Collision Theory

10 Key excerpts on "Collision Theory"

• 

  eBook - PDF

  Fundamental Chemical Kinetics

  An Explanatory Introduction to the Concepts

  • M R Wright(Author)
  • 1999(Publication Date)
  • Woodhead Publishing

    (Publisher)

  7 Simple and Modified Collision Theory In simple Collision Theory reaction occurs when two molecules which have energy greater than a certain critical value collide. This requires calculation of two quantities: (i) the total rate of collision of the reactant molecules, (ii) the fraction of molecules which have at least a certain critical value of the energy. The resultant equation can be compared with the empirical Arrhenius equation (7.1) Simple Collision Theory assumes that the colliding molecules are hard spheres, and ignores the molecular structure and details of internal motion such as vibration and rotation. Likewise it does not consider the products of reaction nor their internal structure. Modem Collision Theory which is based on molecular beams and laser induced fluorescence studies, looks at a collision in much more detail. Now the internal states of the colliding molecules, the internal states of the products of a collision and the distribution of energy among the product molecules become of fundamental importance. 7.1 Simple Collision Theory Reaction can be between like molecules A + A ~ products and the total rate of collision is modified to account for the fact that only those collisions which have the critical energy or greater can lead to reaction. When reaction is between two unlike molecules A + B ~ products only collisions between A and B have any chance of leading to reaction, so that the appropriate total rate of collision is for collisions between A and B only. Collisions between A and A, or B and B do not count as they can never lead to reaction. Again the appropriate collision rate has to be modified to account for the fact that not all collisions will cause reaction.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Introduction to Chemical Engineering Kinetics and Reactor Design

  • Charles G. Hill, Thatcher W. Root(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  4.2.7 Cautionary Note on Reaction Mechanisms

  It is appropriate to conclude our discussion of reaction mechanisms on a note of caution. A mechanism is merely a logical hypothesis as to the sequence of molecular events that occur during the course of a chemical reaction. Reaction mechanisms should not be regarded as experimental facts. They are plausible explanations of experimental data that are consistent with the data, but that may be subject to revision as new data are obtained. Even if a proposed mechanism gives agreement with all available experimental facts, this is not evidence that the mechanism is unique or that other mechanisms could not give such agreement.

  4.3 Molecular Theories of Chemical Kinetics

  A “complete” theory of reaction kinetics would provide a basis for calculating the rate of an elementary reaction from a knowledge of the properties of the reacting molecules and their concentrations. In terms of the present state of our theoretical knowledge, a complete theory can be regarded as a goal that is far, far down the road. While existing theories are extremely unsatisfactory, chemical engineers must be cognizant of their primary features.

  4.3.1 Simple Collision Theory

  Before a chemical reaction can occur, energy must be available and localized such that it is possible to break and make certain chemical bonds in the reactant molecules. Moreover, the participants in the reaction must be in a spatial configuration such that it is possible for the necessary atomic and electronic rearrangements to occur. The most common means by which such redistributions of energy and changes in geometric configurations can occur are molecular collision processes. In this sense all theories of reaction are collision theories. However, we use this term in a more limited sense. We restrict its use to the theory that links chemical kinetics to the kinetic theory of gases by the use of the theoretical expression for bimolecular collision frequencies.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Rates and Equilibria of Organic Reactions

  As Treated by Statistical, Thermodynamic and Extrathermodynamic Methods

  • John E. Leffler, Ernest Grunwald(Authors)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  4

  Concerning Rates of Reaction

  No single thing abides, but all things flow. Fragment to fragment clings and thus they grow Until we know and name them. Then by degrees they change and are no more The things we know.

  Lucretius

  There are two principal theories in use for dealing with the problem of reaction rates. The Collision Theory is based largely on the kinetic theory of gases and uses a mechanical model; the transition state theory is based largely on thermodynamics and uses a three-dimensional surface as a model, the vertical coordinate being the energy. Either theory is simple enough so that a useful qualitative insight into the nature of rate processes can be gained by visualizing the model for a given reaction. Although the transition state theory is the more generally useful of the two, particularly for organic reactions, the Collision Theory is nevertheless convenient for certain special purposes and is of historical importance because of the influence it has. had on modes of thinking about reaction mechanisms.

  THE Collision Theory

  The basic assumption of the Collision Theory is that reaction is the result of a collision but that the collision is ineffective unless the kinetic energy of the colliding molecules along their line of centers equals or exceeds a critical value called the activation energy. The necessity for proper orientations and other requirements independent of the energy of the colliding molecules gives rise to an additional parameter in the theory, the probability factor, P. The rate constant or rate at unit concentrations of the reagents is given by equation 1.

  (1)

  The factor Z is the frequency at which collisions occur between the reagent molecules when they are present at unit concentration. According to the kinetic theory of gases, the frequency of collisions between molecules of two species A and B

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Combustion Physics

  • Chung K. Law(Author)
  • 2010(Publication Date)
  • Cambridge University Press

    (Publisher)

  Typical reaction rate profile for large activation energy reactions. 62 Chemical Kinetics three-body recombination reactions, mentioned earlier, in which the requirement for the consummation of the reaction is the presence of the third body to carry away the excess energy instead of the availability of the activation energy to initiate the reaction. Frequently these reactions are highly exothermic, and hence are the sources of thermal energy in the flow. 2.2.3. Collision Theory of Reaction Rates The Collision Theory of reaction rates equates the reaction rate with the rate of molec- ular collision having a collision energy exceeding the activation energy. Thus if we assume that the collision energy necessary to effect molecular change is derived from the relative translational energy between the colliding molecules, that the gas is suf- ficiently dilute such that only two-body collisions are of importance, and that the equilibrium Maxwell velocity distribution function can still be used for the highly transient process of chemical reaction, then the reaction rate can be determined by summing over all possible collisions satisfying the requirement of minimum collision energy. A detailed derivation of this theory allowing for three-dimensional collision dy- namics, and the subsequent comparison with experimental results (Fowler & Guggen- heim 1939), show that the effective collision energy is the component of the relative translational energy along the line of centers instead of the total relative translational energy. Physically this component of the relative motion represents a head-on col- lision situation, while the other two components normal to the line of centers only affect the dynamics of the center of mass, and therefore are not effective in chemical transformation. In view of the above considerations, we shall present a simplified derivation in- volving only one-dimensional, head-on collisions.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  The Routledge Handbook of Mechanisms and Mechanical Philosophy

  • Stuart Glennan, Phyllis Illari, Stuart Glennan, Phyllis Illari(Authors)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  6 The Transition State Theory, on the other hand, was taken up by organic chemists who are principally interested in reactions that take place in solution. The Transition State Theory, described in (Hammett, 1940, pp. 115–18) and (Ingold, 1953, pp. 43–52), is an extension or articulation of the thermodynamics of chemical equilibria onto the problem of reaction rates. To appreciate its significance, it is first important to see how organic chemists were able to use chemical thermodynamics, in conjunction with their newly refined understanding of chemical bonding, to understand or rationalize the effects of changes in chemical structure or medium on a chemical equilibrium.

  According to chemical thermodynamics, the eventual balance between reactants and products in a chemical reaction depends on their difference in a thermodynamic quantity known as the “free” energy. Subject to some important caveats and exceptions, it is often possible in the sorts of circumstances relevant to the organic chemist to make predictions (typically qualitative or relative) about how this free energy difference will change as a result of changes in either the chemical structures of the species in equilibrium or the medium in which the equilibrium takes place. So, for instance, by appealing to Ingold’s inductive effect, one might predict that replacing one atom in a reactant structure with a more electronegative atom would result in products that are, relatively speaking, of even lower energy. This would result in changes to the overall free energy change in the reaction, thereby changing the eventual balance between reactants and products in an anticipatable way. In other words, chemical thermodynamics, in concert with the updated accounts of chemical bonding and interaction, allows for a structural analysis of the eventual balance between reactants and products. This is a further step on the path of fulfilling Butlerov’s ambition for structural chemistry in that features of a chemical reaction (the eventual balance between reactants and products) can be explained in terms of the structures of the reacting species.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Concepts of Modern Catalysis and Kinetics

  • I. Chorkendorff, J. W. Niemantsverdriet(Authors)
  • 2017(Publication Date)
  • Wiley-VCH

    (Publisher)

  Chapter 2 , since the prefactor can not be related to the change of entropy of the system. Hence, Collision Theory is not in accordance with thermodynamics.

  3.6 Activation of Reacting Molecules by Collisions: The Lindemann Theory

  A question that intrigued several kineticists around 1920 was the following. For bimolecular reactions of the type A + B = Products, Collision Theory gave at least a plausible conceptual picture: if the collision between A and B is sufficiently vigorous, the energy barrier separating reactants and products can be crossed. How, though, can one explain the case of monomolecular elementary reaction, for example, an isomerization, such as cyclopropane to propylene, or the decomposition of a molecule such as sulfuryl, SO2 Cl2 , into SO2 and Cl2 ? Highly original, though not always realistic, explanations were suggested. For instance, Jean Perrin proposed in 1919 that the walls of the reaction vessel radiated a kind of reaction energy that enabled the reaction. Frederick Lindemann, the later Lord Cherwell and Minister of Defense in Churchill’s Second World War cabinet, was strongly against Perrin’s “radiation theory of chemical action” and in 1921 he proposed an alternative explanation, which is still generally accepted today [1].

  According to the Lindemann–Christiansen hypothesis, formulated independently by both scientists in 1921, all molecules acquire and lose energy by collisions with surrounding molecules. This is expressed in the simplified form of the Lindemann mechanism, in which we use an asterisk to indicate a highly energetic or activated molecule, which has sufficient energy to cross the barrier towards the product side, and M is a molecule from the surroundings; M may be from the same type as A:

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Chemically Reacting Flow

  Theory, Modeling, and Simulation

  • Robert J. Kee, Michael E. Coltrin, Peter Glarborg, Huayang Zhu(Authors)
  • 2017(Publication Date)
  • Wiley

    (Publisher)

  The rate at which chemical reactions occur depends (among other factors) on the rate at which molecules collide. Energy can be transferred from one molecule to another during collisions. It can also be converted from one form to another; for example, translational energy can be converted into rotational or vibrational energy of one or both of the collision partners. If energy accumulates as vibrational excitation in a particular bond of a molecule, the bond may break, causing a chemical reaction. The reverse of any of these energy-transfer processes may also occur via molecular collisions. Thus, it is important to know the frequency of such collisions. This section will derive the collision rates between gas-phase molecules, either between two different chemical species (denoted “1-2 collisions”) or between like molecules (“1-1 collisions”).

  A collision between a gas molecule and a surface sometimes leads to a heterogeneous reaction. An expression for the rate of molecule–wall collisions will also be presented here.

  13.1.2.1 Relative Velocities

  The kinetic energy associated with the velocity of one molecule relative to another is important in understanding molecular collisions. That is, the velocities relative to the stationary “laboratory frame of reference” are not the key, but relative velocities with respect to the center of mass of the collision pairs are important.

  The reduced mass for the collision of molecules of mass m1 and m2 is defined as

  (13.31)

  The relative velocity distributions obey the Maxwell–Boltzmann distribution (Eq. 13.24 ), with the mass replaced by the reduced mass m12 :

  (13.32)

  and the average relative speed is

  (13.33)

  13.1.2.2 Collisions between Unlike Molecules

  The frequency of molecular collisions is an important factor governing gas-phase reaction rates. Consider two molecules of radius r1 and r2

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Reaction Kinetics and Reactor Design

  • John B. Butt(Author)
  • 2000(Publication Date)
  • CRC Press

    (Publisher)

  2 The Mechanisms of Chemical Reactions in Homogeneous Phases There is something fascinating about science. One gets such wholesale returns of conjecture out of such trifiling investment of fact. — Mark Twain It was stated in Chapter 1 that theoretical justification for rate laws of the power-law form as applied to elementary steps could be provided. Our present purpose is to provide this justification in terms of several theories in sufficient detail to permit a basic comprehension of the origins and limitations of rate laws. Since we are not attempting a treatise on chemical kinetics, the presentation is selective, with much of the material relating specifically to reactions in the gaseous phase. The discussion is based on the fundamentals of the kinetic theory of gases with extensions to the transition-state theory of reaction rates. We shall follow the procedure of building a simple theory, criticizing it, building an improved theory, criticizing that, and so on —eventually reaching some reasonable level of theoretical background for ultimate engineering application. 2.1 Elementary Kinetic Theory The simplest way in which to visualize a reaction between two chemical species is in terms of a collision between the two. Physical proximity is obviously a necessary condition for reaction, for there can be no interaction between two molecules that are well-separated from each other. In fact, though, collisions are rather difficult to define as discrete events, since the interaction between two molecules extends over a distance that depends on their individual potential energy fields. Fortunately, many useful results can be obtained by using simplified models; for gases the two most useful are the ideal gas (point particle) model and the hard-sphere model. In the ideal gas model a molecule is pictured as a point particle (i.e., dimensionless) of mass equal to the molecular weight with given position and velocity coordinates.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Chemistry

  Structure and Dynamics

  • James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  CH 3 CH 3 CH 3 C Br(aq) OH  (aq)  CH 3 CH 3 CH 3 C OH(aq) Br  (aq)  The rate law for this reaction is first-order in (CH 3 ) 3 CBr, but it is zero-order in the OH  ion. It is important to recognize the difference between the molecularity and the order of a reaction. The molecularity of a reaction, or a step within a reaction, describes what happens on the molecular level. The order of a reaction describes what happens on the macroscopic scale. We determine the order of a reaction experimentally by watching the products of a reaction appear or the starting mate- rials disappear. The molecularity of the reaction is something we deduce to explain the experimental results. 14.8 A Collision Theory Model of Chemical Reactions The Collision Theory model of chemical reactions introduced in Section 10.4 can be used to explain the observed rate laws for both one-step and multistep reac- tions. This model of chemical reactions assumes that the rate of any step in a reaction depends on the frequency of collisions between the particles involved in that step. Consider the following simple, one-step reaction, for example. Figure 14.4 provides a basis for understanding the implications of the Collision Theory model for this reaction. The kinetic molecular theory assumes that the num- ber of collisions per second in a gas depends on the number of particles per unit volume. Thus the rate at which NO 2 and ClNO are formed in the reaction should be directly proportional to the concentrations of both ClNO 2 and NO. The Collision Theory model suggests that the rate of any step in a reaction is proportional to the concentrations of the reagents consumed in that step. The rate law for a one-step reaction should therefore agree with the stoichiometry of the reaction. The following reaction, for example, occurs in a single step.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Principles of Chemical Kinetics

  • Gorden Hammes(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  No account is taken of the internal motions of the reactants. The fact that every combination of initial and final states must be characterized by a different reaction cross section is not considered. In fact, the simplified-kinetic-theory treatment is based entirely on classical mechanics. Finally, although reaction cross sections are complicated averages of many inelastic cross sections associated with all possible processes by which reactants in a wide variety of initial states are converted to products in a wide variety of final states, the simplified kinetic theory approximates such cross sections by elastic cross sections appropriate to various transport properties, by cross sections deduced from crystal spacings or thermodynamic properties, or by order-of-magnitude estimates based on scientific experience and intuition. It is apparent, therefore, that the usual Collision Theory of reaction rates must be considered at best an order-of-magnitude approximation; at worst it is an oversimplification that may be in error in principle as well as in detail. 2-3 COLLISION DYNAMICS BY COMPUTER SIMULATION A straightforward approach toward the problem of calculating reaction rates is to divide the process into three distinct parts. First, the multidimensional potential energy surface reflecting the energy of interaction between all atoms must be determined. The many complexities involved in such a determination have already been discussed; it is sufficient to say here that an exact surface is not yet known for any chemical reaction. However, given a potential energy surface, the second part of the problem is to solve the quantum-mechanical or classical equations of motion as a function of all initial states 44 2. Theories of Chemical Kinetics of reactants and final states of products. The solution of these equations gives the cross sections for reaction.

  Sign up to read

  Learn more about book