣ‬− ln ݇ = −

‫ܧ‬஺ ܴܶ

‫ܧ‬஺ 1 ൬ ൰ + ln ‫ܣ‬ ܴ ܶ

The equation includes the rate constant ݇, the activation energy ‫ܧ‬஺ , the universal gas law constant

‫ܬ‬ ܴ = 8.314 ൗ݉‫ ܭ ∙ ݈݋‬, the Kelvin temperature ܶ, and the proportionality constant ‫ܣ‬, which is a temperature-

dependent frequency factor related to the number of collisions and the percentage of collisions that have the correct geometry.

4 UNIT FOUR: THE CONTROL OF CHEMICAL REACTIONS Chapter 15: Principles of Reactivity, Chemical Ch emical Kinetics (Text from Barron’s AP Chemistry and Chemistry, by Kotz, Treichel, and Weaver)

Principles of Reactivity: Chemical Kinetics (Chapter Fifteen) Catalysts are substances that speed up the rate of a chemical reaction, providing a different pathway with a lower energy of activation level for the reaction. They are not consumed in the reaction. A homogeneous catalyst is one that is present in the same phase as the reacting substance. Reaction intermediates are substances formed in one step of the reaction and consumed in a later step.

The Transition-State Theory and Reaction-Coordinate Diagrams (Reaction Profiles) The transitiontransition -state theory states that during the collision process, kinetic energy is converted to potential energy. If this potential energy meets or exceeds the activation energy, the reaction can occur. The transition state is where the energy of the system reaches a maximum—this is where sufficient energy has been concentrated in the appropriate bonds. This theory is similar to the collision theory, but involves more details about the energy and shapes of molecules upon collision. When a collision occurs, molecules will be in the activated complex where an existing bond is half-broken and a new bond is half-formed. If the activated complex has the proper structure, it will successfully break apart into products, but if it has the incorrect structure, molecules will remain as the original reactants. The reactionreaction profile), reaction -coordinate diagram (reaction profile plots the increase in potential energy of the reactants as they approach, reaching a maximum at the moment of collision, and then the decrease in potential energy as the products form. The energy (y-axis) of the reactants and products is plotted against reaction progress (x-axis).




∆‫ܧܲ = ܪ‬௣௥௢ௗ௨௖௧௦ − ܲ‫ܧ‬௥௘௔௖௧௔௡௧௦ : For endothermic reactions, reactions the potential energy of the products is greater than the potential energy of the reactants. The reverse is true for exothermic reactions. reactions The activation energy is the difference between the potential energy of the reactants and the maximum energy of the curve. Catalysts will provide an alternate reaction pathway that has a lower energy barrier in the reaction profile. Enzymes are a class of natural catalysts found in living organisms that catalyze very specific reactions.

15.6 Reaction Mechanisms Reaction mechanisms refer to the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to products. Each step in a multistep reaction sequence is referred to as an elementary step. Elementary reactions usually involve the collision of only two reactant molecules. It is extremely rare that three molecules will collide simultaneously. The molecularity of the elementary step indicates how many reactant molecules come together. A reaction is unimolecular if one molecule is the only reactant, while a reaction is bimolecular if two molecules come together (the molecules may be identical or different). A termolecular elementary step involves three

5 UNIT FOUR: THE CONTROL OF CHEMICAL REACTIONS Chapter 15: Principles of Reactivity, Chemical Ch emical Kinetics (Text from Barron’s AP Chemistry and Chemistry, by Kotz, Treichel, and Weaver)

Principles of Reactivity: Chemical Kinetics (Chapter Fifteen) molecules and is not likely, unless one of the molecules is involved in high concentrations, such as a solvent molecules. Most termolecular processes involve the collision of two reactant molecules and a third, inert molecule which has the purpose of absorbing excess energy.

In elementary reactions, the rate equation is given by the product of the rate constant and the stoichiometric coefficients of the reactants in that step. The molecularity of an elementary step and its order are the same. In other words, a unimolecular elementary step must be first order, a bimolecular elementary step must be second order, etc. This cannot be applied to the overall reaction. The products of a reaction cannot be produced at a rate faster than the rate of the slowest step. This is similar to the concept of a limiting reactant. If the slow step determines the rate of the equation, it is called the raterate -determining step or the rate limiting step. Given the overall reaction and the overall rate equation, it is possible to determine which elementary step is the slow step, since its rate equation will be equivalent to that of the overall rate equation. Another common two-step reaction mechanism involves a fast first elementary reaction producing an intermediate, with the intermediate being consumed in the slow second elementary reaction. In order to write a rate law with respect to the reactants only, a series of steps can be followed. 1.

The ste ad y -sta te a ssu mp tio n can be used to say that if the second-step is the rate-determining step, the first reaction must be relatively fast and reversible. 2. This means that the first reaction, which produces an intermediate, reaches a state of equilibrium where the rate of formation of the intermediate and the rate of disappearance of the intermediate are equivalent. 3. Since the forward and reverse rates are the same, it is possible to solve for the concentration of the intermediate in terms of the reactants. 4. Substitute into the second step, combine all of the rate constants, and write the rate law.