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AP* CHEMISTRY KINETICS Rate Laws, Differential, Integrated, and Arrhenius
KINETICS: Rate Laws, Differential, Integrated, and Arrhenius Objective To review the student on the concepts, processes and problem solving strategies necessary to successfully answer questions over principles of reaction rates. Standards The topic of kinetics is addressed in the topic outline of the College Board AP Chemistry Course Description Guide as described below. III Reactions D. Kinetics 1. Concept of rate of reaction 2. Use of experimental data and graphical analysis to determine reactant order, rate constants, and reaction rate laws 3. Effect of temperature change on rates 4. Energy of activation; the role of catalysts 5. The relationship between the rate-determining step and a mechanism
AP Chemistry Exam Connections The 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 Free Response Questions 2008 Question 3 (parts df) 2008 B Question Question 6 (part d) 2005 B Question Question B Question 3 (part b) 2004 Question 3 (part e) 2003 B Question 8 (part d) 2003 Question Question Question Question 6 (parts de)
What I Absolutely Have to Know to Survive the AP Exam The 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 law FACTORS THAT AFFECT REACTION RATE Temperature Reaction rate increases with increasing temperature Concentration 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 catalyst Surface Area Reaction rate increases with increased surface area of the reactant.
EXPRESSING REACTION RATE Reaction 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 N 2 O 5 is equal to half the rate of the production of NO 2 and equal to twice the production of O 2 ……Or better yet… NO 2 is produced at twice the rate at which N 2 O 5 is consumed O 2 is produced at the half the rate at which N 2 O 5 is consumed
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.
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.
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).
Integrated Rate The 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.
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.
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.
Reaction Mechanisms (cont.) The coefficients of the reactants in the rate determining step of the mechanism must correspond to the exponents or order of 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 the reaction 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.
Collision Theory and Activation Energy For 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 J mol1 K1 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.
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
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.
Kinetics Cheat Sheet (cont.) Discuss number of effective collisions in relation to increasing 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
Connections Stoichiometry using up one component of the system might indicate a limiting reactant in effect Electrochemistry if reaction is redox in nature rate problems could come in play Thermochemistry Ea and Δ H°rxn and reaction diagrams
Potential Pitfalls Units on k = always time 1 and one less M1 than overall order. Ex: 2nd order overall has a k with units of M 1 s 1
2 x = 2
E If it is zero order with respect to [A], then A 0 equals one, thus [A] is not included in the rate expression.
D To be second order with respect to A and third order overall, reactant B must be first order.
B The rate law expression shows that reactant X is second order, therefore a plot of reciprocal concentration vs. time will yield a straight line.
B I is incorrect. The reactant graphed is first order, if it were 2nd order the graph would have reciprocal concentration on the y-axis and have a straight line with a positive slope. II is a correct statement. III is incorrect, for a 1st order reaction the units for k are time 1
7. Each of the following factors can affect the rate of a chemical reaction EXCEPT (A) increasing temperature (B) decreasing reactant concentration (C) adding a catalyst (D) removing products (E) breaking up solid reactants D Chemical reactions occur because molecules collide with sufficient energy and orientation to break and make bonds. Heat em up and speed em up. The reactions are more energetic with an increase in temperature, more effectively oriented in the presence of a catalyst, more common if the container is crowded or the reactants have more surface area.
8. As the above reaction proceeds at constant temperature, the reaction rate (A) remains the same since there is no catalyst present (B) remains the same since the temperature is constant (C) increases because the rate constant is a large number (D) increases because the rate of effective collisions increases over time (E) decreases because the concentrations of the reactants decrease as the reaction progresses
E As the reaction proceeds at constant temperature, the concentration of its reactants are decreasing thus the reaction rate is decreasing. The rate of effective collisions remains constant at constant temperature with no catalyst.
C Trials 1 & 2 held [B] constant and double the [A]; the rate doubled therefore the reaction is 1st order for reactant A. Trials 1 & 3 held [A] constant and doubled [B]; the rate doubled therefore the reaction is 1 st order for reactant B.
C Cross off any intermediates, in this case F atoms. Focus on only the slow or rate determining step. In this case it is the first step. therefore the mechanism gives an overall rate law as shown. Rate = k[NO 2 ][F 2 ]