Kinetics. Mary J. Bojan Chem Rate: change that occurs in a given interval of time.

Transcription

1 Kinetics Rates of reaction average rates instantaneous rates Dependence of rate on concentration rate constant rate laws order of the reaction Dependence of rate on time First order Second order Half-life Mary J. Bojan Chem Rate: change that occurs in a given interval of time. We can measure the average rate or the instantaneous rate of a chemical reaction. Chem 112 2

2 Rate: change that occurs in a given interval of time. Average rate is change in concentration in a given interval of time rate = [ A] [ A] f! [ A] i " " t = t f! t (a)! (b) Calculate average rate of disappearance of A between 0 and 20 sec. i volume = 1 L mol/l = M (b)! (c) Calculate average rate of appearance of B between 20 and 40 sec. Chem Rate: change that occurs in a given interval of time. Average rate is change in concentration in a given interval of time (a)! (b) rate =!" A "t = rate = +" [ B] = "t (a)! (c) rate = [ A] [ A] f! [ A] i " " t =!(0.54!1.00) = 0.023Ms!1 20 s +(0.46! 0.00) = 0.023Ms!1 20 s rate =!"[ A] = Ms!1 "t t f! t i (b)! (c) rate = +" [ B] = Ms!1 "t Chem 112 4

3 Chemical Rate Laws describe instantaneous rates in terms of a change in concentration vs. time. Average rate Instantaneous rate Chem Instantaneous rate: the slope of a line tangent to the curve at any point! Initial rate instantaneous rate at t=0. Calculate the instantaneous rate at t= 600s. Chem 112 6

4 Rates of reactions are measured experimentally. We can express the rate of reaction in terms of: 1. appearance of products 2. disappearance of reactants Stoichiometry of reaction tells us how these are related. General case: aa + bb! cc + dd reactants products (a, b, c, d are stoichiometric coefficients) rate = "1 a # A = "1 b # B = +1 c #[ C] = +1 d #[ D] Mary J. Bojan Chem Compare the rate of formation and loss of the reactants and products for this reaction. 2HI(g)! H 2 (g) + I 2 (g) If 6 moles of HI in a 1 L flask are converted to I 2 and H 2 in 1 min. What is the rate of disappearance of HI? rate =!"[ HI] = "t What is the rate of appearance of H 2? rate = +" [ H 2] = "t Mary J. Bojan Chem 112 8

5 FACTORS THAT AFFECT THE RATE OF REACTIONS 1. The reactants Chemical identity + physical state (solid, liq, gas, solute, fine particles,!) 2. Concentration of reactants Increasing conc. " faster rates (usually) 3. Temperature Increasing T " faster rates (almost always) 4. Presence of a catalyst Chem Demonstration: what happens when the state of the reactants changes? PbNO 3 + KI! PbI 2 + KNO 3 Which is faster? Solid reactants: PbNO 3 (s) + KI(s) Aqueous phase reactants PbNO 3 (aq) + KI(aq) Mary J. Bojan Chem

6 Demonstration: What happens to a reaction rate when concentration changes? As concentration increases: Mary J. Bojan Chem Rate Law: relationship between the rate of a reaction and concentration of its reactants. We can measure concentrations of reactants" General reaction: aa + bb! cc + dd reactants products rate = Mary J. Bojan Chem

7 Examples of Rate Laws (order of reaction) Chem Rate Law: relationship between the rate of a reaction and concentration of its reactants. We can measure concentrations of reactants" The rate law is: rate = k[a] x [B] y k is the rate constant independent of [A] and [B]; varies with T x and y are exponents " 0, not necessarily integers Order of reaction = sum of exponents Overall order of reaction = x + y Mary J. Bojan Chem

8 DETERMINING THE RATE LAW Method of initial rates: General reaction: aa + bb! cc + dd reactants products MUST DO EXPERIMENTS 1. Start with known amounts of [A] and [B] (and [C] = [D] = 0) initial rate = k 1 [A] 0x [B] y 0 0! initial (t = 0) 2. Vary [A] 0 and [B] 0, measure initial rates Chem DETERMINING THE RATE LAW Method of initial rates Sample problem Given the following data for the reaction A + B!Z What is the overall reaction order? [A] 0 [B] 0 initial rate 1) 1.0M 1.0M 0.8x10 #2 M/s 2) x10 #2 3) x10 #2 4) x10 #2 Rate = k [A] a [B] b What is k? a = b= overall order = a + b Mary J. Bojan Chem

9 FYI: Solution to Sample Problem 1. Compare Rate 1 to Rate 2 Rate 1 Rate 2 = R 1 R 2 = 0.8 "10#2 M /s 1.6 "10 #2 M /s = 1 2 Using the rate laws to compare rates: R 1 = k A R 2 k A a b 1 [ B] 1 a 2 [ B] = A a 1 b 2 [ A] = [ 1M ] a a 2 [ 2M] = 1 a 2 Recall that [B] in trials 1 and 2 does not change so the ratio of ([B] 1 /[B] 2 ) b = 1 regardless of the value of the exponent. # " % 1& $ 2' a ( = 1 2 Chem Take the log of both sides and solve for a! -a log (2) = -log (2)! a must be one FYI: Solution to Sample Problem 2. Compare Rate 2 to Rate 3 Using the rate laws to compare rates: Rate 2 Rate 3 = R 2 R 3 = 1.6 "10#2 M /s 6.4 "10 #2 M /s = 1 4 R 2 = k A R 3 k A a b 2 [ B] 2 a 3 [ B] = B b 2 b 3 [ B] = [ 1M ] b b 3 [ 2M] = 1 b 4 # " % 1& $ 2' b ( = 1 4 Take the log of both sides and solve for b # b log (2) = # log (4) b = log(4) log(2) = 2 Chem

10 SUMMARY Reaction Rate can be written in terms of disappearance of reactant or appearance of products. The reaction stoichiometry gives the relationship. General reaction: aa + bb! cc + dd rate = "1 a reactants #[ A] = "1 b products #[ B] The rate is a positive number. = +1 c #[ C] = +1 d #[ D] Mary J. Bojan Chem SUMMARY Measure the instantaneous rate of a reaction: this is a number. Measure or the rate of loss of a reactant the rate of appearance rate = " # [ A ] of a product rate = + " C "t Repeat the experiment to determine the concentration dependence: Rate Law rate = " # [ A ] = k[ A] x [ B] y Differential rate Law: gives rate as a function of concentration Chem

11 FYI: EFFECT OF CONCENTRATION rate = k[a] x [B] y Are x, y the same as a, b? Sometimes yes, in general, no (depends on reaction mechanism) NOTE: dependence of rate on concentration MUST be determined experimentally It CANNOT be predicted from overall reaction experiment " rate law # mechanism (exponents x, y) Examples of Rate Laws: Rate = k[a] = k[b] = k[a] 2 = k[a][b] Chem Sample Problem The following data were collected for the rate of disappearance of NO in the reaction below 2 NO(g) + O 2 (g)! 2NO 2 (g) Experiment # [NO] (M) [O 2 ] (M) Initial Rate (M/s) x 10 # x 10 # x 10 #2 (a) What is the rate law for the reaction? (b) What are the units of the rate constant? (c) What is the rate of disappearance of [O 2 ] at the concentrations given in experiment 1? Chem

12 Defined Reaction rates Average rate Summary so far Instantaneous rate Showed how to get the reaction rate as a function of concentration (experimentally). Showed how the rate of loss of a reactant is related to rates of loss or appearance of other reactants and products Can we determine rates without doing experiments? NO! Chem Rate Law as a function of time We are studying a chemical reaction e.g., for aa " products We measure the concentration as a function of time. We can use this data to determine rate, and find the rate law. rate = "#[ A] (the rate law) = k[ A] x But how does concentration change with time? Qualitatively: Can we be quantitative? rate =!" A "t = k [ A] Chem

13 Integrated first order rate law is an equation that gives concentration as a function of time. This is a differential equation. 1 st order reaction (x = 1): Integration gives [A] as a function of t rate =!" A "t = k [ A] (the rate law) Integrate to get: Chem Plot the experimental results for the following first order reaction: [A] =[A] t=0 e #kt!n [A] =!n[a] 0 # k t Integrated first order rate law: concentration as a function of time Mary J. Bojan Chem

14 FYI: derivation of integrated first order rate law Differential first order rate law Rearrange If $[A]! d[a] as $t! 0 then Integrate: at t = 0, [A] = [A] 0 rate = "# [ A ] [ A] [ A] " A [ A] = k[ A] = # k"t Integrated first order rate law: concentration as a function of time d A = " kdt t d A " = # k " dt A [ A] 0 ln[ A] # ln[ A] 0 = ln 0 [ A] A 0 = # kt Chem Integrated 2nd order rate law is an equation that gives concentration as a function of time. 2 nd order reaction (x = 2): rate = "# [ A ] = k[ A] 2 differential rate law Integrate to get: 1 A = k t + 1 A 0 Chem

15 FYI: derivation of integrated second order rate law Differential second order rate law Rearrange If $[A]! d[a] as $t! 0 then Integrate: at t = 0, [A] = [A] 0 rate = "# [ A ] "[ A] A " [ A] = k[ A] 2 2 = # k"t d[ A] [ A] = " kdt 2 2 t d A # = k # dt A [ A] 0 1 [ A] " 1 A Integrated 2 nd order rate law: concentration as a function of time 0 0 = kt Chem We can use these relationships to interpret experimental data. Reaction: NO 2 (g)! NO + % O 2 Measure [NO 2 ] as a function of time. Is reaction first or second order? (How do you know?) Take data Calculate these Time(s) [NO 2 ]M ln [NO 2 ] 1/[NO 2 ] # # # # # Chem

16 Using the integrated rate laws to interpret data. Is reaction first or second order? 0.01 (How do you know?) [NO 2 ]M Method Plot ln [NO 2 ] vs. time Is either plot linear? Plot 1/[NO 2 ] vs. time TIME (SEC) Chem Plots of ln [NO 2 ] and 1/[NO 2 ] vs. time Reaction: NO 2 (g)! NO + 1/2O 2 1st order plot 2nd order plot slope = k Rate = k[no 2 ] 2 Integrated rate law: 1 [ NO 2 ] = k t + 1 NO 2 0 y = m x + b Mary J. Bojan Chem

17 Half life: t 1/2 : time it takes for the concentration of a reactant to drop to half of its initial value. e.g. A! products t % is where [A] = % [A] 0 For 1 st order reactions: t 1/2 doesn t depend on concentration Mary J. Bojan Chem Plot of concentration vs. time for a first order reaction Mary J. Bojan Chem

18 The HALF LIFE for a 2 ND ORDER REACTION is defined (and derived) in the same way. Second order integrated rate law 1 A = k t + 1 A 0 To get t 1/2, we let [A] = 1/2 [A] o 2 A 0 = k t A 0 1 t 1/2 = (depends on [A] 0 ) k A 0 Chem Plot of concentration vs. time for a second order reaction Time (sec) Mary J. Bojan Chem

19 Half Life Problem It requires 90.0 seconds for a first-order reaction to go 25.0% of the way to completion. What is the half-life of the reaction? seconds seconds seconds seconds Chem Compare 1 st and 2 nd order reactions Mary J. Bojan Chem