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Chemistry 102(60) Summer 2001 n Instructor: Dr. Upali Siriwardane n e-mail:upali@chem.latech n Office: CTH 311 Phone 257-4941 n Office Hours: n 8:30-10:30 a.m., M, W, Tu,Th, F (Test 1): Chapter 12 (Test 2): Chapter 13. (Test 3): Chapter 14 (Test 4): Chapter 15. (Test 5): Chapter 17.
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Chapter 13. Rates of Reactions Chemical Kinetics n the branch of chemistry dealing with the rates of chemical reactions. n Using chemical kinetics we can find time to complete a reaction, the effect of temperature on the rate n Effect of other substances (catalysts or inhibitors) on the reactions
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How do you measure rates n Rates are related to the time it required to decay reactants or form products. n The rate reaction = change in concentration of reactants/products per unit time
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An example reaction Gas buret Constant temperature bath
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An example reaction n Time (s)Volume STP O 2, mL n 0 0 n 3001.15 n 6002.18 n 9003.11 n 12003.95 n 18005.36 n 24006.50 n 30007.42 n 42008.75 n 54009.62 n 6600 10.17 n 7800 10.53 Here are the results for our experiment.
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Rate n a A --> b B n based on reactants rate = -(1/a) [A]/ t n Based on products rate = +(1/b) [B]/ t [A]= [A] f - [A] I Change in A t= t f - t i Change in t
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Rate of Reaction n 2 N 2 O 5 (g) -----> 4 NO 2 (g) + O 2 (g) based on reactants rate = -(1/2) [N 2 O 5 ]/ t n Based on products rate = +(1/4) [NO 2 ]/ t rate = +(1/1) [O 2 ]/ t n
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Rate of Appearance & disappearance n 2 N 2 O 5 (g) -----> 4 NO 2 (g) + O 2 (g) Disappearance is based on reactants rate = -( [N 2 O 5 ]/ t n Appearance is based on products rate = [NO 2 ]/ t rate = [O 2 ]/ t n converting rates of Appearance.. rate = ( [NO 2 ]/ t = - 4/2 [N 2 O 5 ]/ t [O 2 ]/ t = - 1/2 [N 2 O 5 ]/ t
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Chemical Kinetics Definitions and Concepts n a) rate law n b) rate constant n c) order n d) differential rate law n c) integral rate law n
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n Every chemical reaction has a Rate Law n The rate law is an expression that relates the rate of a chemical reaction to a constant (rate constant-k) and concentration of reactants raised to a power. n The power of a concentration is called the order with respect to the particular reactant. Rate Law
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n E.g. A + B -----> C rate [A] l [B] m n rate = k [A] l [B] m ; k = rate constant n [A] = concentration of A n [B] = concentration of B n l = order with respect to A n m = order with respect to B n l & m have nothing to do with stoichiometric coefficients
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Rate Constant n E.g. A + B -----> C rate [A] l [B] m n rate = k [A] l [B] m ; n k = rate constant n proportionality constant of the rate law
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Rate Law n E.g. n 2 N 2 O 5 (g) -----> 4 NO 2 (g) + O 2 (g) rate [N 2 O 5 ] 1 n rate = k [N 2 O 5 ] 1 ;k = rate constant n [N 2 O 5 ] = concentration of N 2 O 5 n 1 = order with respect to N 2 O 5 n Rate and the order are obtained by experiments
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Order n The power of the concentrations is the order with respect to the reactant. n E.g. A + B -----> C n rate = k [A] 1 [B] 2 n The order of the reaction with respect to A is one (1). n The order of the reaction with respect to B is two (2). n Overall order of a chemical reaction is equal to the sum of all orders(3).
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Finding rate laws n Method of initial rates. n The order for each reactant is found by: Changing the initial concentration of that reactant. Holding all other initial concentrations and conditions constant. Measuring the initial rates of reaction n The change in rate is used to determine the order for that specific reactant. The process is repeated for each reactant.
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How do you find order? n A + B -----> C n rate = k [A] l [B] m ; n Hold concentration of other reactants constant n If [A] doubled, rate doubled n -1st order, [2A] 1 = 2 1 x [A] 1, 2 1 = 2 n b) If [A] doubled, rate quadrupled n -2nd order, [2A] 2 = 2 2 x [A] 2, 2 2 = 4 n c) If [A] doubled, rate increased 8 times -3rd order, [2A] 3 = 2 3 x [A] 3, 2 3 = 8 n
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Method of Initial Rates n A + B ----> C n The rate law : rate = k [A] x [B] y n [A],mol/L [B],mol/L rate, mol/LS n 4.6 x 10 -4 3.1 x 10 -5 2.08 x 10 -3 n 4.6 x 10 -4 6.2 x 10 -5 4.16 x 10 -3 n 9.2 x 10 -4 6.2 x 10 -5 1.664 x 10 -2
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Order wrt A n 1.664 x 10 -2 k (9.2 x 10 -4 ) x (6.2 x 10 -5 ) y n --------------- = -------------------------------------- n 4.16 x 10 -3 k (4.6 x 10 -4 ) x (6.2 x 10 -5 ) y n n 1.664 x 10 -2 (9.2 x 10 -4 ) x n --------------- = -------------- n 4.16 x 10 -3 (4.6 x 10 -4 ) x n 4 = (9.2 x 10 -4 )/(4.6 x 10 -4 ) x = 2 x n 4 = 2 x n x = 2
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Order wrt B n 4.16 x 10 -3 k (4.6 x 10 -4 )x (6.2 x 10 -5 ) y n ----------- = ------------------------------ n 2.08 x 10 -3 k (4.6 x 10 -4 )x (3.1 x 10 -5 ) y n n 4.16 x 10 -3 (6.2 x 10-5) y n ----------- = ------------- n 2.08 x 10 -3 (3.1 x 10-5) y n 2 = (6.2 x 10-5/3.1 x 10-5)y = 2 y n 2 = 2 y n y = 1 n The rate law : rate = k [A] 2 [B] 1
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Units of the Rate Constant n 1 first order: k = ─── = s -1 n s n L second order k = ─── n mol s
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n Rate Law Differential Rate Law Integral Rate rate k [A] 0 [A]/ t =k ; ([A] 0 =1)[A] f -[A] i = -kt n rate k [A] 1 [A]/ t = k [A] ln [A] o /[A] t = kt rate k [A] 2 [A]/ t = k [A] 2 1/ [A] f = kt + 1/[A] i n
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Differential Rate Law n Normal form Differential form n zero order rate = k [A] 0 rate = - [A]/ t n = k ( [A] 0 =1) n first order rate law rate = k [A] 1 rate = - [A]/ t n = k [A] 1
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Integral Rate Law n Differential form Integral form n zero order rate = - [A]/ t = [A] f -[A] i = -kt n = k ( [A] 0 =1) n first order rate law rate = - [A]/ t ln [A] o /[A] t = kt n = k [A] 1
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Finding rate laws Graphical method. R ate integrated Graph Slope Order law rate law vs. time 0 rate = k [A] t = -kt + [A] 0 [A] t -k 1 rate = k[A] ln[A] t = -kt + ln[A] 0 ln[A] t -k 2 rate=k[A] 2 = kt + k 1 [A] 0 1 [A] t 1 [A] t
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Finding rate laws 0 order plot 1st order plot 2nd order plot As you can see from these plots of the N 2 O 5 data, only a first order plot results in a straight line. As you can see from these plots of the N 2 O 5 data, only a first order plot results in a straight line. Time (s) [N 2 O 5 ] 1/[N 2 O 5 ] ln[N 2 O 5 ]
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First order reactions n Reactions that are first order with respect to a reactant are of great importance. n Describe how many drugs pass into the blood stream or used by the body. n Often useful in geochemistry n Radioactive decay n Half-life (t 1/2 ) n The time required for one-half of the quantity of reactant originally present to react.
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First Order Reactions n A ----> B n Differential rate law [A] - ───── =k [A] t [A] t [A] 0 ln ─── = - k t or ln ─── = k t [A] 0 [A] t
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Half-life form of 1st order t 2 is defined as time for [A] 0, the initial concentration to decay half the original value ie 1/2 x [A] 0 = [A] t.
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t 2 equation 0.693 =k t 2 n 0.693 t 2 = ---- n k
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Half-life n The half-life and the rate constant are related. n t 1/2 = n Half-life can be used to calculate the first order rate constant. n For our N 2 O 5 example, the reaction took 1900 seconds to react half way so: n k == = 3.65 x 10 -4 s -1 0.693k 0.693 t 1/2 0.693 1900 s
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Half-life From our N 2 O 5 data, we can see that it takes about 1900 seconds for the concentration to be reduced in half. It takes another 1900 seconds to reduce the concentration in half again. From our N 2 O 5 data, we can see that it takes about 1900 seconds for the concentration to be reduced in half. It takes another 1900 seconds to reduce the concentration in half again. Time (s) [N 2 O 5 ]
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Theories of reaction rates n Collision theory n Based on kinetic-molecular theory. n It assumes that reactants must collide for a reaction to occur. n They must hit with sufficient energy and with the proper orientation so as to break the original bonds and form new ones. n As temperature is increased, the average kinetic energy increases - so will the rate. n As concentration increases, the number of collisions will also increase, also increasing the rate.
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Effective collision n Reactants must have sufficient energy and the proper orientation for a collision to result in a reaction.
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Transition state theory n As reactants collide, they initially form an activated complex. n The activated complex is in the transition state. n It lasts for approximately 10-100 fs. n It can then form products or reactants. n Once products are formed, it is much harder to return to the transition state, for exothermic reactions. n Reaction profiles can be used to show this process.
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What are the factors that affect rates of chemical reactions? n a) Temperature n b) Concentration n c) Catalysts n d) Particle size of solid reactants
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This type of plot shows the energy changes during a reaction. This type of plot shows the energy changes during a reaction. Reaction profile HH activation energy Potential Energy Reaction coordinate
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Potential Energy Curves n Exothermic Reactions n Endothermic Reactions n Effect of catalysts n Effect of temperature
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Examples of reaction profiles Exothermic reaction Endothermic reaction
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Examples of reaction profiles High activation energy Low heat of reaction Low activation energy High heat of reaction
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Arrhenius Equation n Rate constant (k) n k = A e- E a /RT n n A = frequency factor n E a = Activation energy n R = gas constant n T = Kelvintemperature
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Rate and temperature n Reaction rates are temperature dependent. Here are rate constants for N 2 O 5 decomposition at various temperatures. T, o C k x 10 4, s -1 20 0.235 25 0.469 30 0.933 35 1.82 40 3.62 45 6.29 k x 10 4 (s -1 ) Temperature ( o C)
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Rate and temperature Arrhenius equation n The relationship between rate constant and temperature is mathematically described by the Arrhenius equation. n k = A e n Aconstant n E a activation energy n Ttemperature, Kelvin n Rgas law constant -E a / RT
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Rate and temperature n An alternate form of the Arrhenius equation is: n ln k = + ln A n If ln k is plotted against 1/T, a straight line of slope -E a /RT is obtained. Activation energy - E a n Activation energy - E a n The energy that molecules must have in order to react. ( ) 1T1T EaREaR -
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Calculation of E a n k = A e- E a /RT n ln k = ln A - E a /RT n log k = log A - E a / 2.303 RT n using two set of values n log k 1 = log A - E a / 2.303 RT 1 n log k 2 = log A - E a / 2.303 RT 2 n log k 1 - log k 2 = - E a / 2.303 RT 2 + E a / 2.303 RT 1 n log k 1 / k 2 = E a / 2.303 R[ 1/T 1 - 1/T 2 ]
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Calculation of E a from N 2 O 5 data ln k T -1
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Reaction mechanisms n A detailed molecular-level picture of how a reaction might take place. activated complex = bonds in the process of breaking or being formed
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Reaction mechanisms n Elementary process n Each step in a mechanism. n Molecularity n The number of particles that come together to form the activated complex in an elementary process. n 1 - unimolecular n 2 - bimolecular n 3 - termolecular
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Reaction Mechanisms n Consider the following reaction. n 2NO 2 (g) + F 2 (g) 2NO 2 F (g) n If the reaction took place in a single step the rate law would be: n rate = k [NO 2 ] 2 [F 2 ] n However, the experimentally observed rate law is: n rate = k [NO 2 ] [F 2 ]
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Reaction Mechanisms n Since the observed rate law is not the same as if the reaction took place in a single step, we know two things. More than one step must be involved The activated complex must be produced from two species. n A possible reaction mechanism might be: n Step one n Step oneNO 2 + F 2 NO 2 F + F n Step two n Step twoNO 2 + F NO 2 F n Overall n Overall 2NO 2 + F 2 2NO 2 F
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Reaction Mechanism n Elementary Reactions: n NO 2 + F 2 --> NO 2 F + F (slow) n F + NO 2 --> NO 2 F (fast) n Molecularity? Of Elementary Reactions n unimolecular, bimolecular, termolecular?
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Reaction Mechanisms n Rate-determining step. slow n When a reaction occurs in a series of steps, with one slow step, it is the slow step that determines the overall rate. n Step one n Step oneNO 2 + F 2 NO 2 F + F n Expected to be slow. It involves breaking an F-F bond. n Step two n Step twoNO 2 + F NO 2 F n Expected to be fast. A fluorine atom is very reactive.
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Reaction Mechanisms n Since step one is slow, we can expect this step to determine the overall rate of the reaction. n NO 2 + F 2 NO 2 F + F n This would give a rate expression of: n rate = k 1 [NO 2 ] [ F 2 ] n This agrees with the experimentally observed results.
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Catalysis n Catalyst A substance that changes the rate of a reaction without being consumed in the reaction. Provides an easier way to react. Lower activation energy. Still make the same products. n Enzymes n Enzymes are biological catalysts. n Inhibitor A substance that decreases the rate of reaction.
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Catalysts Lowers E a
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Catalysis Types of catalysts Homogeneous Homogeneous - same phase Catalyst is uniformly distributed throughout the reaction mixture Example - I - in peroxide. Heterogeneous Heterogeneous - different phase Catalyst is usually a solid and the reactants are gases or liquids Example - Automobile catalytic converter.
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Heterogeneous catalysis
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Enzymes n Biological catalysts Typically are very large proteins. Permit reactions to ‘go’ at conditions that the body can tolerate. Can process millions of molecules every second. substrates Are very specific - react with one or only a few types of molecules (substrates).
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Classification of enzymes n Based on type of reaction n Oxireductase n Oxireductase catalyze a redox reaction n Transferase n Transferasetransfer a functional group n Hydrolase n Hydrolasecause hydrolysis reactions n Lyase n Lyasebreak C-O, C-C or C-N bonds n Isomerases n Isomerasesrearrange functional groups n Ligase n Ligasejoin two molecules
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The active site n Enzymes are typically HUGE proteins, yet only a small part is actually involved in the reaction. The active site has two basic components. catalytic site binding site Model of trios-phosphate-isomerase Model of trios-phosphate-isomerase
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Characteristics of enzyme active sites n Catalytic site n Where the reaction actually occurs. n Binding site n Area that holds substrate in proper place. n Enzymes uses weak, non-covalent interactions to hold the substrate in place based on R groups of amino acids. n Shape is complementary to the substrate and determines the specificity of the enzyme. n Sites are pockets or clefts on the enzyme surface.
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