Collision of two molecules

Equation A3.11.115(a) is also useful as a fonn that enables easy generalization of the potential scattering theory that we have just derived to multistate problems. In particular, if we imagine that we are interested in the collision of two molecules A and B starting out in states then the asymptotic wavefimction analogous to equation (A3.11.106) is... 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

The most common type of elementary process is a bimolecular reaction that results from the collision of two molecules, atoms, or ions. The collision of two NO2 molecules to give N2 O4 is a bimolecular reaction. Here is another example ... 

Because quenching involves the collision of two molecules, its rate is effectively controlled by diffusion processes. The values of kQ for various solvents and temperatures (commonly of the order of kQ = 109-1010mol 1 dm3s 1) are well documented hence a value for the triplet lifetime may be obtained. 

A quantity, /x, used in collision theory for the collision of two molecules having masses mA and OTb It is equal to mAmB/ipiA + OTb). See Hooke s Law Spring Kinetic Isotope Effects... 

This is the product of the collision rate z and the half of the particle number density n, since the collision of two molecules is to be counted as only one collision ... 

If we consider the collisions of two molecules (rather than atom + molecule, as above), the number of coupled channels is approximately the square of the number of accessible internal states of either molecule separately. Thus for rotational excitation of two hydrogen molecules near room temperature, Nc (jmax/2 + = 81 for Jmax = 4> and quantum calculations are... 

It is highly interesting from the point of view of general kinetics that even for such simple and stable molecules as oxygen and nitrogen the chain mechanism presents kinetically an easier path for the reaction than the direction reaction following the collision of two molecules. 

Function (2.2) can be considered as an empirical model used to best fit the experimental concentration-time data. In practice, laws different from (2.2) are also encountered, especially when dependence on the concentration is considered however, a simple theory based on the kinetic theory of gases can only explain the simplest of these empirical rate laws. The general idea of this theory is that reaction occurs as a consequence of a collision between adequately energized molecules of reactants. The frequency of collision of two molecules can explain simple reaction... 

The calculation uses, at least partially, the mechanical properties of the gas model. In particular it uses the laws for the collisions of two molecules in order to calculate, when the type of collision is specified, the domains of state (At) into which two molecules are thrown from given domains of state. 

This distance is often called the mean free path. As we can see, it is inversely proportional to the number of particles per unit volume, or the density, and inversely proportional to the collision cross section. The mean free path is most commonly discussed for the ordinary elastic collisions of two molecules in a gas. For such collisions, the collision cross sections come out of the order of magnitude of the actual cross sectional areas of the molecules that is, of the order of magnitude of... 

This one-step nucleophilic substitution is an example of the SN2 mechanism. The abbreviation SN2 stands for Substitution, Nucleophilic, bimolecular. The term bimolecular means that the transition state of the rate-limiting step (the only step in this reaction) involves the collision of two molecules. Bimolecular reactions usually have rate equations that are second order overall. 

Bimolecular step a reaction involving the collision of two molecules. (15.6)... 

A reaction of this sort, in which the reaction occurs on collision of two molecules, is called a bimolecular reaction. 

In this type of reaction, reactant molecule A can be activated coherently by photochemical irradiation using a femtosecond laser pulse, and activated A undergoes a subsequent reaction without collision with other molecules. It is very difficult, in principle, to adjust collisions of two molecules coherently. Therefore, it is rather difficult to apply femtosecond laser pulse technology to conduct a bimolecular reaction, shown in Equation (2.2), like a unimolecular reaction. It is difficult to achieve the collision of two molecules A and B coherently. 

It is also worth noting that many reactions consist of two or more reaction components in chemical synthesis, because they are useful to construct molecules however, most reaction dynamics studies deal with unimolecular reactions because it is difficult to arrange coherent collisions of two molecules. In time-efficient chemical synthesis, it is also important to know how to achieve collisions of two molecules in a very short period to accelerate bimolecular reactions. 

Reactions that require the collision of two molecules are called bimolecular, and they are schematically represented as follows ... 

Thus, in this single act of collision, the reactants disappear and the products are formed. The reverse of this reaction is also an elementary reaction, the collision of two molecules of HI to form H2 and I2. 

Apparently the reaction as written is elementary and involves the simultaneous collision of two molecules of NO with one molecule of O2. A remarkable feature of this reaction is that th rate of the reaction decreases with increase in temperature. This behavior is exhibited by only a very few reactions. 

The reason for the equality between the rate of reaction in the gas and that in the solution can be explained rather simply in terms of the collision theory. Suppose a reaction requires the collision of two molecules in a pure gas A ... 

The most favored decomposition reaction is the cleavage of SiCU, which, after numerous repetitions, should lead to Si02 and SiCU. Considering the discussed decomposition reactions from a molecular view point (kinetic aspect) also leads to a clear preference for decomposition reaction (a) For reaction (a) to occur, only the necessary activation energy from a collision with an energy-rich molecule or the (hot) wall of the reaction vessel has to be supplied. For reactions (b) and (c) to become operative, however, a collision of two molecules of equal composition is necessary. This is rather improbable in the complex reaction mixture. Unimolecular reactions which lead to products under (b) or (c) are not conceivable. 

The collision of two molecules does not alter the overall energy of both molecules. 

In contrast to intramolecular, solution-based fission, diffusional fission requires the collision of two molecules, one photoexcited and the other in its ground state, to produce a triplet exciton on each molecule (Fig. 5). Two important faetors distinguish collisional singlet fission systems molecules have the geometric freedom to find an optimal singlet fission geometry, and the singlet fission rate is limited to the rate of the diffusion of the molecules in the solvent. 

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