Rates of molecular collisions

For a soluble enzyme that is not part of a multi-enzyme complex, the fastest rate of enzyme-inhibitor association is determined by the rate of molecular collisions between the two binding partners (i.e., the enzyme and the inhibitor) in solution. The rate of molecular collisions is in turn controlled by the rate of diffusion. The diffusion-limited rate of molecular collisions is dependent on the radii of the two binding molecules and the solution temperature and viscosity (Fersht, 1999) ... 

In this section, we consider the total rate of molecular collisions without considering whether they result in reaction. This treatment introduces many of the concepts used in collision-based theories the criteria for success are included in succeeding sections. 

Both parts (a) and (b) of Example 6-1 illustrate that rates of molecular collisions are extremely large. If collision were the only factor involved in chemical reaction, the rates of all reactions would be virtually instantaneous (the rate of N2-02 collisions in air calculated in Example 6-l(a) corresponds to 4.5 X107 mol L-1 s-1 ). Evidently, the energy and orientation factors indicated in equation 6.4-2 are important, and we now turn attention to them. 

With all other variables held constant, choice (D) would reduce the rate of molecular collisions, but increasing the volume is analogous to decreasing the concentration. 

The rate of molecular collisions with a wall of area A given by 1 N ... 

We now want to study the rate of molecular collisions in our model hard-sphere gas of a single substance. In this model system a molecule moves at a constant velocity between collisions. We first pretend that only particle number 1 is moving while the others are stationary and distributed uniformly throughout the container. The mean number of stationary particles per unit volume is given by... 

Several closures have been proposed to calculate the collision density for molecules in gas mixtures [109] (pp. 52-55). To derive these expressions for the collision density one generally perform an analysis of the particle-particle interactions in an imaginary container [80, 109, 135], called the conceptual collision cylinder in kinetic theory, as outlined in Sect. 2.4.2.5. A fundamental assumption in this concept is that the rate of molecular collisions in a gas depends upon the size, number density, and average speed of the molecules. Following Maxwell [95] each type of molecules are considered hard spheres, resembling billiard balls, having diameter dg, mass ntg and number density These hard spheres exert no forces on... 

Will Flask b react faster or slower or at the same rate as Flask a By how much Explain your reasoning in terms of molecular collisions. 

Chemical processes, in contrast, are processes that are not limited by rates of energy transfer. In thermal processes, chemical reactions occur under conditions in which the statistical distribution of molecular energies obey the Maxwell-Boltzmann form, i.e., the fraction of species that have an energy E or larger is proportional to e p(—E/RT). In other words, the rates of intermolecular collisions are rapid enough that all the species become thermalized with respect to the bulk gas mixture (Golden and Larson, 1984 Benson, 1976). 

EXAM PLE 9.6 Rate of Atomic Collisions as a Function of Pressure. Assuming 1019 atoms per square meter as a reasonable estimate of the density of atoms at a solid surface, estimate the time that elapses between collisions of gas molecules at 10 6 torr and 25°C with surface atoms. Use the kinetic molecular theory result that relates collision frequency to gas pressure through the relationship Z = 1/4 vNIV, for which the mean velocity of the molecules v = (BRTI-kM) 12 and NIV is the number density of molecules in the gas phase and equals pNJRT. Repeat the calculation at 10 8 and 10 10 torr. 

The bubbling occurs as the result of a reaction between the Alka-Seltzer tablet and the water. In the alcoholic beverage there is a lower proportion of water molecules, which leads to a slow rate of reaction. In terms of molecular collisions, with fewer water molecules around, the probability of collisions between the molecules of the Alka-Seltzer and the water is less in the alcoholic beverage. 

Equation (3.35) is a precursor to the Arrhenius equation relating the rate constant [k in Eq. (3.30)] to the probability of molecular collisions (to) and the activated energy (Ea) of a reaction. Polysaccharide viscous flow is characterized by a modified Arrhenius equation in which T j/i 0 replaces k ... 

The concept of potential-energy surface (or just potentials) is of major importance in spectroscopy and the theoretical study of molecular collisions. It is also essential for the understanding of the macroscopic properties of matter (e.g., thermophysical properties and kinetic rate constants) in terms of structural and dynamical parameters (e.g., molecular geometries and collision cross sections). Its role in the interpretation of recent work in plasmas, lasers, and air pollution, directly or otherwise related to the energy crisis, makes it of even greater value. 

The Collision Theory of Bimolecular Gaseous Reactions. This is the earliest theory of reaction rates. Since reaction between two species takes place only when they are in contact, it is reasonable to suppose that the reactant species must collide before they react. Since our knowledge of molecular collisions is more complete for the gaseous phase than for the liquid phase (in the latter case we speak of encounters rather than collisions), we will restrict our discussion to bimolecular reactions in the gaseous phase. 

For elementary reactions and ideal reaction mixtures, the reaction rate is proportional to the concentration of each of the reactants, since the number of molecular collisions per unit time is proportional to it. For example, for a bimolecular elementary reaction ... 

Collisions lie at the very heart of chemistry, because chemical reactions can occur only when molecules collide with one another. The kinetic theory of gases provides methods for estimating the frequency of molecular collisions and the average distance traveled by a molecule between collisions, both important in understanding the rates of chemical reactions (See Chapter 18). 

If we knew enough about the process and geometry of molecular collisions, of course, we could calculate the probabilities referred to above then the first observed experimental rate of conversion would serve to test the success... 

The kinetic molecular theory of gases (p. 178) postulates that gas molecules frequently collide with one another. Therefore, it seems logical to assume—and it is generally true—that chemical reactions occur as a result of collisions between reacting molecules. In terms of the collision theory of chemical kinetics, then, we expect the rate of a reaction to be directly proportional to the number of molecular collisions per second, or to the frequency of molecular collisions ... 

The collision theory is intuitively appealing, but the relationship between rate and molecular collisions is more complicated than you might expect. The implication of... 

Apo Al, like apo B, is secreted mainly from liver and intestinal cells. Unlike apo B, however, apo Al is secreted in lipid-free or lipid-poor from. The cholesterol and phospholipids that are transferred to HDLs move down concentration gradients driven by the plasma enzyme lecithinxholesterol acyltransferase (LCAT). LCAT, which is bound to HDL, converts cholesterol and phosphatidylcholine to insoluble CE and lysophos-phatidylcholine (Section 3.4), which is soluble and is transferred to albumin in the plasma. Cholesterol has a small but significant solubility and, as a result, can be transferred spontaneously from cell and lipoprotein surfaces to apo Al. Cholesterol may also be transferred as a result of molecular collision between lipoprotein particles. The LCAT reaction consumes equal amounts of cholesterol and phospholipids, but the rate at which phospholipids are transferred spontaneously between cells and lipoproteins is much lower... 

The rate of a chemical reaction is determined by the number of molecular collisions with sufficient energy and with the proper orientation in a given period of time (Section 3.7) ... 

An approximate estimate of the effects of molecular collisions, i.e. convection, on the sublimation rate can be derived with the aid of the... 

Think of the excited state electrons as objects on a shelf. The electrons will have a natural tendency to fall off the shelf at a rate ( intrinsic) that will depend on the specific molecular structure. If, in addition, the shelf is being rattled by the continual Brownian motion bombardment of surrounding molecules and groups, then the electrons may be displaced by environmental interactions. The rate at which this occurs ( environmental) will depend on the frequency of molecular collisions (temperature) and on the size and polarity of the colliding species. For example, more polar molecules in the surrounding solvent will tend to interact more readily with the excited state electrons owing to electrostatic forces. So we might anticipate that fluorescence intensities will be reduced by an increase in temperature or by transfer to a more polar solvent. 

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