CMY 282 Chemical Kinetics PDF Lecture Notes

Chemical Kinetics Lecture 1 joule Physical Chemistry CMY 282 Presented by Prof Liezel van der Merwe [email protected]  Chemical Kinetics Prof. Liezel van der Merwe liezel.va...

Chemical Kinetics Lecture 1 joule Physical Chemistry CMY 282 Presented by Prof Liezel van der Merwe [email protected]  Chemical Kinetics Prof. Liezel van der Merwe [email protected] Source - Atkins’ Physical Chemistry, 11th edition: Chapter 17: Topics 17A, 17B, 17D, pp. 720 - 745 Resource section, Part 3, Data, pp. 865-894 or Source - Atkins’ Physical Chemistry, 12th edition: Chapter 17: Topics 17A, 17B, 17D, pp. 739 - 761 Resource section, Part 3, Data, pp. 884-909 Additional reading: Chemistry & Chemical Reactivity by Kotz, Treichel and Townsend, Chapter 15 Chang, Physical Chemistry for the chemical sciences: Chapter 15. Themes 15.1-15.2, 15.5 Mortimer, Physical Chemistry: Chapter 12. Themes 12.1-12.3. 2  1. Chemical 2. The properties of gases Kinetics 3. The First Law of Thermodynamics CMY 282 Course overview 4. The Second and 5A. Physical transformation Third Laws of of pure substances 5B. Simple mixtures Thermodynamics Çà €†¾¸ Á∆ ¸ÆŒ ∙ Æ †ˉ †€€ ‡ ı Œ ˉŒÆ †€ְ ∙ Áš ≥ ˉŒ ¼ ≥ ∆ˉÁ‡ ∆Œ ˉ¸š ı ˉŒ ∙ÆŒ ı € ¸ֵ Çà РÃÁ€≥ Ð∙ šŒ € ¸Á‡ Á∙ ∆Œ∙ ≥¸ ≥ ¼Œ†šŒÁ∙ ¸ ¾ÃŒ Æ Ã ˉ ˜ÐŒ ˉ ‡ Áˉ †ÆÆÐˉ†š ≥ ¸Æ ˉŒ ı šŒ Á∙ ¸ֵ 3 Lecture 1 Lecture 2 The rates of chemical reactions Determination of reaction order Monitoring the progress of a reaction Method of initial rates The rates of reactions Integrated rate laws: Rate laws and rate constants - Zero order reactions Rate laws and stoichiometry - First order reactions Reaction order - Second order reactions Half-life method Lecture 3 Lecture 4 Determination of reaction order Temperature dependence of reaction rates and Example problems reaction mechanisms The Arrhenius equation Catalysts Reaction mechanisms 4  Topic 17A: The rates of chemical reactions Atkins pp. 723-730 / 739-746 Why do you need to know this material? (watch this short video at home) Studies of the rates of consumption of reactants and formation of products make it possible to predict how quickly a reaction mixture approaches equilibrium. They also lead to detailed descriptions of the molecular events that transform reactants into products. Kinetics is the study of the rates of chemical processes in an effort to understand what it is that influences these rates, and to develop theories which can be used to predict them. empirical: derived from or relating to experiment and observation rather than theory Collins English Dictionary – Complete and Unabridged, What is the key idea? 12th Edition 2014 Reaction rates are expressed as rate laws, which are empirical summaries of the rates in terms of the concentrations of reactants and, in some cases, products. 5  Topic 17A.1 : Monitoring the progress of a reaction Atkins pp. 723-725 / 739-741 Reaction rate might depend on concentration pressure temperature presence of a catalyst; we can optimize the rate by the appropriate choice of conditions. The study of reaction rates also leads to an understanding of the mechanisms of reactions, their analysis into a sequence of elementary steps. Therefore, to perform a kinetic investigation: 1. detect and identify intermediates and products and their stoichiometry 2. determine the concentration of all species 3. select appropriate experimental method of following the rate 4. kinetic analysis (obtain rate law) 5. determine the mechanism 6  Experimental Techniques Atkins p. 723 / 740 Method used to monitor concentrations depends on species involved rapidity with which their concentrations change How do we monitor the progress of a reaction? Concentration can be measured by "classical" methods of chemical analysis, such as titrations. Rxn in which at least one component is a gas might result in an overall change in pressure in a system of constant volume, so its progress may be followed by recording the variation of pressure with time By using analytical instrumentation 7 Examples of methods to monitor reaction progress: Atkins p. 723 / 740 Spectrophotometry Measurement of absorption of radiation in a particular spectral region Especially useful when one substance in rxn mixture has strong characteristic absorption in conveniently accessible region of the electromagnetic spectrum. Example: H2(g) + Br2(g) → 2HBr(g) rxn progress can be followed by measuring the absorption of visible light by bromine. Electrical conductivity / pH measurements A rxn that changes the number or type of ions present in a solution may be followed by monitoring the electrical conductivity of the solution. Example: (CH3)3CCl(aq) + H2O(ℓ) → (CH3)3COH(aq) + H+(aq) + Cl-(aq) pH Emission spectroscopy Mass spectrometry Gas chromatography Nuclear magnetic resonance (NMR) …AND MANY OTHERS! 8 Example: Monitoring reaction progress using UV-visible absorbance technique not examinable (a) Absorbance spectra over the course of the reaction (sampled every 5 min for 145 min). (b) Images of the reaction solution over time, showing the color transition as product is formed. (c) Absorbance time series for 650 nm light. The product is known to absorb at this wavelength. Figures obtained from Arcadia et. al., Chem. Sci., 2021,12, 5464-5472. 9  Topic 17A.2 : The rates of reactions d = delta Atkins pp. 725-730 / 741-746 NB: Reaction rates depend on the composition and temperature of the rxn mixture We use the Greek symbol ν (“nu”) to indicate reaction rates. Definition of instantaneous rate: the slope of the tangent drawn to the curve showing the variation of concentration with time. Consider A (reactant) → P (product) at constant volume. For negative slopes, the sign is changed when reporting the rate, so all reaction rates are positive. Instantaneous* rate of consumption of a reactant: 𝑑𝑑[𝐴𝐴] rate = νA = - NB: signs!! 𝑑𝑑𝑡𝑡 rate of consumption Instantaneous rate of formation of one of the products: 𝑑𝑑[𝑃𝑃] rate = νP = note the difference in sign 𝑑𝑑𝑡𝑡 rate of formation Rate (ν) is a positive quantity *rate of change at a particular moment 10 Instantaneous rate vs Initial rate What is the difference? d [P ] rate = dt d [R ] rate = − dt 11 Reaction rates – what about reaction stoichiometry? For a reaction Atkins p. 724 / 741 aA + bB  yY + zZ occuring at constant volume, the overall rate of reaction (𝝂𝝂) is 1 𝑑𝑑[𝐴𝐴] 1 𝑑𝑑[𝐵𝐵] 1 𝑑𝑑[𝑌𝑌] 1 𝑑𝑑[𝑍𝑍] note inclusion of 𝜈𝜈 = − = − = + = + stoichiometric coefficients 𝑎𝑎 𝑑𝑑𝑑𝑑 𝑏𝑏 𝑑𝑑𝑑𝑑 𝑦𝑦 𝑑𝑑𝑑𝑑 𝑧𝑧 𝑑𝑑𝑑𝑑 Using the notation νA: rate of consumption of A; νY: rate of formation of Y: ν : rate of reaction 𝜐𝜐𝐴𝐴 𝜐𝜐𝐵𝐵 𝜐𝜐𝑌𝑌 𝜐𝜐𝑍𝑍 νx : rate of consumption or 𝜈𝜈 = = = = formation 𝑎𝑎 𝑏𝑏 𝑦𝑦 𝑧𝑧 The time derivatives of the concentrations are the rates of Negative sign for reactants consumption (e.g. νA = - ) or formation (νY =+ 𝑑𝑑[𝐴𝐴] 𝑑𝑑[𝑌𝑌] ). 𝑑𝑑𝑡𝑡 𝑑𝑑𝑡𝑡 Since stoichiometric coefficients and therefore extents of reaction depend on the way in which the reaction is written, the stoichiometric equation must be given when rates of reaction are given. Taken from Laidler et al, Physical Chemistry, 4th edition, Houghton Mifflin, p 364 12 Example: Rates of formation and consumption The rate of formation of NO in the reaction 2 NOBr(g)  2 NO(g) + Br2(g) is reported as 0.16 mmol dm−3 s−1. (a) What is the rate of the reaction? NB: determine for stoichiometry as written above (b) What is the rate of consumption of NOBr? (c) What is the rate of reaction for NOBr(g)  NO(g) + ½Br2(g) Answer: (a) The rate of formation of NO is given, 𝜐𝜐𝑁𝑁𝑁𝑁 = 0.16 mmol dm−3 s−1 Using reaction stoichiometry, 𝜈𝜈 = = 0.08 mmol dm−3 s−1 𝜐𝜐𝑁𝑁𝑁𝑁 2 (b) Rate of consumption of NOBr = rate of formation of NO 𝜐𝜐𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 = 𝜐𝜐𝑁𝑁𝑁𝑁 = 0.16 mmol dm−3 s−1 (same stoichiometry) (c) The rate of rxn in (c) will be half the rate of rxn in (a) Therefore, rate of rxn (c) = ½(0.08 mmol dm−3 s−1) = 0.04 mmol dm−3 s−1 13 Homework problem The rate of consumption of CH3 radicals in the reaction 2 ·CH3(g) → CH3CH3(g) Was reported as 1.2 mol L-1 s-1 under a certain set of conditions. (a) What is the rate of formation of CH3CH3(g) ? Answer: d[CH3CH3 ] = 0.6 mol L-1 s-1 dt (b) What is the rate of the reaction? Answer: ν = 0.6 mol L-1 s-1 17  Rate laws and rate constants Atkins p. 726 / 742 Reaction rate is proportional to the concentrations of reactants and/or products in the balanced rxn: For example, for a balanced reaction A + B → C, the rate law may be 𝑑𝑑 𝐴𝐴 α β For homogenous gas phase 𝜈𝜈 = − = 𝑘𝑘𝑟𝑟 𝐴𝐴 𝐵𝐵 reactions, the rate can also 𝑑𝑑𝑑𝑑 be expressed in terms of written from experimentally partial pressures stoichiometry determined rate law The rate constant (symbol: k or kr) is a constant of proportionality and is – independent of the concentrations – dependent on the temperature. An experimentally determined equation of this kind is called the rate law of the reaction. rate constant (kr): A constant of proportionality between the reaction rate and the concentration of reactants and/or products. rate law: An experimentally determined expression for the reaction rate in terms of the concentrations of the species that occur in the overall chemical reaction. 18  Reaction order Atkins p. 727 / 743 Consider the rate law expression 𝑑𝑑 𝐴𝐴 α β 𝜈𝜈 = − = 𝑘𝑘𝑟𝑟 𝐴𝐴 𝐵𝐵 𝑑𝑑𝑑𝑑 The power to which the concentration of a species (a product or a reactant) is raised in a rate law of this kind is the order of the reaction with respect to that species. The overall order of a reaction is the sum of the individual orders. Example: For a reaction with the rate law ν = kr[A]2[B] The reaction is second-order in A and first-order in B. The overall order of this reaction is third-order. 19 Note that: A reaction need not have an integral order, and many gas-phase reactions do not. For example, a reaction having the rate law 1 𝑑𝑑 𝐴𝐴 𝜈𝜈 = − = 𝑘𝑘𝑟𝑟 𝐴𝐴 2 𝐵𝐵 𝑑𝑑𝑑𝑑 is half-order in A, first-order in B, and three-halves-order overall. Some reactions obey a zero-order rate law, and therefore have a rate that is independent of the concentration of the reactant (so long as some is present). The catalytic decomposition of phosphine (PH3) on hot tungsten at high pressures: PH3(g) → P(g) + 3/2 H2(g) has the rate law 𝝂𝝂 = 𝒌𝒌𝒓𝒓 zero order! 20 The rate law of the reaction between hydrogen and bromine 3 𝑘𝑘 𝐻𝐻2 𝐵𝐵𝐵𝐵2 2 𝜈𝜈 = 𝐵𝐵𝐵𝐵2 + 𝑘𝑘 ′ 𝐻𝐻𝐻𝐻𝐻𝐻 shows that the reaction is first-order in H2 the reaction has an indefinite order with respect Br2 and HBr the reaction has no overall order 21  Units of reaction rate and the rate constant (k or kr) For a balanced reaction A + B → C, the rate law may be 𝑑𝑑 𝐴𝐴 α β 𝜈𝜈 = − = 𝑘𝑘𝑟𝑟 𝐴𝐴 𝐵𝐵 𝑑𝑑𝑑𝑑 What is the unit of rate, 𝜈𝜈? The unit of rate is determined from the ratio concentration per time, e.g. mol L-1 s-1, mol L-1 h-1, atm s-1 What about the units of kr? Rate law ν = kr ν = kr[A] ν = kr[A][B] ν = kr[A]2[B] Overall order 0th order 1st order 2nd order 3rd order Unit of rate mol L-1 s-1 mol L-1 s-1 mol L-1 s-1 mol L-1 s-1 The units of kr depends on Unit of kr mol L-1 s-1 s-1 L mol-1 s -1 L2 mol-2 s -1 the overall reaction order! 22  Units of reaction rate and the rate constant (k or kr) The units of kr are always such as to convert the product of concentrations, each raised to the appropriate power, into a rate expressed as a change in concentration divided by time. Example: For v = kr[A][B] with concentrations expressed in mol dm-3, the units of kr will be dm-3 mol-1 s-1 because If the concentrations are expressed in molecules cm−3, and the rate in molecules cm−3 s−1, then kr is expressed in cm3 molecule−1 s−1. How do we convert between these different units of kr? See next slide…. 23  Units of the rate constant (k or kr) Atkins p. 727 / 743 Taken from Atkins’ Physical Chemistry, 11th edition, p. 727 24  Rate laws and stoichiometry Consider the reaction aA + bB + cC → products For this reaction, the rate law can be presented as Revise! Do not confuse the concepts ν = kr[A]α[B]β[C]γ “reaction rate” and “rate law”! Note that: The rate law is an experimentally determined equation (α, β and γ are experimentally determined) The rate law does not depend on the stoichiometric coefficients (a, b, c) of the balanced reaction equation α, β and γ are often positive whole numbers, but can be negative, fractions or zero. The rate constant, kr is independent of the concentrations but depends on the temperature. 25 Example: Atkins p. 726 / 742 Reaction of hydrogen and bromine has a very simple stoichiometry H2(g) + Br2(g) → 2 HBr(g) but its rate law is complicated: 3 𝑘𝑘 𝐻𝐻2 𝐵𝐵𝐵𝐵2 2 𝜈𝜈 = 𝐵𝐵𝐵𝐵2 + 𝑘𝑘 ′ 𝐻𝐻𝐻𝐻𝐻𝐻 In certain cases the rate law does reflect the stoichiometry of the reaction, BUT that is either a coincidence or reflects a feature of the underlying reaction mechanism (see later). A note on good practice: A general rate constant is denoted kr to distinguish it from the Boltzmann constant k. In some texts k is used for the rate constant and kB for Boltzmann constant. When expressing the rate constants in a more complicated rate law, we use ka, kb or k, k’ and so on. 26  Rate constants and stoichiometry Consider a balanced reaction A + 2B → 3Z. For this reaction, the reaction rate can be expressed as 𝑑𝑑 𝐴𝐴 1 𝑑𝑑 𝐵𝐵 1 𝑑𝑑 𝑍𝑍 𝜈𝜈 = − =− = + 𝑑𝑑𝑑𝑑 2 𝑑𝑑𝑑𝑑 3 𝑑𝑑𝑑𝑑 1 1 Revise! See slide 12 𝑜𝑜𝑜𝑜 𝜈𝜈 = 𝜈𝜈𝐴𝐴 = 𝜈𝜈𝐵𝐵 = 𝜈𝜈𝑍𝑍 2 3 The rate of this reaction can also be expressed by the rate law 𝜈𝜈= k[A]α[B]β where k, α and β are independent of concentration and time. Similarly, the rate of consumption can be expressed by 𝜈𝜈A = kA[A]α[B]β while the rate of formation can be expressed by 𝜈𝜈Z = kZ[A]α[B]β In these equations, k, kA and kZ are not necessarily the same, being related by their stoichiometric coefficients as follows: 𝑘𝑘 = 𝑘𝑘𝐴𝐴 = 𝑘𝑘𝐵𝐵 = 𝑘𝑘𝑍𝑍 (note the similarity to the expression for reaction rate, 𝜐𝜐) 1 1 2 3 Adapted from Laidler et al, Physical Chemistry, 4th edition, Houghton Mifflin, p 364 27  Example A radical is an atom, molecule, or ion that has an Consider the dissociation of ethane into methyl radicals: unpaired valence electron. Radicals are usually formed when a single covalent bond breaks to leave an unpaired C2H6 → 2 ·CH3 electron on each of the two species created by the bond breaking (homolysis). If a reaction shows time-independent stoichiometry, it is possible to evaluate its rate of reaction from the stoichiometry. For this example, the rate of reaction (𝝂𝝂) is equal to the rate of consumption of ethane or one-half the rate of formation of methane: 𝑑𝑑 C H 1 𝑑𝑑 ·CH3 𝜈𝜈 = − 2 6 = 𝑑𝑑𝑑𝑑 2 𝑑𝑑𝑑𝑑 The rate of formation of methyl radicals is twice the rate of consumption of methane, 𝜈𝜈𝐶𝐶𝐶𝐶3 = 2 𝜈𝜈𝐶𝐶2𝐻𝐻6 so that 1 1 but we write rate expressions according to the given 𝜈𝜈 = 𝜈𝜈𝐶𝐶2𝐻𝐻6 = 𝜈𝜈 𝑘𝑘𝑟𝑟 = 𝑘𝑘𝐶𝐶2𝐻𝐻6 = 𝑘𝑘𝐶𝐶𝐶𝐶3 2 𝐶𝐶𝐶𝐶3 2 stoichiometry! Note: It is therefore important to specify the species to which a rate constant applies Whenever possible, the rate constant should be evaluated with respect to the rate of reaction. Adapted from Laidler et al, Physical Chemistry, 4th edition, Houghton Mifflin, p 364 28 Practical applications of rate laws: 𝝂𝝂 = 𝒌𝒌𝒓𝒓 𝑨𝑨 𝜶𝜶 𝑩𝑩 𝜷𝜷   If rate law and value of rate constant is known, we can predict the rate of  reaction from the composition of the mixture.    By knowing the rate law, rate constant and rate of reaction, we can predict the composition of the reaction mixture at a later stage of the reaction. A rate law is a guide to the mechanism of the reaction, for any proposed mechanism must be consistent with the observed rate law. 29 You should now be able to do the following end-of-chapter and tutorial problems: Atkins 11th edition, p. 769: Exercises E17A.3(a), E17A.4(a), E17A.5(a), E17A.7(a)(i) or Atkins 12th edition, p. 785: Exercises E17A.11, E17A.12, E17A.14, E17A.16(i) and Tutorial 1: Questions 1, 2 30