The Arrhenius Equation Indicates the Relationship Between the Reaction Temperature
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Rate Constants and Kinetic Isotope Effects for Methoxy Radical Reacting with NO2 and O2 Jiajue Chai, Hongyi Hu, Theodore
Rate Constants and Kinetic Isotope Effects for Methoxy Radical Reacting with NO2 and O2 Jiajue Chai, Hongyi Hu, Theodore. S. Dibble* Department of Chemistry, College of Environmental Science and Forestry, State University of New York, Syracuse, New York 13210, United States Geoffrey. S. Tyndall,* and John. J. Orlando Atmospheric Chemistry Division, National Center for Atmospheric Research, Boulder, Colorado 80307, United States Abstract Relative rate studies were carried out to determine the temperature dependent rate constant ratio k1/k2a: CH3O• + O2 → HCHO + HO2• (R1) CH3O• + NO2 (+M) → CH3ONO2 (+ M) (R2a) over the temperature range 250-333 K in an environmental chamber at 700 Torr using FTIR detection. Absolute rate constants k2 were determined using laser flash photolysis/laser induced fluorescence under the same conditions. The analogous experiments were carried out for the reactions of perdeuterated methoxy radical (CD3O•). Absolute rate constants k2 were in excellent agreement with the recommendations of the JPL Data Evaluation panel. The combined data (i.e., 3 -1 k1/k2 and k2) allow determination of k1 as cm s , corresponding to 1.4 × 10-15 cm3 s-1 at 298 K. The rate constant at 298 K is in excellent agreement with previous work, but the observed temperature dependence is less than previously reported. The deuterium isotope effect, kH/kD, can be expressed in Arrhenius form as The deuterium isotope effect does not appear to be greatly influenced by tunneling, which is consistent with previous theoretical work by Hu and Dibble (Hu, H.; Dibble, T. S., J. Phys. Chem. A 2013, 117, 14230–14242). Keywords: methylnitrite, formaldehyde, methylnitrate, alkoxy radicals, kinetic isotope effect * [email protected], [email protected] 1 I. -
Eyring Equation
Search Buy/Sell Used Reactors Glass microreactors Hydrogenation Reactor Buy Or Sell Used Reactors Here. Save Time Microreactors made of glass and lab High performance reactor technology Safe And Money Through IPPE! systems for chemical synthesis scale-up. Worldwide supply www.IPPE.com www.mikroglas.com www.biazzi.com Reactors & Calorimeters Induction Heating Reacting Flow Simulation Steam Calculator For Process R&D Laboratories Check Out Induction Heating Software & Mechanisms for Excel steam table add-in for water Automated & Manual Solutions From A Trusted Source. Chemical, Combustion & Materials and steam properties www.helgroup.com myewoss.biz Processes www.chemgoodies.com www.reactiondesign.com Eyring Equation Peter Keusch, University of Regensburg German version "If the Lord Almighty had consulted me before embarking upon the Creation, I should have recommended something simpler." Alphonso X, the Wise of Spain (1223-1284) "Everything should be made as simple as possible, but not simpler." Albert Einstein Both the Arrhenius and the Eyring equation describe the temperature dependence of reaction rate. Strictly speaking, the Arrhenius equation can be applied only to the kinetics of gas reactions. The Eyring equation is also used in the study of solution reactions and mixed phase reactions - all places where the simple collision model is not very helpful. The Arrhenius equation is founded on the empirical observation that rates of reactions increase with temperature. The Eyring equation is a theoretical construct, based on transition state model. The bimolecular reaction is considered by 'transition state theory'. According to the transition state model, the reactants are getting over into an unsteady intermediate state on the reaction pathway. -
Estimation of Viscosity Arrhenius Pre-Exponential Factor and Activation Energy of Some Organic Liquids E
ISSN 2350-1030 International Journal of Recent Research in Physics and Chemical Sciences (IJRRPCS) Vol. 5, Issue 1, pp: (18-26), Month: April 2018 – September 2018, Available at: www.paperpublications.org ESTIMATION OF VISCOSITY ARRHENIUS PRE-EXPONENTIAL FACTOR AND ACTIVATION ENERGY OF SOME ORGANIC LIQUIDS E. IKE1 and S. C. EZIKE2 1,2Department of Physics, Modibbo Adama University of Technology, P. M. B. 2076, Yola, Adamawa State, Nigeria. Corresponding Author‟s E-mail: [email protected] Abstract: Information concerning fluid’s physico-chemical behaviors is of utmost importance in the design, running and optimization of industrial processes, in this regard, the idea of fluid viscosity quickly comes to mind. Models have been proposed in literatures to describe the viscosity of liquids and fluids in general. The Arrhenius type equations have been proposed for pure solvents; correlating the pre-exponential factor A and activation energy Ea. In this paper, we aim at extending these Arrhenius parameters to simple organic liquids such as water, ethanol and Diethyl ether. Hence, statistical method and analysis are applied using viscosity data set from the literature of some organic liquids. The Arrhenius type equation simplifies the estimation of viscous properties and the calculations thereafter. Keywords: Viscosity, organic liquids, Arrhenius parameters, correlation, statistics. 1. INTRODUCTION All fluids are compressible and when flowing are capable of sustaining shearing stress on account of friction between the adjacent layers. Viscosity (η) is the inherent property of all fluids and may be referred to as the internal friction offered by a fluid to the flow. For water in a beaker, when stirred and left to itself, the motion subsides after sometime, which can happen only in the presence of resisting force acting on the fluid. -
Tables of Rate Constants for Gas Phase Chemical Reactions of Sulfur Compounds (1971-1979)
NBSIR 80-2118 Tables of Rate Constants for Gas Phase Chemical Reactions of Sulfur Compounds (1971-1979) Francis Westley Chemical Kinetics Division Center for Thermodynamics and Molecular Science National Measurement Laboratory National Bureau of Standards U.S. Department of Commerce Washington. D.C. 20234 July 1980 Interim Report Prepared for Morgantown Energy Technology Center Department of Energy Morgantown, West Virginia 26505 Fice of Standard Reference Data itional Bureau of Standards ashington, D.C. 20234 c, 2 Jl 1 m * rational bureau 07 STANDARDS LIBRARY NBSIR 80-2118 wov 2 4 1980 TABLES OF RATE CONSTANTS FOR GAS f)Oi Clcc -Ore PHASE CHEMICAL REACTIONS OF SULFUR COMPOUNDS (1971-1979) 1 5 (o lo-z im Francis Westley Chemical Kinetics Division Center for Thermodynamics and Molecular Science National Measurement Laboratory National Bureau of Standards U.S. Department of Commerce Washington, D.C. 20234 July 1980 Interim Report Prepared for Morgantown Energy Technology Center Department of Energy Morgantown, West Virginia 26505 and Office of Standard Reference Data National Bureau of Standards Washington, D.C. 20234 U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary Luther H. Hodges, Jr., Deputy Secretary Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director . i:i : a 1* V'.OTf in. te- ?') t aa.‘ .1 J Table of Contents Abstract 1 Introduction 2 Guidelines for the User 4 Table of Arrhenius Parameters for Chemical Reactions of Sulfur Compounds 12 Reactions of: S(Sulfur atom) 12 $2(Sulfur dimer) 20 S0(Sulfur monoxide) 21 S02(Sulfur dioxide 23 S0 (Sulfur trioxide) 28 3 S20(Sul fur oxide^O) ) 29 SH (Mercapto free radical) 29 H2S (Hydroqen sulfide 31 CS (Carbon monosulfide free radical) 32 CS2 (Carbon disulfide) 33 COS (Carbon oxide sulfide) 35 CH^S* ( Methyl thio free radical) 36 CH^SH (Methanethiol ) 36 cy-CF^CF^S (Thiirane) 37 CH^SCF^* (Methyl, (methyl thio)-, free radical) ... -
Classical and Modern Methods in Reaction Rate Theory
J. Phys. Chem. 1988, 92, 3711-3725 3711 loss associated with the transition between states is offset by a For the Re( MQ+)-based complexes an additional complication gain in energy in the intramolecular vibrations (eq 3). to intramolecular electron transfer exists arising from a "flattening" On the other hand, if (AGe,,2 + A0,2) > (AG,,l + A,,,) (Figure of the relative orientations of the two rings of the MQ+ ligand 4B) and nuclear tunneling effects in the librational modes are when it accepts an However, the analysis presented unimportant, intramolecular electron transfer can not occur in here does provide a general explanation for the role of free energy a frozen environment. The situation is the same as in Figure 3A. change in environments where dipole motions are restricted. For Even direct Re(1) - MQ' excitation (process a in Figure 4B) a directed, intramolecular electron transfer such as reaction 1, must either lead to the ground state by emission or to the Re- the change in electronic distribution between states will, in general, (11)-bpy'--based MLCT state by reverse electron transfer: lead to a difference between Ao,l and A0,2. This difference creates a solvent dipole barrier to intramolecular electron transfer. It [ (bpy)Re"(CO) 3( MQ')] 2+* -+ (bpy'-)Re"( CO) 3(MQ')] 2'* follows from eq 4 that if light-induced electron transfer is to occur (5) in a frozen environment, the difference in solvent reorganizational The inversion in the sense of the electron transfer in the frozen energy, A& = bS2- A,,, must be compensated for by a favorable environment is induced energetically by the greater solvent re- free energy change, A(AG) = - AGes,l,as organizational energy for the lower excited state, A0,2 > Ao,l - Aces,~- AGes.2 > Ao-2 - &,I (AGes,2 - AGes,l)* or In a macroscopic sample, a distribution of solvent dipole en- vironments exists around the assembly of ground states. -
Eyring Activation Energy Analysis of Acetic Anhydride Hydrolysis in Acetonitrile Cosolvent Systems Nathan Mitchell East Tennessee State University
East Tennessee State University Digital Commons @ East Tennessee State University Electronic Theses and Dissertations Student Works 5-2018 Eyring Activation Energy Analysis of Acetic Anhydride Hydrolysis in Acetonitrile Cosolvent Systems Nathan Mitchell East Tennessee State University Follow this and additional works at: https://dc.etsu.edu/etd Part of the Analytical Chemistry Commons Recommended Citation Mitchell, Nathan, "Eyring Activation Energy Analysis of Acetic Anhydride Hydrolysis in Acetonitrile Cosolvent Systems" (2018). Electronic Theses and Dissertations. Paper 3430. https://dc.etsu.edu/etd/3430 This Thesis - Open Access is brought to you for free and open access by the Student Works at Digital Commons @ East Tennessee State University. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of Digital Commons @ East Tennessee State University. For more information, please contact [email protected]. Eyring Activation Energy Analysis of Acetic Anhydride Hydrolysis in Acetonitrile Cosolvent Systems ________________________ A thesis presented to the faculty of the Department of Chemistry East Tennessee State University In partial fulfillment of the requirements for the degree Master of Science in Chemistry ______________________ by Nathan Mitchell May 2018 _____________________ Dr. Dane Scott, Chair Dr. Greg Bishop Dr. Marina Roginskaya Keywords: Thermodynamic Analysis, Hydrolysis, Linear Solvent Energy Relationships, Cosolvent Systems, Acetonitrile ABSTRACT Eyring Activation Energy Analysis of Acetic Anhydride Hydrolysis in Acetonitrile Cosolvent Systems by Nathan Mitchell Acetic anhydride hydrolysis in water is considered a standard reaction for investigating activation energy parameters using cosolvents. Hydrolysis in water/acetonitrile cosolvent is monitored by measuring pH vs. time at temperatures from 15.0 to 40.0 °C and mole fraction of water from 1 to 0.750. -
Reaction Rates: Chemical Kinetics
Chemical Kinetics Reaction Rates: Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant → Products A → B change in number of moles of B Average rate = change in time ∆()moles of B ∆[B] = = ∆t ∆t ∆[A] Since reactants go away with time: Rate=− ∆t 1 Consider the decomposition of N2O5 to give NO2 and O2: 2N2O5(g)→ 4NO2(g) + O2(g) reactants products decrease with increase with time time 2 From the graph looking at t = 300 to 400 s 0.0009M −61− Rate O2 ==× 9 10 Ms Why do they differ? 100s 0.0037M Rate NO ==× 3.7 10−51 Ms− Recall: 2 100s 0.0019M −51− 2N O (g)→ 4NO (g) + O (g) Rate N O ==× 1.9 10 Ms 2 5 2 2 25 100s To compare the rates one must account for the stoichiometry. 1 Rate O =×× 9 10−−61 Ms =× 9 10 −− 61 Ms 2 1 1 −51−−− 61 Rate NO2 =×× 3.7 10 Ms =× 9.2 10 Ms Now they 4 1 agree! Rate N O =×× 1.9 10−51 Ms−−− = 9.5 × 10 61Ms 25 2 Reaction Rate and Stoichiometry In general for the reaction: aA + bB → cC + dD 11∆∆∆∆[AB] [ ] 11[CD] [ ] Rate ====− − ab∆∆∆ttcdtt∆ 3 Rate Law & Reaction Order The reaction rate law expression relates the rate of a reaction to the concentrations of the reactants. Each concentration is expressed with an order (exponent). The rate constant converts the concentration expression into the correct units of rate (Ms−1). (It also has deeper significance, which will be discussed later) For the general reaction: aA+ bB → cC+ dD x and y are the reactant orders determined from experiment. -
Time-Temperature Superposition WHICH VARIABLES ARE TEMPERATURE DEPENDENT in the ROUSE and REPTATION MODELS?
Time-Temperature Superposition WHICH VARIABLES ARE TEMPERATURE DEPENDENT IN THE ROUSE AND REPTATION MODELS? Rouse Relaxation Modulus: N ρ(T )RT X 2 G(t) = e−tp /λR M p=1 Rouse Relaxation Time: a2N 2ζ(T ) λ = R 6π2kT Reptation Relaxation Modulus: N 8 ρ(T )RT 1 2 X −p t/λd G(t) = 2 2 e π Me p p odd Reptation Relaxation Time: a2N 2ζ(T ) M λd = 2 π kT Me Both models have the same temperature dependence. This is hardly surprising, since reptation is just Rouse motion confined in a tube. Modulus Scale G ∼ ρ(T )T ζ(T ) Time Scale λ ∼ ∼ λ T N Since the friction factor is related to the shortest Rouse mode λN . a2ζ(T ) λ = N 6π2kT 1 Time-Temperature Superposition METHOD OF REDUCED VARIABLES All relaxation modes scale in the same way with temperature. λi(T ) = aT λi(T0) (2-116) aT is a time scale shift factor T0 is a reference temperature (aT ≡ 1 at T = T0). Gi(T0)T ρ Gi(T ) = (2-117) T0ρ0 Recall the Generalized Maxwell Model N X G(t) = Gi exp(−t/λi) (2-25) i=1 with full temperature dependences of the Rouse (and Reptation) Model N T ρ X G(t, T ) = G (T ) exp{−t/[λ (T )a ]} (2-118) T ρ i 0 i 0 T 0 0 i=1 We simplify this by defining reduced variables that are independent of temperature. T ρ G (t) ≡ G(t, T ) 0 0 (2-119) r T ρ t tr ≡ (2-120) aT N X Gr(tr) = Gi(T0) exp[−tr/λi(T0)] (2-118) i=1 Plot of Gr as a function of tr is a universal curve independent of tem- perature. -
A First Course on Kinetics and Reaction Engineering Example 4.6
A First Course on Kinetics and Reaction Engineering Example 4.6 Problem Purpose This example illustrates the use of an Arrhenius plot to determine the best values of a pre- exponential factor and an activation energy. Problem Statement Kinetic studies were performed at a number of different temperatures to find the value of a second order rate coefficient at each of the temperatures. The results are given in the table below. Determine whether the temperature dependence of this rate coefficient is consistent with the Arrhenius equation, and find the best values for the pre-exponential factor and the activation energy. Temperature Rate Coefficient (°C) (L mol-1 min-1) 10 2.63 x 10-4 22 4.78 x 10-4 40 1.52 x 10-3 54 4.18 x 10-3 65 9.07 x 10-3 78 2.14 x 10-2 89 4.2 x 10-2 103 9.42 x 10-2 Problem Analysis This problem clearly involves the use of the Arrhenius expression for the temperature dependence of a rate coefficient. The Arrhenius expression contains two unknown constants, the pre-exponential factor and the activation energy. Here we are given the value of the rate coefficient at eight different temperatures. If we substituted each of those eight data points into the Arrhenius expression, we would have eight equations in two unknowns. Unless the data were “made up” using the Arrhenius expression, there won’t be a single value of the pre-exponential factor and a single value of the activation energy that together satisfy the eight equations. -
Enthalpy and Free Energy of Reaction
KINETICS AND THERMODYNAMICS OF REACTIONS Key words: Enthalpy, entropy, Gibbs free energy, heat of reaction, energy of activation, rate of reaction, rate law, energy profiles, order and molecularity, catalysts INTRODUCTION This module offers a very preliminary detail of basic thermodynamics. Emphasis is given on the commonly used terms such as free energy of a reaction, rate of a reaction, multi-step reactions, intermediates, transition states etc., FIRST LAW OF THERMODYNAMICS. o Law of conservation of energy. States that, • Energy can be neither created nor destroyed. • Total energy of the universe remains constant. • Energy can be converted from one form to another form. eg. Combustion of octane (petrol). 2 C8H18(l) + 25 O2(g) CO2(g) + 18 H2O(g) Conversion of potential energy into thermal energy. → 16 + 10.86 KJ/mol . ESSENTIAL FACTORS FOR REACTION. For a reaction to progress. • The equilibrium must favor the products- • Thermodynamics(energy difference between reactant and product) should be favorable • Reaction rate must be fast enough to notice product formation in a reasonable period. • Kinetics( rate of reaction) ESSENTIAL TERMS OF THERMODYNAMICS. Thermodynamics. Predicts whether the reaction is thermally favorable. The energy difference between the final products and reactants are taken as the guiding principle. The equilibrium will be in favor of products when the product energy is lower. Molecule with lowered energy posses enhanced stability. Essential terms o Free energy change (∆G) – Overall free energy difference between the reactant and the product o Enthalpy (∆H) – Heat content of a system under a given pressure. o Entropy (∆S) – The energy of disorderness, not available for work in a thermodynamic process of a system. -
Empirical Chemical Kinetics
Empirical Chemical Kinetics time dependence of reactant and product concentrations e.g. for A + 2B → 3C + D d[A] 1 d[B] 1 d[C] d[D] rate =− =− = = d2d3ddtttt =ν In general, a chemical equation is 0∑ ii R i nt()− n (0 ) The extent of a reaction (the advancement) = ii ν i For an infinitesmal advancement dξ each reactant/product =ν ξ concentration changes by d[Ri ]i d . d1d[R]ξ By definition, the rate == i ν ddtti Reaction rates usually depend on reactant concentrations, e.g., rate= k [A]xy [B] order in B total order = x+y rate constant In elementary reaction steps the orders are always integral, but they may not be so in multi-step reactions. The molecularity is the number of molecules in a reaction step. Rate Laws d[A] Zero order: −=k dt 0 [A] = [A]00 -[A]t kt [A]0 t1 = 2 2k 0 0 t −=d[A] First order: k1[A] [A] ln[A] dt − = kt1 [A]t [A]0 e ln 2 0 t 0 t t1 = 2 k1 d[A] 2 Second order: −=2[A]k [A] dt 2 [A] [A] = 0 t + 12[A]kt20 0 t -1=+ -1 [A]t [A]02 2kt 1 t1 = 2 2[A]k20 [A]-1 0 t Second-order Kinetics: Two Reactants A + B k → products da rate=− =kab a = [A], b =[B] dt =− − ka()()00 x b x ddxa Since aa=− x, =− 0 ddtt dx So =−ka()() x b − x dt 00 x dx kt = ∫ ()()−− 0 axbx00 −111x =−dx ()−−−∫ ()() ab000 ax 0 bx 0 −1 ab = ln 0 ()− ab00 ab 0 or more usefully, aa=+−0 ln ln ()abkt00 bb0 Data Analysis “Classical” methods of data analysis are often useful to explore the order of reactions, or to display the results (e.g. -
Kinetics and Atmospheric Chemistry
12/9/2017 Kinetics and Atmospheric Chemistry Edward Dunlea, Jose-Luis Jimenez Atmospheric Chemistry CHEM-5151/ATOC-5151 Required reading: Finlayson-Pitts and Pitts Chapter 5 Recommended reading: Jacob, Chapter 9 Other reading: Seinfeld and Pandis 3.5 General Outline of Next 3 Lectures • Intro = General introduction – Quick review of thermodynamics • Finlayson-Pitts & Pitts, Chapter 5 A. Fundamental Principles of Gas-Phase Kinetics B. Laboratory Techniques for Determining Absolute Rate Constants for Gas-Phase Reactions C. Laboratory Techniques for Determining Relative Rate Constants for Gas-Phase Reactions D. Reactions in Solution E. Laboratory Techniques for Studying Heterogeneous Reactions F. Compilations of Kinetic Data for Atmospheric Reactions 1 12/9/2017 Kinetics and Atmospheric Chemistry • What we’re doing here… – Photochemistry already covered – We will cover gas phase kinetics and heterogeneous reactions – Introductions to a few techniques used for measuring kinetic parameters • What kind of information do we hope to get out of “atmospheric kinetics”? – Predictive ability over species emitted into atmosphere • Which reactions will actually proceed to products? • Which products will they form? • How long will emitted species remain before they react? Competition with photolysis, wash out, etc. • Pare down list of thousands of possible reactions to the ones that really matter – Aiming towards idea practical predictive abilities • Use look up tables to decide if reaction is likely to proceed and determine an “atmospheric lifetime”