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Notes – Unit 6 Kinetics Vocabulary Rate law expresses how the rate depends on concentration of reaction Chemical Kinetics area of chemistry that concerns reaction rates Reaction Rate the change in concentration of a reactant per unit time Rate Constant the proportionality constant in the relationship between rxn rate and reactant concentration Order the dependency of a rate on a particular reactant, appears in the rds Overall Reaction Order sum of the individual orders “m” and “n” Enzyme biological protein catalyst Catalyst a substance that increases the rate of a reaction without being consumed; by lowering the activation energy, Ea Heterogeneous Catalyst exists in a different phase, usually a solid Homogeneous Catalyst present in a different phase, usually as the reacting molecules Instantaneous Rate the value of the rate at a particular time (because rate is not constant but typically decreases as the amount of product increases) Half Life the time required for a reactant to reach half of its initial concentration Reaction Mechanism yhe series of chemical reaction steps that occur in a chemical reaction Intermediate a substance that is not a reactant or a product but is made and used during the reaction mechanism Rate determining step- (rds) the slow step of a reaction mechanism, determines overall rate; A reaction is only as fast as its’ slowest step Collision model a model based on the idea molecules must collide with proper angle and energy to react; used to observe characteristics of reaction rates Activation energy the energy that must be added to start a chemical reaction Notes – Unit 6 Kinetics Reaction Order and Rate Laws Order – the dependency of a rate on a particular reactant (never include products) - there are three order: 0, 1st, and 2nd Order 0 1 2 [react] 2x 2x 2x Subsequent rate 2 so no change in the rate (goes away in rate law). 21 so 2x change in the rate 22 so 4x change in the rate 0 Rate Laws - Math equations that govern the relationship between the rate and the reactant concentrations. Rate is the change in concentration over time so it can be a derivative d[x]/dt. However,… Generally if A B C D then, the format of the rate law is: Rate k [A]m B n where: m and n are the orders for A and B respectively mol L1 s 1 unit for rate are mol or L s k is the proportaionality constant known as the rate constant with units of m n 1 L m n 1 mol s Note that the rate constant is temperature dependent due to the Arhenius equation (listed later) and thus the rate constant k expresses why the speed of a reaction changes with temperature. “[ ]’s” mean concentration, and the unit is mol L Methods for determining the Rate Law 1. From the mechanism Mechanism is a sequence of chemical steps for how the rxn happens The order (and thus the rate law) is determined by how many times the reactant appears in the Rate Determining Step (rds) also known as the slow step fast step: A B (no reverse reaction) slow step: C D (forward and reverse) Example: Determine the rate law for each mechanism. Step 1: Step 2: overall: A B F C (slow) A B F C (fast) (fast) FBD FBD A 2B C D A 2B C D note that “F” is an intermediate rds is step 1 where A-once, B once so, the order of A=1 Order of A = 1 Order of B = 1 Rate k[ A][B] (slow) rds is step 2 where F-once, B-once F is intmd’t from A + B so, A-once, B-twice (1+1) Order of A = 1 Order of B = 2 Rate k[ A][B] 2 Notes – Unit 6 Kinetics 2. From ratio of initial rate data You will be given a table of Expt’s that contain data of initial rates and conc’s The order (and thus the rate law) is determined by analyzing (through 2 expt’s) how the concentration of a reactant is changed and the subsequent effect on the rate Example: Determine the rate law for the reaction: Experiment 2CO2 NH 3 products [CO2 ]0 mol [NH 3 ]0 mol L 1 2 3 L 0.10 0.10 0.20 0.05 0.10 0.10 mol l Initial Rate s 1.2 x 10-3 2.4 x 10-3 9.6 x 10-3 Determining the Order: CO 2 (compare experiments 2&3) [CO2 ] 2 x rate 4 x 2 2 2 nd order NH 3 (compare 1&2) [ NH 3 ] 2 x rate 2 x 1st order 2 1 So the rate law = k[CO2 ] [ NH 3 ] * The long way (how you should do it on the AP test) m n rate3 k[CO2 ]3 [ NH 3 ]3 rate2 k[CO2 ]2 m [ NH 3]2 n CO2: (solve for m) 9.6 x10 3 (0.20) m (0.10) n 2.4 x10 3 (0.10) m (0.10) n 4 2m NH3: 2m rate2 k[CO2 ]2 m [ NH 3 ]2 n rate1 k[CO2 ]1m [ NH 3]1n (solve for n) 2.4 x103 (0.10) m (0.10) n 1.2 x103 (0.10) m (0.05) n 2 2m 1 m 3. From time and concentration data. You will be given a table of data showing changes in concentration with time. The order (and thus the rate law) is determined by linear regression analysis of three graphs. The graph with the best straight line (r2 closest to 1) determines the order. Note that the absolute value of the slope is the value of the rate constant. The graphs (y vs x): - Zeroeth Order: [A] vs. t has an equation of [A] = -kt + [A]o - First Order: ln[A] vs. t has an equation of ln[A] = -kt + ln[A]o - Second Order: [A]-1 vs. t has an equation of [A] -1 = -kt + [A]o-1 Notes – Unit 6 Kinetics Methods for Determining Half-life 1. First order [ A]o kT [ A] [ A]o b. [ A] when t1 / 2 t 2 a. 2. c. Half-life independent of initial concentration. d. A plot of ln [A] vs. t is always a straight line. Second Order a. Half-life is dependent on [A] initial concentration b. 3. ln Each successive half-life [A]o is halved so that t1 / 2 1 k[ A]0 c. A plot of 1/[A] vs. t will produce a straight line where slope=k Zero Order a. Zero order has constant rate unlike 1st and 2nd it doesn’t change with concentration b. A plot of [A] vs. t gives a straight line where the slope= -k Order and Half-life Equations Order Zero Rate Law: Integrated Rate Law Rate k [ A] kt [ A]o t First Rate k[ A] ln[ A] kt ln[ A]o t Plot needed to give a straight line [A] versus Relationship of rate constant to the slope of straight line Half-life Slope k Slope k t 12 [ A]o 2k t 12 ln[A] versus 0.693 k Second Rate k[ A] 2 1 1 kt [ A] Ao 1 versus t [ A] Slope k t 12 1 k[ A]o More on Reaction Mechanism 1. 2. Terms a. b. Elementary Step- a reaction whose rate law can be written from its’ molecularity Molecularity- the number of species that must collide in the Rate determining step to produce the reaction indicated. c. Unimolecular Step- reaction involving only one molecule (always 1st order) d. Bimolecular Step- reaction involving collision of two species (always 2 nd order) e. Termolecular Step- reaction involving collision of three species. (Rare) Reaction Mechanism (scientific definition): Series of elementary steps that must satisfy two requirements. a. Sum of elementary steps yields the overall equation for the reaction b. Mechanism must agree with experimentally determined rate law. Notes – Unit 6 Kinetics 3. Overview: Elementary Step AProduct 2AProduct A+BProduct 2A+BProduct A+B+CProduct Molecularity Unimolecular Bimolecular Bimolecular Termolecular Termolecular Rate Law Rate=k [A] Rate=k [A]2 Rate=k [A] [B] Rate=k [A]2[B] Rate=k [A] [B] [C] How does a Chemist deduce a mechanism? First by determining the rate law then using rate law to make reaction mechanism that follows the 2 rules. Through trial and error to eliminate false mechanisms. (Note: A reaction Mechanism can never be proved absolutely) Activation Energy: Propose by Svante Arrhenius during the 1880s. a. b. c. d. Through collision models energy comes when kinetic energy in the molecules prior to a collision converting into potential energy to break and make bonds. Transition State- high point The higher activation energy the slower the reaction is at a given temperature. Higher temperature means more collisions thus more energy Ea e. f. a. b. c. RT Number of collision with Ea ( total # of collisions )e To collide successfully i. Collision must involve enough energy to produce the reaction collision energy must be activation energy ii. Relative Orientation of the reactant must allow formation of any new bonds necessary to produce products. Arrhenius Equation k Ae Ea RT The fact that most rate constants obey the Arrhenius equation to a good approximation proves that the collision model for chemical reaction is physically reasonable. The Arrhenius Equation is a linear equation (y=mx+b) ln( k ) Catalysts - Ea 1 ( ) ln( A) RT T Catalysts increase the rates of reactions, does not affect the energy difference, E, between products and reactants Catalysts speed up the reaction without being consumed, lowers activation energy