Chem.414 - Physical Chemistry II Spring 2016

Chemical Kinetics

Study of Chemical Kinetics Rate of reaction Dependence of concentration of species Dependence of temp., pressure, catalyst Control of reactions Mechanisms [Dominating step (fast vs. slow)] Guide to chemical intuition

C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) Reaction Rates Reaction Rate and Stoichiometry For the reaction C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) we know In general for aA + bB  cC + dD

C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)

EXCEL Time / s [N2O5] / M ln [N2O5] d[N2O5]/dt (tangential slope) 1 4. Consider the following N2O5 reaction:  2 N2O5(soln)  ---->  4 NO2(soln)  +  O2(g)      Let:    C = [N2O5]      (a) Using a graph of C vs. t, obtain tangential slopes and plot dC/dt vs. C. Calculate k after fitting with linear regression.     (b) Plot ln C vs. t. Calculate k after fitting with linear regression.     (c) Plot C vs. t. Fit the data with an appropriate function.  Display the equation in standard IRL form with the appropriate variable names for this reaction.     (d) Calculate half-live (t2) and life-time (t).   Compare them to the interpolated values from the plot of C vs. t.   Time / s [N2O5] / M ln [N2O5] d[N2O5]/dt (tangential slope) 1 1.00 2 200 0.88 3 400 0.78 4 600 0.69 5 800 0.61 6 1000 0.54 7 1200 0.48 8 1400 0.43 9 1600 0.38 10 1800 0.34 11 2000 0.30 EXCEL

The Change of Concentration with Time Isomeric Transformation of Methyl Isonitrile to Acetonitrile First Order Reactions (to one component)

Differential and Integrated Rate Laws n-th Order to One Component (Generalized Rate Laws) Let: C = concentration of reactant A remaining at time t Co = initial concentration of reactant A (i.e. t=0) k = rate constant (units depends on n) DRL: IRL:

Differential and Integrated Rate Laws

Rate Law: First Order to One Component

The Change of Concentration with Time Second Order Reactions

Rate Law: Second Order to One Component

Gas-Phase Decomposition of Nitrogen Dioxide Time / s [NO2] / M 0.0 0.01000 50.0 0.00787 100.0 0.00649 200.0 0.00481 300.0 0.00380 Is this reaction first or second order? k = 0.543 unit?

Half-Lives, Rate Constants and Co

Half-Lives, Rate Constants and Co - II

Zeroth Order to One Component - Catalysis Provide the DRL. Determine the IRL. Sketch the IRL: Co=1.00 mol L-1 , k = 5.00x10-3 mol L-1 s-1 . Use Mathcad (or EXCEL) to generate the IRL graph. Obtain the half-life expression. How many half-lives would it take for the reaction to reach equilibrium (i.e. completion)? [ Hint: Solve the IRL for time when C=0. Confirm by graph. ]

Summary of Rate Laws to One-Component First-Order Second-Order Zeroth-Order DRL (-dC/dt) kC kC2 k IRL C = Co·e-kt ln C = -kt + ln Co 1/C = kt + 1/Co C = -kt + Co Linear Equation ln C vs. t 1/C vs. t C vs. t Linear Plot Half-Life ln(2)/k 1/kCo Co/2k Units on k time-1 M-1 time-1 M time-1 m = -k b = ln Co m = k b = 1/Co m = -k b = Co

Concentration and Rate Exponents in the Rate Law For a general reaction with rate law we 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.

Method of Initial/Comparative Rates Expt # [NH4+]o / M [NO2-]o / M (Rate)o / M s-1 1 0.100 0.0050 1.35x10-7 2 0.0100 2.70x10-7 3 0.200 5.40x10-7

Three Component Rate Law Expt # [BrO3-]o / M [Br-]o / M [H+]o / M (Rate)o / M s-1 1 0.10 8.0x10-4 2 0.20 1.6x10-3 3 3.2x10-3 4

Techniques for Multiple Component Rate Laws Integration Approach: Second Order – First Order to each of two components Flooding Technique: Rate = k [A]x [B]y [C]z

Applications of First-Order Processes Radioactive Decay Bacterial Growth Interest and Exponential Growth [Credit Card] Loan Balance

Temperature 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 (8.3145 J K-1 mol-1) 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.

Temperature and Rate

Reaction Mechanisms The 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 Steps Elementary step: any process that occurs in a single step.

Reaction 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, and Termolecular: three molecules in the elementary step. It is not common to see termolecular processes (statistically improbable).

Reaction 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, and Termolecular processes are third order. Rate Laws for Multistep Mechanisms Rate-determining step is the slowest of the elementary steps. [example]

Reaction Mechanisms Rate Laws for Elementary Steps

Rate Expressions If elementary steps: -d[A]/dt = vk1[A]v[B]w – vk-1[C]x[D]y -d[B]/dt = wk1[A]v[B]w – wk-1[C]x[D]y d[C]/dt = xk1[A]v[B]w – xk-1[C]x[D]y d[D]/dt = yk1[A]v[B]w – yk-1[C]x[D]y

d[NOBr]/dt = kobs[NO]2[Br2] (or) = kobs’[NO][Br2] Reaction Mechanisms Mechanisms with an Initial Fast Step 2NO(g) + Br2(g)  2NOBr(g) The experimentally determined rate law can be: d[NOBr]/dt = kobs[NO]2[Br2] (or) = kobs’[NO][Br2] Consider the following mechanism

Spring 2014

Spring 2014

General Mechanism Overall Reaction: Proposed Mechanism: Where: D = observable product M = intermediate

Spring 2014

Spring 2014

Hydrogen-Iodine Reaction Overall Reaction: Proposed Mechanism: Where: I• = free radical

Spring 2012

Spring 2012

Rice-Hertzfeld Free Radical Chain Reaction Mechanism Overall Reaction: Proposed Mechanism:

Kinetics

Catalysis

C2H4(g) + H2(g)  C2H6(g), H = -136 kJ/mol. Catalysis Heterogeneous Catalysis Consider 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.

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. The products then move away from the enzyme.

Catalysis Enzymes Only 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 (103 - 107 per second).

Catalysis Enzymes

Mechanism: Two Intermediates Overall Reaction: Experimentally found: Proposed Mechanism: Show that the proposed mechanism is consistent with the observed RL.

Mechanism Overall Reaction: Observed Rate Law: Proposed Mechanism:

Chemical Kinetics