AP* CHEMISTRY KINETICS Rate Laws, Differential, Integrated, and Arrhenius

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2. AP* CHEMISTRYKINETICSRate Laws, Differential, Integrated, andArrhenius

3. KINETICS: Rate Laws, Differential, Integrated, and ArrheniusObjectiveTo review the student on the concepts, processes and problem solving strategies necessary to successfully answer questions over principles of reaction rates.StandardsThe topic of kinetics is addressed in the topic outline of the College Board AP Chemistry Course Description Guide as described below. III Reactions D. Kinetics1. Concept of rate of reaction2. Use of experimental data and graphical analysis to determine reactant order, rate constants, and reaction rate laws3. Effect of temperature change on rates4. Energy of activation; the role of catalysts5. The relationship between the rate-determining step and a mechanism

4. AP Chemistry Exam ConnectionsThe topic of kinetics is tested every year on the multiple choice and many years on the free response portions of the exam. The list below identifies free response questions that have been previously asked recently. These questions are available from the College Board and can be downloaded free of charge from AP Central http://apcentral.collegeboard.com.Free Response Questions2008 Question 3 (parts d−f) 2008 B Question 22006 Question 6 (part d) 2005 B Question 32005 Question 3 2004 B Question 3 (part b)2004 Question 3 (part e) 2003 B Question 8 (part d)2003 Question 3 2002 Question 72001 Question 6 2000 Question 6 (parts d−e)

5. What I Absolutely Have to Know to Survive the AP ExamThe following might indicate the question deals with kinetics: Rate; time; concentration; order; rate constant; mechanisms; rate determining step; intermediate; catalyst; half-life; instantaneous rate; relative rate; activation energy; integrated rate law; rate expression; rate lawFACTORS THAT AFFECT REACTION RATETemperature Reaction rate increases with increasing temperatureConcentration Reaction rate typically increases with increasing concentration of reactants (pressure changes have the same effect on gaseous reactions)Catalyst Reaction rate increases with the addition of a catalystSurface Area Reaction rate increases with increased surface area of the reactant.

6. EXPRESSING REACTION RATEReaction rate is expressed in terms of how fast the concentration of a substance changes; which is expressed mathematically as shown below. It does not whether you measure the products or the reactants as they are stoichiometrically linked. Translated… The rate of consumption of N2O5 is equal to half the rate of the production of NO2 and equal to twice the production of O2 ……Or better yet…  NO2 is produced at twice the rate at which N2O5 is consumed  O2 is produced at the half the rate at which N2O5 is consumed

7. Instantaneous Rate: Instantaneous rate is the rate at any one point and time during the experiment. To find instantaneous rate you find the slope of the curve at the time in question (for those of you in calculus aka…derivative) i.e. the slope of the tangent line to that point in time. Notice:The rate at any point is constantly decreasing over time; because the concentration of reactants is constantly decreasing as the reaction proceeds.

8. Rate Laws The reaction rate depends only on the concentration of the reactants (assuming the reverse reaction does not contribute to the rate) For the following reaction… 2 X + Y → Z The general form of the rate is… rate = k[X]m [Y]n Where… k is the rate constant  The exponent m represents the order of the reaction with respect to reactant X  The exponent n represents the order of the reaction with respect to reactant Y  The sum of m + n represents the overall order of the reaction. Reactant orders must be determined experimentally; they cannot be written from a balanced equation.

9. Rate generally refers to the initial rate.  The initial rate is the fastest rate of the reaction and occurs at the very beginning of the reaction. At this point there are few competing reactions. It should be noted when using the initial rate the concentration of the reactants are initial concentrations.  The rate law is a mathematical equation which relates the instantaneous rate at a particular point in the progress of a chemical reaction to the concentration of the reacting specie(s).

10. Integrated RateThe rate law expresses rate as a function of reactant concentration(s) at an instant in time (hence instantaneous rate)Integrated rates express the reactant concentrations as a function of time.

14. Graphical Analysis It is imperative that you can determine reaction order simply by analyzing a graph.What is important?  What is plotted on each axis?  What does the slope of the line indicate? If you know this, the order and rate constant can easily be determined.

17. Reaction Mechanisms  Rxn mechanisms attempt to describe the stepwise sequence of elementary reactions that take reactants to products.  The mechanism describes in detail the bonds that are broken and formed as the reaction proceeds.  Each elementary step of a mechanism typically involves 1, 2, or 3 reactants combining to form products.  Every mechanism consists of a series of stepwise reactions. Each reaction in a mechanism has a rate associated with it.  The overall speed of the reaction depends upon the slowest step of the mechanism. The rate law of this step is identical to the experimental rate law. The slow step of the mechanism is also called the rate determining step of the mechanism.  The sum of all the steps of the mechanism must equal the overall balanced chemical equation.

18. Reaction Mechanisms (cont.)The coefficients of the reactants in the rate determining step of the mechanism must correspond to the exponents or orderof the reactants in the experimental rate law.Catalysts and Intermediates…  A catalyst is used up early in a reaction (reactant) and is regenerated (product) in a subsequent step.  A catalyst is a substance that acts to increase the rate of a chemical reaction by providing an alternate path for thereaction to occur. This means that there will be a change in the magnitude of the rate constant and possibly achange in the order of the reaction.  An intermediate is produced early in the reaction (product) and used up (reactant) in a subsequent step.

19. Collision Theory and Activation EnergyFor a reaction to happen two things must occur:1. Molecules must collide with enough kinetic energy to react – i.e. they must meet or exceed the energy of activation, Ea.2. The molecules must collide with the appropriate orientation for a reaction to occur, i.e. the collisions MUST BE EFFECTIVE.These two factors are summarized in the Arrhenius equation:  k is the rate constant(s)  T is the temperature in Kelvin  R is the gas constant 8.341 J mol−1 K−1  Ea is the activation energy  A is the Arrhenius constant − it describes how many collisions have the appropriate orientation. Two simple atoms that can collide in any Orientation will have a very high A value, while two very complex molecules that must collide in a very specific way will have a low A value.

20. Ea − the activation energy…  Is a measure of the energy barrier colliding molecules must overcome if they are to react rather than recoil from one another.  It is assumed that every pair of reacting species with energy less than Ea will not react and every pair with energy greater than Ea and the proper orientation will react.  See graph on next page

23. Kinetics Cheat Sheet (cont.)  Be able to explain with algebraic equations or words how an order is determined. It is important to state which concentration(s) is/are held constant and which concentration is varied as well the effect that has on the rate of the reaction if you choose not to justify without algebraic equations.  Mechanisms – must agree with the stoichiometry of the reaction and the “summary rate law” must agree up to and including the slow step; identify intermediates and catalysts and clearly state that the correct mechanism “agrees with the experimentally determined rate law”.

24. Kinetics Cheat Sheet (cont.)  Discuss number of effective collisions in relation toincreasing or decreasing rates  Arrhenius – magnitude of k relates directly to the speed of the reaction; large = fast; small = slow Ea also predicts speed but the relationship is an inverse one; high = slow rate; low = fast rate  “rate in terms of” is code for “relative rates” – use stoichiometry ratios on rate value  instantaneous rate = slope of the line tangent to the time point in question

25. ConnectionsStoichiometry − “using up” one component of the system might indicate a limiting reactant in effectElectrochemistry − if reaction is redox in nature rate problems could come in playThermochemistry − Ea and ΔH°rxn and reaction diagrams

26. Potential PitfallsUnits on k = always time−1 and one less M−1 than overall order.Ex: 2nd order overall has a k with units of M −1 s −1

29. 2x= 2

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