Chemical Kinetics

Fundamental questions: Will it take place? Thermodynamics If it does, how long will it take to reach completion or equilibrium? Chemical kinetics: is the study of the speeds, or rates, of chemical reactions A2(g) + B2(g) 2 AB(g)

Outline Why study kinetics? Factors affecting rates Measuring rates reactant concentration temperature action of catalysts surface area. Concentration vs. Rate (Rate Laws) Concentration vs. Time (Integrated Rate Laws) Theories about Rxn Rates Activation Energy Mechanisms Catalysts

The rate of the reaction is a measure of how fast the changes are taking place. Rate of appearance of AB = D[AB] Dt Rate of disappearance of A2 = -D[A2] Dt Unit: mol/liter S = mol / L  s = mol dm-3 s-1

Factors affecting reaction rates The nature of the reactants 2 NO+ O2 2 NO2 fast reaction at 25°C 2 CO + O2 2 CO2 very slow at 25°C 2. The concentration of reactants Rate equation or rate law The rate of reaction is proportional to the rate of disappearance of reactants: -D[A2] Dt = k [A] mol dm-3 s-1 Rate constant (in the simplest case: A products)

Rate Laws: Basic Assumptions aA + bB  cC + dD Simple rate laws depend only on the concentrations of the reactants, not the products. Rate = k[A]x[B]y k = rate constant, units depend on the values of x and y. x and y = the orders of A and B respectively x + y = overall order of the rxn 3 unknowns (x, y, k)  3 experiments

Slope (Rate) Changes w/ Time Rate is a function of concentration. When the concentration is high, the rate is large. Concentration is a function of time. When the reaction starts the concentration changes the most. 2HI  H2 + I2

Factors affecting reaction rates Zero order reaction: 2 N2O 2 N2 + O2 Au rate = k First order reaction: 2 N2O5 4 NO2 + O2 rate = k [A] rate = k [N2O5]

Second order reaction: 2 A products A+B products rate = k [A]2 rate = k [A] [B] Third order reaction: 3 A products rate = k [A] [B] [C] rate = k [A]3 A + B + C products rate = k [A]2 [B] 2 A + B products

rate = k [A]m [B]n [C]p …. order = m + n + p + … The order of a reaction is given by the sum of the exponents of the conc. terms in the rate equation. rate = k [A]m [B]n [C]p …. order = m + n + p + …

Temperature and Rate Constants (k) Since the rate law has no temperature term in it, the rate constant must depend on temperature. The size of k depends on T. Greater T gives a larger k Consider the reaction H2(g) + I2(g)  2HI(g).

3. The temperature of the reaction. Collision theory of reaction rates No of molecules Minimum energy required for reaction Ea effective collisions most probable energy at t1 t2

n = n0e k = Ae log k = log A - ln k = ln A - -Ea/RT Maxwell-Boltzmann distribution law k = Ae -Ea/RT Arrhenius equation ln k = ln A - Ea RT log k = log A - 2.303 RT Ea = activation energy A = frequency factor K = rate constant

Arrhenius Equation K = rate constant A = frequency factor Ea = activation energy T = temperature R = 8.314 J/mol K

Frequency Factor Solve for A T (K) k (L/mol s) 400 7.8 410 10 420 14 430 18 Effective collisions / 6.02 x 1023

Temperature Increases Rate 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 chemi-luminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light.

Half-Life Half-lives are typically reported for radioactive materials, medications, toxins…etc. 238U has a t½ = 5 x 109 y 234P has a t½ = 7 h Amount of time required for half of the compound to react. Half life equations are found from the integrated rate laws. Find the time required for the concentration to be one half the initial concentration.

The Collision Model Low T Collision High T Collision Observations: rates of reactions are affected by concentration and temperature. Concentration terms already accounted for in rate laws R = k[A]x Goal: develop a model that explains why rates of reactions increase as temperature increases. Low T Collision High T Collision

The Rules of Reaction Mechanisms Elementary step: any process that occurs in a single step. Molecularity: the number of molecules present in an elementary step. Unimolecular: one molecule in the elementary step, Bimolecular: two molecules in the elementary step, and Termolecular: three molecules in the elementary step. It is not common to see termolecular processes (statistically improbable).

Unimolecular reaction A products A unimoleculare reaction is first order Biomolecular reaction A + B products 2A products Termolecular reaction A + B + C products 2A + B products 3A products They are not common!

Energy of Collision Chemical rxns usually occur with bonds breaking and bonds forming. Collision energy supplies the energy needed to break the bonds. With increased temperature, collision energy increases and the rate of rxn increases.

Effective Collisions The right molecules must collide. The collision must be energetic enough. The molecules must collide in the proper orientation. All of the above conditions must be met for a rxn to occur! There are far more collisions between the wrong molecules or in the wrong orientation or with the wrong energy! Some estimate that only 1 in 1018 collisions are effective.

Molecular Orientation If H2 and I2 collide, they can collide along any possible trajectory. However, only one trajectory leads to a rxn.

Top of the Peak ‡ H I At the top of the peak, we have… Maximum potential energy Transition state Point where reactants change to products Bonds breaking and bonds forming Intermediate structures The [activated complex]‡ H I Potential Energy 2 HI H2 + I2 Progress of Rxn

Activation Energy In order to form products, bonds must be broken in the reactants. Bond breakage requires energy Arrhenius: molecules must posses a minimum amount of energy to react.. Ea is the minimum energy required to initiate a chemical reaction.

Progress of Reaction Diagrams Relates the PE of the rxn to time. For example, an exothermic rxn between A + B is shown on the right. Progress of Rxn Potential Energy Energy of Collision Activation Energy Ea Reactants Energy of Rxn Enthalpy DH Note: DH and Ea are unrelated! 100% of Ea is returned! Products

Endothermic System is Reversed Products are higher in PE than reactants. Progress of Rxn Potential Energy Energy of Collision Activation Energy Ea Products Energy of Rxn Enthalpy DH Note: Less than 100% of Ea is returned. Reactants

Reaction Mechanisms 2NO2Cl(g) Cl2(g) + 2NO2(g) Rate Laws of 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 Step It is possible for an intermediate to be a reactant. … 2NO2Cl(g) Cl2(g) + 2NO2(g)

The rate equation for a reaction must be determined by experimentation Reaction mechanisms: The rate equation for a reaction must be determined by experimentation E1 E2 Two step mechanism Rate-determining step (intermediate)

4. The surface area of a solid Increasing the surface area of a solid reactant will increase the rate of reaction (explosion of flour dust) 5. The catalysis A catalyst is a substance that increases the rate of a chemical reaction without being used up in the reaction reactants products Uncatalysed reaction Catalysed reaction

Catalysis A catalyst changes the rate of a chemical reaction. There are two types of catalyst: homogeneous, and heterogeneous. Chlorine atoms are catalysts for the destruction of ozone. Homogeneous Catalysis The catalyst and reaction is in one phase. Hydrogen peroxide decomposes very slowly: 2H2O2(aq)  2H2O(l) + O2(g).

homogeneous Catalyst heterogeneous positive (accelerate…) negative or inhibitor (retard…) Promoters catalytic poisons

Catalysis Homogeneous Catalysis 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. Generally, catalysts operate by lowering the activation energy for a reaction.

Catalysis Homogeneous Catalysis

Catalysis Heterogeneous Catalysis

Catalysis Enzymes Enzymes are biological catalysts. Most enzymes are protein molecules with large molecular masses (10,000 to 106 amu). 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.

1. S + E ES 2. ES E + P Natural catalysts = enzymes (very specific) Michaelis – Menten mechanism: 1. S + E ES Substrate (reactant) Enzyme Enzyme-substrate complex 2. ES E + P Product

At low concentrate: Rate of disappearence of S = k [S] Reaction rate Concentration of substrate Zero order First order At low concentrate: Rate of disappearence of S = k [S] At high concentrate: Rate of disappearence of S = k’ [S]0 = k’ The enzyme is saturated!

Catalysis Enzymes