3Necessary Math Previously, we talked about logarithms 10x = y log10(y) = xYou could define a logarithm in any base34 = 81log3(81) = 4
4Necessary Math We can define the natural logarithm as: loge(y) = ln(y) =xWe can define the natural logarithm graphicallyThis base, e, is used for a lot of things, such as exponential decaye= …
5Factors that Affect Reaction Rates Kinetics is the study of how fast chemical reactions occur.There are 4 important factors which affect rates of reactions:Reactant ConcentrationTemperatureCatalysisMechanism
6Reaction RatesSpeed of a reaction is measured by the change in concentration with time.For a reaction A BSuppose A reacts to form B. Let us begin with 1.00 mol A.
8Reaction RatesAt t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no BAt t = 20 min, there is 0.54 mol A and 0.46 mol B.At t = 40 min, there is 0.30 mol A and 0.70 mol B.
9Reaction RatesFor the reaction A B there are two ways of measuring rate:the speed at which the products appear (i.e. change in moles of B per unit time), orthe speed at which the reactants disappear (i.e. the change in moles of A per unit time).
10C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) Reaction RatesChange of Rate with TimeMost useful units for rates are to look at molarity. Since volume is constant, molarity and moles are directly proportional.Consider:C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
12C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) Reaction RatesChange of Rate with TimeC4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)We can calculate the average rate in terms of the disappearance of C4H9Cl.The units for average rate are mol/L·s or M/s.The average rate decreases with time.We plot [C4H9Cl] versus time.The rate at any instant in time (instantaneous rate) is the slope of the tangent to the curve.Instantaneous rate is different from average rate.We usually call the instantaneous rate the rate.
14C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) Reaction RatesReaction Rate and StoichiometryFor the reactionC4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)we knowIn general foraA + bB cC + dDAppearance of Product = Disappearance of Reactant
15Concentration and Rate In general rates increase as concentrations increase.NH4+(aq) + NO2-(aq) N2(g) + 2H2O(l)
16Concentration and Rate For the reactionNH4+(aq) + NO2-(aq) N2(g) + 2H2O(l)as [NH4+] doubles with [NO2-] constant the rate doubles,as [NO2-] doubles with [NH4+] constant, the rate doubles,We conclude rate [NH4+][NO2-].Rate law:The constant k is the rate constant.Note that the rate constant does not depend on concentration.
17Concentration and Rate Exponents in the Rate LawFor a general reaction with rate lawwe say the reaction is mth order in reactant 1 and nth order in reactant 2.The overall order of reaction is m + n + ….A reaction can be zeroth order if m, n, … are zero.Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry.
18Concentration and Rate Using Initial Rates to Determines Rate LawsA reaction is zero order in a reactant if the change in concentration of that reactant produces no effect.A reaction is first order if doubling the concentration causes the rate to double.A reacting is nth order if doubling the concentration causes an 2n increase in rate.
19The Change of Concentration with Time First Order ReactionsGoal: convert rate law into a convenient equation to give concentrations as a function of time.For a first order reaction, the rate doubles as the concentration of a reactant doubles.
20The Change of Concentration with Time First Order ReactionsA plot of ln[A]t versus t is a straight line with slope -k and intercept ln[A]0.In the above we use the natural logarithm, ln, which is log to the base e.Recall the beginning of this lecture.
21The Change of Concentration with Time First Order Reactions
22The Change of Concentration with Time Second Order ReactionsFor a second order reaction with just one reactantA plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0For a second order reaction, a plot of ln[A]t vs. t is not linear.
23The Change of Concentration with Time Second Order Reactions
24The Change of Concentration with Time Half-LifeHalf-life is the time taken for the concentration of a reactant to drop to half its original value.For a first order process, half life, t½ is the time taken for [A]0 to reach ½[A]0.Mathematically,
26The Change of Concentration with Time Half-LifeFor a second order reaction, half-life depends in the initial concentration:
27Temperature and Rate The Collision Model Most reactions speed up as temperature increases. (E.g. food spoils when not refrigerated.)When two light sticks are placed in water: one at room temperature and one in ice, the one at room temperature is brighter than the one in ice.The chemical reaction responsible for chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light.
28Temperature and Rate The Collision Model As temperature increases, the rate increases.
29Temperature and Rate The Collision Model Since the rate law has no temperature term in it, the rate constant must depend on temperature.Consider the first order reaction CH3NC CH3CN.As temperature increases from 190 C to 250 C the rate constant increases from 2.52 10-5 s-1 to 3.16 10-3 s-1.The temperature effect is quite dramatic. Why?Observations: rates of reactions are affected by concentration and temperature.
30Temperature and Rate The Collision Model Goal: develop a model that explains why rates of reactions increase as concentration and temperature increases.The collision model: in order for molecules to react they must collide.The greater the number of collisions the faster the rate.The more molecules present, the greater the probability of collision and the faster the rate.
31Temperature and Rate The Collision Model The Orientation Factor The higher the temperature, the more energy available to the molecules and the faster the rate.Complication: not all collisions lead to products. In fact, only a small fraction of collisions lead to product.The Orientation FactorIn order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products.
32Temperature and Rate The Orientation Factor Consider: Cl + NOCl NO + Cl2There are two possible ways that Cl atoms and NOCl molecules can collide; one is effective and one is not.
34Temperature and Rate Activation Energy Arrhenius: molecules must posses a minimum amount of energy to react. Why?In order to form products, bonds must be broken in the reactants.Bond breakage requires energy.Activation energy, Ea, is the minimum energy required to initiate a chemical reaction.
35Temperature and Rate Activation Energy Consider the rearrangement of methyl isonitrile:In H3C-NC, the C-NC bond bends until the C-N bond breaks and the NC portion is perpendicular to the H3C portion. This structure is called the activated complex or transition state.The energy required for the above twist and break is the activation energy, Ea.Once the C-N bond is broken, the NC portion can continue to rotate forming a C-CN bond.
37Temperature and Rate Activation Energy The change in energy for the reaction is the difference in energy between CH3NC and CH3CN.The activation energy is the difference in energy between reactants, CH3NC and transition state.The rate depends on Ea.Notice that if a forward reaction is exothermic (CH3NC CH3CN), then the reverse reaction is endothermic (CH3CN CH3NC).
38Temperature and Rate Activation Energy How does a methyl isonitrile molecule gain enough energy to overcome the activation energy barrier?
40Maxwell–Boltzmann Distributions Temperature is defined as a measure of the average kinetic energy of the molecules in a sample.At any temperature there is a wide distribution of kinetic energies.
41Maxwell–Boltzmann Distributions As the temperature increases, the curve flattens and broadens.Thus at higher temperatures, a larger population of molecules has higher energy.
42Maxwell–Boltzmann Distributions If the dotted line represents the activation energy, as the temperature increases, so does the fraction of molecules that can overcome the activation energy barrier.As a result, the reaction rate increases.
43Maxwell–Boltzmann Distributions This fraction of molecules can be found through the expression:where R is the gas constant and T is the temperature in Kelvin .
44activation energy; asserted solutions of salts contained ions. Svante A. Arrhenius*Developed concept ofactivation energy; assertedsolutions of salts containedions.1111
45Temperature and Rate The Arrhenius Equation Arrhenius discovered most reaction-rate data obeyed the Arrhenius equation:k is the rate constant, Ea is the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K.A is called the frequency factor.A is a measure of the probability of a favorable collision.Both A and Ea are specific to a given reaction.
46Temperature and Rate Determining the Activation Energy If we have a lot of data, we can determine Ea and A graphically by rearranging the Arrhenius equation:From the above equation, a plot of ln k versus 1/T will have slope of –Ea/R and intercept of ln A.
48Temperature and Rate Determining the Activation Energy If we do not have a lot of data, then we recognize
49Reaction MechanismsThe balanced chemical equation provides information about the beginning and end of reaction.The reaction mechanism gives the path of the reaction.Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction.Elementary StepsElementary step: any process that occurs in a single step.
50Reaction Mechanisms Elementary Steps Molecularity: the number of molecules present in an elementary step.Unimolecular: one molecule in the elementary step,Bimolecular: two molecules in the elementary step, andTermolecular: three molecules in the elementary step.It is not common to see termolecular processes (statistically improbable).
51Reaction Mechanisms Multistep Mechanisms Some reaction proceed through more than one step:NO2(g) + NO2(g) NO3(g) + NO(g)NO3(g) + CO(g) NO2(g) + CO2(g)Notice that if we add the above steps, we get the overall reaction:NO2(g) + CO(g) NO(g) + CO2(g)
52Reaction Mechanisms Multistep Mechanisms If a reaction proceeds via several elementary steps, then the elementary steps must add to give the balanced chemical equation.Intermediate: a species which appears in an elementary step which is not a reactant or product.
53Reaction Mechanisms Rate Laws for Elementary Steps The rate law of an elementary step is determined by its molecularity:Unimolecular processes are first order,Bimolecular processes are second order, andTermolecular processes are third order.
54Reaction MechanismsRate Laws for Elementary Steps
55Reaction Mechanisms Rate Laws for Multistep Mechanisms Rate-determining step: is the slowest of the elementary steps.Therefore, the rate-determining step governs the overall rate law for the reaction.Mechanisms with an Initial Fast StepIt is possible for an intermediate to be a reactant.Consider2NO(g) + Br2(g) 2NOBr(g)
56Reaction Mechanisms Mechanisms with an Initial Fast Step 2NO(g) + Br2(g) 2NOBr(g)The experimentally determined rate law isRate = k[NO]2[Br2]Consider the following mechanism
57Reaction Mechanisms Mechanisms with an Initial Fast Step The rate law is (based on Step 2):Rate = k2[NOBr2][NO]The rate law should not depend on the concentration of an intermediate (intermediates are usually unstable).Assume NOBr2 is unstable, so we express the concentration of NOBr2 in terms of NOBr and Br2 assuming there is an equilibrium in step 1 we have
58Reaction Mechanisms Mechanisms with an Initial Fast Step By definition of equilibrium:Therefore, the overall rate law becomesNote the final rate law is consistent with the experimentally observed rate law.
59Catalysis A catalyst changes the rate of a chemical reaction. There are two types of catalyst:homogeneous, andheterogeneous.Chlorine atoms are catalysts for the destruction of ozone.Homogeneous CatalysisThe catalyst and reaction is in one phase.
60Catalysis Homogeneous Catalysis Hydrogen peroxide decomposes very slowly:2H2O2(aq) 2H2O(l) + O2(g)In the presence of the bromide ion, the decomposition occurs rapidly:2Br-(aq) + H2O2(aq) + 2H+(aq) Br2(aq) + 2H2O(l).Br2(aq) is brown.Br2(aq) + H2O2(aq) 2Br-(aq) + 2H+(aq) + O2(g).Br- is a catalyst because it can be recovered at the end of the reaction.
61Catalysis Homogeneous Catalysis Generally, catalysts operate by lowering the activation energy for a reaction.
63Catalysis Homogeneous Catalysis Catalysts can operate by increasing the number of effective collisions.That is, from the Arrhenius equation: catalysts increase k be increasing A or decreasing Ea.A catalyst may add intermediates to the reaction.Example: In the presence of Br-, Br2(aq) is generated as an intermediate in the decomposition of H2O2.
64Catalysis Homogeneous Catalysis When a catalyst adds an intermediate, the activation energies for both steps must be lower than the activation energy for the uncatalyzed reaction. The catalyst is in a different phase than the reactants and products.Heterogeneous CatalysisTypical example: solid catalyst, gaseous reactants and products (catalytic converters in cars).Most industrial catalysts are heterogeneous.
65Catalysis Heterogeneous Catalysis First step is adsorption (the binding of reactant molecules to the catalyst surface).Adsorbed species (atoms or ions) are very reactive.Molecules are adsorbed onto active sites on the catalyst surface.
67C2H4(g) + H2(g) C2H6(g), H = -136 kJ/mol. CatalysisHeterogeneous CatalysisConsider the hydrogenation of ethylene:C2H4(g) + H2(g) C2H6(g), H = -136 kJ/mol.The reaction is slow in the absence of a catalyst.In the presence of a metal catalyst (Ni, Pt or Pd) the reaction occurs quickly at room temperature.First the ethylene and hydrogen molecules are adsorbed onto active sites on the metal surface.The H-H bond breaks and the H atoms migrate about the metal surface.
68Catalysis Heterogeneous Catalysis Enzymes When an H atom collides with an ethylene molecule on the surface, the C-C bond breaks and a C-H bond forms.When C2H6 forms it desorbs from the surface.When ethylene and hydrogen are adsorbed onto a surface, less energy is required to break the bonds and the activation energy for the reaction is lowered.EnzymesEnzymes are biological catalysts.Most enzymes are protein molecules with large molecular masses (10,000 to 106 amu).
69Catalysis Enzymes Enzymes have very specific shapes. Most enzymes catalyze very specific reactions.Substrates undergo reaction at the active site of an enzyme.A substrate locks into an enzyme and a fast reaction occurs.The products then move away from the enzyme.
70CatalysisEnzymesOnly substrates that fit into the enzyme lock can be involved in the reaction.If a molecule binds tightly to an enzyme so that another substrate cannot displace it, then the active site is blocked and the catalyst is inhibited (enzyme inhibitors).The number of events (turnover number) catalyzed is large for enzymes ( per second).