Billiard ball reaction

Not every collision, not every punctilious trajectory by which billiard-ball complexes arrive at their calculable meeting places leads to reaction. 

It is easier to explain why W, = Q3 if we say that the energy fV, was stored in the chemical substances H2(g) and O (g). We assign to these (and all other) substances the capacity to store energy and we call it heat content. This permits us to say that energy is conserved at all times during a chemical reaction as it is in billiard ball collisions and in stretched rubber bands. 

Conservation of energy in a billiard ball collision, 114 in a chemical reaction, 115 in a stretched rubber band, 114 law of, 113, 117, 207 Constant heal summation law, 111 Contact process, HtSO<, 227 Coordination number, 393 Copper... 

The time at which the reactions occur is, of course, of vital importance in helping to arrive at reasonable views of possible mechanisms, and represents one of the most tantalizing questions in the field. While at one time it was thought possible that the reactions could be simple, high-energy, billiard-ball collisions (54, 58), the likelihood of that occurring is small (95) and in any event could not account for the formation of compounds other than the parent. It is probable that the reformation of most molecules occurs in a stepwise fashion ... 

If we assume that molecules can be considered as billiard balls (hard spheres) without internal degrees of freedom, then the probability of reaction between, say, A and B depends on how often a molecule of A meets a molecule of B, and also if during this collision sufficient energy is available to cross the energy barrier that separates the reactants, A and B, from the product, AB. Hence, we need to calculate the collision frequency for molecules A and B. 

First, we recognize that reaction is likely to occur only when reactants meet. An encounter between two molecules in a gas is a collision, so the model we are about to build is called the collision theory of reactions. In this model, we suppose that molecules behave like defective billiard balls they bounce apart if they collide at low speed, but they might smash into pieces when the impact is really energetic. If two molecules collide with less than a certain kinetic energy, they simply bounce apart. If they meet with more than that energy, bonds can break and new bonds can form (Fig. 13.16). Let s denote the minimum kinetic energy needed for reaction by Emin. 

The simplest way of including the full interaction of the two final-state electrons is to use the impulse approximation. In its simplest plane-wave form this approximation is obtained from (10.14) by neglecting v and vi in the definition of the collision state T ( (k/,kj)). It retains the two-electron function (/> (k, r). In the spirit of this approximation it replaces x + (ko)) with a plane wave. We expect the plane-wave impulse approximation to describe kinematic regions where the two-electron collision dominates the reaction mechanism such as the higher-energy billiard-ball range. 

A molecule swimsy dtspersing its functionality scattering Us reactive centers. Not every collisioriy not every punctilious trajectory by which billiard-ball complexes arrive at their calculable rneeiin places leads to reaction. Most encounters end in a harmless sideways swipe. An exchange of momentumy a mere deflection. And so it is for us. 

A collision between atoms, molecules, or ions is not like one between two hard billiard balls. Whether or not chemical species collide depends on the distance at which they can interact with one another. For instance, the gas-phase ion-molecule reaction CH4+ + CH4 CH5+ + CH3 can occur with a fairly long-range contact. This is because the interactions between ions and induced dipoles are effective over a relatively long distance. By contrast, the reacting species in the gas reaction CH3 + CH3 C2H are both neutral. They interact appreciably only through very short-range forces between induced dipoles, so they must approach one another very closely before we could say that they collide. ... 

Carceplexes have also been synthesized using templates from cavitands with functionalities other than phenols. Cram synthesized benzylthia-bridged carceplex 13 guest through the shell-closure reaction between tetra(benzyl chloride) cavitand 11 and tetra-benzylthiol cavitand 12 in the solvents 2-butanone, 3-pentanone, ethanol/benzene (1 2), dimethylformamide (DMF), methanol/benzene (2 1), and acetonitrile/benzene (2 1), yielding carceplexes 13-2-butanone, 13-3-pentanone, 13-ethanol, 13-DMF, 13-2 methanol, and 13-2 MeCN respectively (Scheme 4-6) [22]. Technically, 13-2 MeCN is a hemicarceplex, as one acetonitrile molecule was found to escape the interior of the host via a billiard-ball effect, leaving 13-MeCN when heated in toluene [22]. The forma-... 

The billiard ball atom-atom collisions favouring the easier replacement of D do not explain the observed experimental deuterium isotope effects in substitution reactions with hot tritium. The linear structures, T— H—R , of the transition states have also been rejected. An attempt has been made to rationalize the experimental findings by... 

W. F. Libby USA Billiard ball collision concepts in hot atom chemical reentry reaction... 

The SCT model considers reaction between chemical species A and B, each considered to be structureless, spherical masses that interact according to the hard sphere potential V(r) — 0, r>dAB V(r) = CO, r — dAB, and all collisions result in reaction. The last may be restated as a reaction probability the probability of chemical reaction, F(r), is 1 when r — <7ab and 0 otherwise. The collision diameter, <7ab — (<5 a + <5 b)/ 2, where <7a and <7b are the molecular diameters of A and B, respectively, defines the interaction distance for these billiard ball-like collisions. The collision rate, Zab, is... 

There are two types of nuclear reactions. The first is the radioactive decay of bonds within the nucleus that emit radiation when broken. The second is the billiard ball type of reaction where the nucleus, or a nuclear particle (like a proton), is struck by another nucleus or nuclear particle. It is easy to remember these with the following element decay radiation (see Figure 11.3). 

A collision between atoms, molecules, or ions is not like one between two hard billiard balls. Whether or not chemical species collide depends on the distance at which they can interact with one another. For instance, the gas-phase ion-molecule reaction... 

Starting at the top of the first column, recall how some early laws had firmly established that chemical compounds are always made up of the same definite composition by mass (Proust) and that this mass is always conserved in various reactions (Lavoisier). These empirical (from experiment) facts led to the first concrete atomic theory, developed at the outset of the nineteenth century by the English chemist John Dalton. Dalton assumed that atoms were hard, impenetrable spheres much like miniature billiard balls. He had no occasion (at least in writing) to speculate about their inner structures. 

Consider a reaction between molecules A and B. The rate expression for molecules that are essentially billiard balls, or hard spheres, will be discussed first. Later studied will be features due to the presence of internal degrees of freedom, which are absent in hard spheres. The description of reaction rates in terms of the kinetic theory of collisions was given by Max Trautz in 1916 and William Lewis in 1918. The rate for collisions between hard spheres is... 

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