Chemical Kinetics Chapter 12

Chemical Kinetics Thermodynamics – does a reaction take place? Kinetics – how fast does a reaction proceed? Reaction rate is the change in the concentration of a reactant or a product with time (M/s). A B rate = - D[A] Dt D[A] = change in concentration of A over time period Dt rate = D[B] Dt D[B] = change in concentration of B over time period Dt Because [A] decreases with time, D[A] is negative. 12.1

A B time rate = - D[A] Dt rate = D[B] Dt 12.1

Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g) slope of tangent slope of tangent slope of tangent average rate = - D[Br2] Dt = - [Br2]final – [Br2]initial tfinal - tinitial instantaneous rate = rate for specific instance in time 12.1

rate a [Br2] rate = k [Br2] k = rate [Br2] = rate constant = 3.50 x 10-3 s-1 13.1

Factors that Affect Reaction Rate Temperature Collision Theory: When two chemicals react, their molecules have to collide with each other with sufficient energy for the reaction to take place. Kinetic Theory: Increasing temperature means the molecules move faster. (10°C increase usually doubles rate) Concentrations of reactants More reactants mean more collisions if enough energy is present Catalysts Speed up reactions by lowering activation energy Surface area of a solid reactant More area for reactants to be in contact Grain dust/coal dust explosion compared to charcoal Aqueous solutions are ultimate exposure!!! Pressure of gaseous reactants or products Increased number of collisions

Cool videos about reaction rate: Mythbusters Coffee Creamer Burning Steel Wool in Oxygen

Factors that Affect Reaction Rate 6. Nature of the reactants Phase of matter gasoline (l) vs. gasoline (g) Two solids may not react, but there aqueous solutions will Chemical identity Usually ions of opposite charge react rapidly The more bonds between reacting atoms, the slower the rate. Why? Intermediate steps during a reaction mechanism slow down a reaction: Photosynthesis is slow even when heated due to may intermediate steps

When collisions occur with enough energy (Ea), successful collisions overcome the attraction from bonds and form new bonds (as products).

The collisions must occur with enough energy to overcome the e-/e- repulsion of the VSE’s of the reaction species and must have enough energy to transform translational energy into vibrational energy in order to penetrate into each other so that the e- can rearrange and form new bonds. These are known as “effective collisions.” Activated complex

Maxwell-Boltzmann distribution When T increases, more molecules collide increasing the chances of a reaction New Ea with catalyst kinetic

The Rate Law The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers. aA + bB cC + dD Rate = k [A]x[B]y reaction is xth order in A reaction is yth order in B reaction is (x +y)th order overall 13.2

Relative Rate Expressions What are the relative rates of change in concentration of the products and reactant in the synthesis of aluminum oxide? 4 Al + 3 O2  2 Al2O3

Think of “order” like this… Did the rate double (2)1 when the other reactant doubled? 1st order 2* Rate = (2)1 Did the rate quadruple (2)2 when the other reactant doubled? 2nd order 4*Rate = (2)2 Did the rate increase by a factor of 8 (2)3 when the other reactant doubled? 3rd order 8*Rate = (2)3 Did the rate remain constant (2)0 when the other reactant doubled? zero order Rate = 1

Ch. 12 HW Part 1 Due Tuesday 

Double [F2] with [ClO2] constant F2 (g) + 2ClO2 (g) 2FClO2 (g) rate = k [F2]x[ClO2]y Double [F2] with [ClO2] constant Rate doubles x = 1 rate = k [F2][ClO2] Quadruple [ClO2] with [F2] constant Rate quadruples y = 1 13.2

Run # Initial [A] ([A]0) Initial [B] ([B]0) Initial Rate (v0) 1 1.00 M 1.25 x 10-2 M/s 2 2.00 M 2.5 x 10-2 M/s 3 What is the order with respect to A? What is the order with respect to B? What is the overall order of the reaction? 1 1

Initial Rate (mol dm-3 s-1) [NO(g)] (mol dm-3) [Cl2(g)] (mol dm-3) Initial Rate (mol dm-3 s-1)  0.250  1.43 x 10-6 0.500  2.86 x 10-6 1.14 x 10-5 What is the order with respect to Cl2? What is the order with respect to NO? What is the overall order of the reaction? 1 2 3

Rate Laws Rate laws are always determined experimentally. Reaction order is always defined in terms of reactant (not product) concentrations. The order of a reactant is not related to the stoichiometric coefficient of the reactant in the balanced chemical equation. F2 (g) + 2ClO2 (g) 2FClO2 (g) 1 rate = k [F2][ClO2] 13.2

Sec. 12.4 The Integrated Rate Law

First-Order Reactions rate = - D[A] Dt rate = k [A] [A] = [A]0e-kt [A] is the concentration of A at any time t ln[A] = - kt + ln[A]0 [A]0 is the concentration of A at time t=0 13.3

Decomposition of N2O5 13.3

The reaction 2A B is first order in A with a rate constant of 2 The reaction 2A B is first order in A with a rate constant of 2.8 x 10-2 s-1 at 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ? ln[A] = - kt + ln[A]0 [A]0 = 0.88 M [A] = 0.14 M 13.3

First-Order Reactions The half-life, t½, is the time required for the concentration of a reactant to decrease to half of its initial concentration. t½ = t when [A] = [A]0/2 ln [A]0 [A]0/2 k = t½ Ln 2 0.693 What is the half-life of N2O5 if it decomposes with a rate constant of 5.7 x 10-4 s-1? t½ ln 2 k = 0.693 5.7 x 10-4 s-1 = = 1200 s = 20 minutes How do you know decomposition is first order? units of k (s-1) 13.3

First-order reaction A product # of half-lives [A] = [A]0/n 1 2 2 4 3 8 4 16 13.3

13.3

The decomposition of N2O5 in the gas phase was studied at constant temperature. 2N2O5(g)  4NO2(g) + O2(g) The following results were collected: Using these data, verify that the rate law is first order in [N2O5], and calculate the value of the rate constant, where the rate = -Δ[N2O5]/ Δt.

Using the data given in Example 12 Using the data given in Example 12.2, calculate [N2O5] at 150 s after the start of the reaction.

A certain first-order reaction has a half-life of 20.0 minutes. a. Calculate the rate constant for this reaction. b. How much time is required for this reaction to be 75% complete.

Second-Order Reactions rate = - D[A] Dt [A] is the concentration of A at any time t rate = k [A]2 [A]0 is the concentration of A at time t=0 Half life for second order 1 [A] - [A]0 = kt t½ = t when [A] = [A]0/2 t½ = 1 k[A]0 13.3

a) Is the reaction first of second order? Butadiene reacts to form it's dimer according to the equation 2C4H6(g) ->C8H12(g). The following data were collected for this reaction at a given temperature: C4H6mol/L...................time(+/- 1s) .0100.............................0 .00625...........................1000 .00467...........................1800 .00370...........................2800 .00313...........................3600 .00270...........................4400 .00241...........................5200 .00208...........................6200 a) Is the reaction first of second order? b) What is the value of the rate constant for this reaction? c) What it the half-life for the reaction under initial conditions of this experiment?

[A] - [A]0 = kt Zero-Order Reactions D[A] rate = - rate = k [A]0 = k Dt rate = k [A]0 = k [A] is the concentration of A at any time t [A] - [A]0 = kt [A]0 is the concentration of A at time t=0 Half life for zero order t½ = t when [A] = [A]0/2 t½ = [A]0 2k 13.3

Summary of the Kinetics of Zero-Order, First-Order and Second-Order Reactions Order Rate Law Concentration-Time Equation Half-Life t½ = [A]0 2k rate = k [A] - [A]0 = - kt t½ Ln 2 k = 1 rate = k [A] ln[A] - ln[A]0 = - kt 1 [A] - [A]0 = kt t½ = 1 k[A]0 2 rate = k [A]2 13.3

Textbook HW: due Monday  Chapter 12 #37, 38, 39, 45, 46, 47, 49, 50, 52, 53

Most chemical reactions are redox… (don’t gag) Just means there’s an exchange of electrons Who would cause a faster rate??? The atoms that are able to donate electrons the easiest  LOW IONIZATION ENERGY Tends to be atoms on the left side of the periodic table Who would have the lowest IE? K, Ca2+, F, S2-

A + B C + D Exothermic Reaction Endothermic Reaction The activation energy (Ea) is the minimum amount of energy required to initiate a chemical reaction. 13.4

Temperature Dependence of the Rate Constant k = A • exp( -Ea/RT ) (Arrhenius equation) Ea is the activation energy (J/mol) R is the gas constant (8.314 J/K•mol) T is the absolute temperature A is the frequency factor Ln k = - -Ea R 1 T + lnA 13.4

N2O2 is detected during the reaction! Reaction Mechanisms The overall progress of a chemical reaction can be represented at the molecular level by a series of simple elementary steps or elementary reactions. The sequence of elementary steps that leads to product formation is the reaction mechanism. 2NO (g) + O2 (g) 2NO2 (g) N2O2 is detected during the reaction! Elementary step: NO + NO N2O2 Overall reaction: 2NO + O2 2NO2 + Elementary step: N2O2 + O2 2NO2 13.5

Reaction Intermediates Intermediates are species that appear in a reaction mechanism but not in the overall balanced equation. An intermediate is always formed in an early elementary step and consumed in a later elementary step. Elementary step: NO + NO N2O2 N2O2 + O2 2NO2 Overall reaction: 2NO + O2 2NO2 + 13.5

Rate Laws and Rate Determining Steps Writing plausible reaction mechanisms: The sum of the elementary steps must give the overall balanced equation for the reaction. The rate-determining step should predict the same rate law that is determined experimentally. The rate-determining step is the slowest step in the sequence of steps leading to product formation. 13.5

Rate Laws and Elementary Steps Unimolecular reaction A products rate = k [A] Bimolecular reaction A + B products rate = k [A][B] Bimolecular reaction A + A products rate = k [A]2 13.5

ratecatalyzed > rateuncatalyzed A catalyst is a substance that increases the rate of a chemical reaction without itself being consumed. Ea k uncatalyzed catalyzed ratecatalyzed > rateuncatalyzed 13.6

Energy Diagrams Exothermic Endothermic Activation energy (Ea) for the forward reaction Activation energy (Ea) for the reverse reaction (c) Delta H 50 kJ/mol 300 kJ/mol 150 kJ/mol 100 kJ/mol -100 kJ/mol +200 kJ/mol

What is the equation for the overall reaction? The experimental rate law for the reaction between NO2 and CO to produce NO and CO2 is rate = k[NO2]2. The reaction is believed to occur via two steps: Step 1: NO2 + NO2 NO + NO3 Step 2: NO3 + CO NO2 + CO2 What is the equation for the overall reaction? NO2+ CO NO + CO2 What is the intermediate? Catalyst? NO3 NO2 What can you say about the relative rates of steps 1 and 2? rate = k[NO2]2 is the rate law for step 1 so step 1 must be slower than step 2 13.5

Write the rate law for this reaction. Rate = k [HBr] [O2] List all intermediates in this reaction. HOOBr, HOBr None List all catalysts in this reaction.

Ostwald Process 4NH3 (g) + 5O2 (g) 4NO (g) + 6H2O (g) Pt catalyst 4NH3 (g) + 5O2 (g) 4NO (g) + 6H2O (g) 2NO (g) + O2 (g) 2NO2 (g) Hot Pt wire over NH3 solution 2NO2 (g) + H2O (l) HNO2 (aq) + HNO3 (aq) Pt-Rh catalysts used in Ostwald process 13.6

Catalytic Converters CO + Unburned Hydrocarbons + O2 CO2 + H2O 2NO + 2NO2 2N2 + 3O2 13.6

Enzyme Catalysis 13.6