Chemical reaction rates, collision rate constant

Because the collisions between ions and molecules in the gas phase are governed by physical (ion-dipole, ion-induced dipole) rather than chemical forces, it is possible to calculate rather accurately the collision rate constant (6, 7). We then express the efficiency of the reaction as the fraction of collisions which lead to products. 

Equation (15.10) is a linear equation of the type y = mx + b, where y = ln( ), m = —EJR = slope, x = 1/T, and b = ln(A) = intercept. Thus, for a reaction where the rate constant obeys the Arrhenius equation, a plot of n(k) versus 1/T gives a straight line. The slope and intercept can be used to determine the values of a and A characteristic of that reaction. The fact that most rate constants obey the Arrhenius equation to a good approximation indicates that the collision model for chemical reactions is physically reasonable. 

Su T, Chesnavich WJ. (1982) Parametrization of the ion-polar molecule collision rate-constant by trajectory calculations. J. Chem,. Phys. 76 5183-5185. Troe J, Lorquet JC, Manz J, Marcus RA, Herman M. (1997) Recent advances in statistical adiabatic channel calculations of state-specific dissociation dynamics. Chemical Reactions and Their Control on the Femtosecond Time Scale XXth Solvay Conference on Chemistry, Vol. 101, pp. 819-851. 

We define the reaction cross-section, ctr, in a way suggested by the definition of the total collision cross-section (Section 2.1.5). For molecules colliding with a well-defined relative velocity v, the reaction cross-section is defined such that the chemical reaction rate constant k v) is given by... 

II. Weak collision rate constants. Berichte Bunsenges. Phys. Chem. 87, 169-177 (1983) Gillespie, D.T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403-434 (1976)... 

Different from conventional chemical kinetics, the rates in biochemical reactions networks are usually saturable hyperbolic functions. For an increasing substrate concentration, the rate increases only up to a maximal rate Vm, determined by the turnover number fccat = k2 and the total amount of enzyme Ej. The turnover number ca( measures the number of catalytic events per seconds per enzyme, which can be more than 1000 substrate molecules per second for a large number of enzymes. The constant Km is a measure of the affinity of the enzyme for the substrate, and corresponds to the concentration of S at which the reaction rate equals half the maximal rate. For S most active sites are not occupied. For S >> Km, there is an excess of substrate, that is, the active sites of the enzymes are saturated with substrate. The ratio kc.AJ Km is a measure for the efficiency of an enzyme. In the extreme case, almost every collision between substrate and enzyme leads to product formation (low Km, high fccat). In this case the enzyme is limited by diffusion only, with an upper limit of cat /Km 108 — 109M. v 1. The ratio kc.MJKm can be used to test the rapid... 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

Another factor that affects the rate of a chemical reaction is the concentration of reactants. As noted, most reactions take place in solutions. It is expected that as the concentration of reactants increases more collisions occur. Therefore, increasing the concentrations of one or more reactants generally leads to an increase in reaction rate. The dependence of reaction rate on concentration of a reactant is determined experimentally. A series of experiments is usually conducted in which the concentration of one reactant is changed while the other reactant is held constant. By noting how fast the reaction takes place with different concentrations of a reactant, it is often possible to derive an expression relating reaction rate to concentration. This expression is known as the rate law for the reaction. 

We have seen that the polarization forces cause very large collision cross sections between ions and molecules, and it is experimentally observed that a chemical reaction occurs on almost every collision. Some observed ion molecule reactions and their observed rate constants and cross sections are tabulated in Table IV. In addition, several free radical reactions are shown for comparison purposes. Let us look at the reactions at the top of Table IV and try to understand why the reaction occurs. 

At sufficiently high pressure, kum is typically independent of pressure. The high-pressure limit of the rate constant will be denoted kunji00. Intermolecular collisions of C with other C molecules or with other chemical species present in the gas provide the energy needed to surmount the barrier to reaction, such as the breaking of a bond. The partner in such collisions will be genetically denoted M. 

In reaction 9.132, molecules A and B form the excited (energized) reactive intermediate species C. Translational energy of the reactant molecules from their relative motion before collision is converted to internal (vibrational, rotational) energy of C. Reaction 9.132 provides a chemical activation (excitation) of the unstable C, with rate constant ka. Note that 9.132 does not involve a third body M for creation of the excited intermediate species, which differs from the unimolecular initiation event in Eq. 9.100. 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

Reaction 10.99 converts translational energy from a C-M collision, where M generically represents any chemical species present in the gas, into internal energy of the (excited) C intermediate species. The energized C molecules can decompose to form product molecules A and B, reaction 10.100, with rate constant kd. Alternatively, C can be stabilized (deactivated) through collision with another molecule in the gas, the reverse of 10.99. 

The law of mass action (Equation 15-2) is always stated as applying to a given temperature, and it appears not to have temperature involved in its statement. Yet the rates of chemical reaction invariably increase markedly with increase in temperature. Because concentrations will be negligibly affected by temperature, the temperature-sensitive factor in the law of mass action must be the rate constant, 1. As a good approximation, we say that k is proportional to the fraction of molecules (or collisions) that have the required enthalpy of activation ... 

The temporal resolution of both methods is limited by the risetime of the IR detectors and preamplifiers, rather than the delay generators (for CS work) or transient recorders (SS) used to acquire the data, and is typically a few hundred nanoseconds. For experiments at low total pressure the time between gas-kinetic collisions is considerably longer, for example, approximately 8 /is for self-collisions of HF at lOmTorr. Nascent rotational and vibrational distributions of excited fragments following photodissociation can thus be obtained from spectra taken at several microseconds delay, subject to adequate SNR at the low pressures used. For products of chemical reactions, the risetime of the IR emission will depend upon the rate constant, and even for a reaction that proceeds at the gas-kinetic rate the intensity may not reach its maximum for tens of microseconds. Although the products may only have suffered one or two collisions, and the vibrational distribution is still the initial one, rotational distributions may be partially relaxed. 

A simple way of analyzing the rate constants of chemical reactions is the collision theory of reaction kinetics. The rate constant for a bimolecular reaction is considered to be composed of the product of three terms the frequency of collisions, Z a steric factor, p, to allow for the fraction of the molecules that are in the correct orientation and an activation energy term to allow for the fraction of the molecules that are sufficiently thermally activated to react. That is,... 

When the chemical reaction step occurs very rapidly (virtually instantaneously upon collision of the reactants), one speaks of a diffusion-controlled reaction and in this case, the reaction rate constant is typically on the order of 1010 M-1 s-1. When the chemical reaction is slow as compared to the collisional process, the reaction is often called an activation-controlled reaction because a high activation energy is needed to yield the products. The rate constant is thus on the order on 1 M-1 s 1. In the general case, the reaction rate constant is a combination of the two processes and is described by the following expression ... 

On the other hand, the effective collision concept can explain the Arrhenius term on the basis of the fraction of molecules having sufficient kinetic energy to destroy one or more chemical bonds of the reactant. More accurately, the formation of an activated complex (i.e., of an unstable reaction intermediate that rapidly degrades to products) can be assumed. Theoretical expressions are available to compute the rate of reaction from thermodynamic properties of the activated complex nevertheless, these expression are of no practical use because the detailed structure of the activated complexes is unknown in most cases. Thus, in general the kinetic parameters (rate constants, activation energies, orders of reaction) must be considered as unknown parameters, whose values must be adjusted on the basis of the experimental data. 

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