Chemical Kinetics Rates of chemical reactions and how they can be measured experimentally and described mathematically

So far, we have worked with reactions that occur almost instantaneously Precipitations –Ba 2+ (aq) + SO 4 2- (aq)  BaSO 4 (s) Acid-base reactions –HCl(aq) + NaOH (aq)  NaCl (aq)+ H 2 O (l)

Lots of reactions are much slower… Rusting –4Fe (s) + 3O 2 (g)  2Fe 2 O 3 (s) Formation of ammonia –N 2 (g) + 3H 2 (g)  2NH 3 (g) Formation of diamond –C (graphite)  C (diamond)

In this chapter we will… Explore the factors that affect rates of reactions Quantify the influence of the above factors on the rates of reactions Determine what happens at the molecular level in reactions

REACTION RATES The change in molar concentration of a reactant or a product per unit time Units are Moles/L s

In an experiment, the decomposition of N 2 O 5 in 100 mL of a 2.00 M CCl 4 solution produced L of oxygen at STP after 200 minutes. Calculate the concentration of unreacted N 2 O 5 at this time. 2N 2 O 5 (in CCl 4 )  4NO 2 (in CCl 4 ) + O 2 (g) ? Moles oxygen produced ? Moles N 2 O 5 reacted ? Moles N 2 O 5 initially ? Moles N 2 O 5 left over ? Moles/L

0.500 L x 1mole = mol O L mol O 2 x 2N 2 O 5 = mol N 2 O 5 1 O 2 Initially… (0.100L) (2.00M) = mol N 2 O mol – mol = mol left over M = mol/ L = 1.55 M

Following this procedure we can calculate the concentration of unreacted N 2 O 5 at any stage of the reaction and plot the data as shown Mol/L Time To find the rate at any instant, draw a tangent to the curve and determine its slope This gives the average rate over time,  [N 2 O 5 ]/  t

If you know the rate of one substance in a reaction, you can determine the rate of any other substance in the reaction by using a mole ratio 2N 2 O 5 (in CCl 4 )  4NO 2 (in CCl 4 ) + O 2 (g) N 2 O 5 decomposes at a rate of 0.23M/s, what is the rate of formation of NO 2 ? 0.23M N 2 O 5 x 4 NO 2 = 0.46 M/s NO 2 s 2 N 2 O 5

Rate Laws Have the general form: rate = k[A] n [A] = concentration of reactants and catalyst k = rate constant n = order of reactant (an integer or fraction)

Initial Rate Method To determine the form of the rate law, one MUST use experimental data Do a series of experiments in which the initial concentrations of the reactants are varied one at a time and record the initial rates of reaction

(OH-) I- (aq) + OCl- (aq)  OI- (aq) + Cl- (aq) initial MRate (mol/Ls) I-OCl- OH- 1) x ) x ) x ) x 10 -4

Rate = k[I-] x [OCl-] y [OH-] z 1:6.1 x = k[0.01] x [0.01] y [0.01] z 2:12.2 x = k[0.02] x [0.01] y [0.01] z Solve for x… 0.5 = 0.5 x X = 1

1:6.1 x = k[0.01] x [0.01] y [0.01] z 3:12.3 x = k[0.01] x [0.02] y [0.01] z Solve for y 0.5 = 0.5 y Y = 1

1:6.1 x = k[0.01] x [0.01] y [0.01] z 4:3.0 x = k[0.01] x [0.01] y [0.02] z Solve for z 2 = 0.5 z (ohhh…this is tricky!) Log 2 = log 0.5 z Z log 0.5 = log 2 Z = log 2/log 0.5 Z = -1

Rate = k[I-][OCl-]/[OH-] The reaction is first order with respect to I- and OCl-, and inverse first order with respect to [OH-]. What is the overall reaction order? (sum of exponents) What are the units of k for this reaction? (plug units into the rate law and solve)

YOU TRY! Do your “You Try!” section now.

Integrated Rate Law Method First Order Rate Laws rate = k [A] 1 = -  [ A ] /  t or rate = -  [A] = k  t [A]

Integrating both sides gives… - l n ( [A] t / [A] 0 ) = kt l n ( [A] 0 / [A] t ) = kt l n [A] t = -kt + l n [A] 0 time ln[A] t slope = - k

Half-life time it takes for the reactant concentration to reach one half of its initial value symbol t ½ for first order: t ½ = ( l n 2) / k

Integrated Rate Law Method Second Order Rate Laws rate = k [A] 2 = -  [ A ] /  t integrating gives 1 / [A] t = kt + 1/[A] 0 t 1/2 = 1 / k[A] 0

2 nd order graph

Integrated Rate Law Method Zero Order Rate Laws rate = k [A] 0 = k integrating gives [A] t = -kt + [A] 0 t 1/2 = [A] 0 / 2k

Rate data was plotted, what is the order of NO 2 ?

What is the order with respect to A?

YOU TRY! Do your “You Try!” section now.

Collision Theory The rate of a reaction depends on the 1. concentration of reactants 2. temperature 3. presence/absence of a catalyst

The value of the rate constant is dependent on the temperature How can we explain the effect of temperature on the rate of a reaction ?

NO(g) + Cl 2 (g) --> NOCl(g) + Cl - (g) At 25 o C:k= 4.9 x L/mol s At 35 o C:k= 1.5 x L/mol s k has increased by a factor of THREE! WHY?

The Collision Theory states that in order to react, molecules have to collide…. with the proper orientation with an energy at least equal to E a activation energy (E a ) = required minimum energy for a reaction to occur

k for a reaction depends on 3 things: Z = collision frequency (# collisions/second) higher temperature means more collisions f = fraction of collisions that occur with E > E a *this factor changes rapidly with T f = e –(Ea/RT) p = fraction of collisions that occur with the proper orientation (independent of T)

Overall: k = pfz = A e -(Ea/RT) where A = pz Arrhenius Equation: l n k = -Ea 1 + l n A R T ln k 2 = E a 1 1 k 1 R T 1 T 2

YOU TRY! Calculate the activation energy for the reaction: 2HI (g) --> H 2 (g) + I 2 (g) GIVEN: k at 650. K = 2.15 x L/mol s and k at 700. K = 2.39 x L/mol s R = J / mol K 1.82 x 10 5 J

Transition State Theory Two reactants come together to form an Activated Complex, or TRANSITION STATE which then separates to form the products.

Potential Energy Diagram 2NO + Cl 2  2NOCl PE Reaction 

In the activated complex, the N—Cl bond has partially formed, while the Cl—Cl bond has partially broken.

Breaking bonds requires an input of energy while forming bonds RELEASES energy. If E reactants > E products then the reaction is EXOTHERMIC IfE reactants < E products then the reaction is ENDOTHERMIC

Catalysis UncatalyzedCatalyzed

A catalyst increases the rate of reaction by… LOWERING THE ACTIVATION ENERGY Homogeneous Catalysis- catalyst is in the same phase as the reactants Heterogeneous Catalysis- catalyst is in a different phase than the reactants

The Haber Process: N H 2  2NH 3

Reaction Mechanisms The overall balanced equation usually represents the SUM of a series of simple reactions called ELEMENTARY STEPS because they represent the progress of the reaction at the molecular level. The sequence of elementary steps is called the REACTION MECHANISM

NO 2 (g) + CO (g)  NO (g) + CO 2 (g) Rate = k [NO 2 ] 2 The above reaction actually takes place in two steps: 1. NO 2 + NO 2  NO 3 + NO SLOW 2. NO 3 + CO  NO 2 + CO 2 FAST

Intermediate- Unimolecular step: Bimolecular step: Termolecular step:

The reaction mechanism must satisfy two requirements: 1) Sum of elementary steps must be the overall reaction 2) The rate law indicated by the mechanism must match the experimentally determined rate law

2 H 2 O 2 (aq)  O 2 (g) + 2 H 2 O(l) by experiment Rate = k[H 2 O 2 ] [I-] H 2 O 2 (aq) + I - (aq)  IO - (aq) + H 2 O(l) SLOW H 2 O 2 (aq) + IO - (aq)  I - (aq) + H 2 O(l) + O 2 (g)

The overall rate of the reaction is controlled by the slow step also known as the….. RATE DETERMINING STEP

H 2 O 2 (aq) + I - (aq)  IO - (aq) + H 2 O(l) SLOW H 2 O 2 (aq) + IO - (aq)  I - (aq) + H 2 O(l) + O 2 (g) When the slow step is used to determine the rate law, we get: What is the intermediate in this reaction? What is the catalyst?

2N 2 O 5 (g) > 4NO 2 (g) + O 2 (g) Rate = k[N 2 O 5 ] Why can’t this be a one-step reaction? If it was a one-step, the overall reaction would be that one step, and the rate law would be rate = k[N 2 O 5 ] 2

Proposed Mechanism N 2 O 5  NO 2 + NO 3 FAST NO 2 + NO 3  NO + O 2 + NO 2 SLOW NO + NO 3  2NO 2 FAST Rate = k[ ]

A general example: E + S  Mfast M  E + Pslow Work out the rate law in terms of reactants and catalyst:

Is this an acceptable mechanism? Why or why not? Overall Reaction = 2NO 2 (g) + F 2 (g)  2NO 2 F (g) Rate = k[NO 2 ] [F 2 ] Proposed Mechanism Step 1: NO 2 + F 2  NO 2 F + Fslow Step 2: F + NO 2  NO 2 Ffast

A 2-step mechanism was proposed for a reaction: Step 1:NO(g) + NO(g)  N 2 O 2 (g)FAST Step 2:N 2 O 2 (g) + O 2 (g)  2NO 2 (g)SLOW a) what is the overall reaction? b) what is the rate law? c) what were the reactants?the product? the intermediate?the catalyst?