Rate of collision

Notice from the rate expressions just written that the rate of an elementary step is equal to a rate constant k multiplied by the concentration of each reactant molecule. This rule is readily explained. Consider, for example, a step in which two molecules, A and B, collide effectively with each other to form C and D. As pointed out earlier, the rate of collision and hence the rate of reaction will be directly proportional to the concentration of each reactant. 

This response time should be compared to the turbulent eddy lifetime to estimate whether the drops will follow the turbulent flow. The timescale for the large turbulent eddies can be estimated from the turbulent kinetic energy k and the rate of dissipation e, Xc = 30-50 ms, for most chemical reactors. The Stokes number is an estimation of the effect of external flow on the particle movement, St = r /tc. If the Stokes number is above 1, the particles will have some random movement that increases the probability for coalescence. If St 1, the drops move with the turbulent eddies, and the rates of collisions and coalescence are very small. Coalescence will mainly be seen in shear layers at a high volume fraction of the dispersed phase. 

According to Trautz and Lewis, who gave the first treatment of reaction rates in terms of the kinetic theory of collisions in 1916-1918, the rate of collisions (not yet reaction) between the spheres A and B is jtd u... 

With the expression for the average velocity we arrive at the following expression for the rate of collisions between A and B per unit volume ... 

As we are particularly interested in surface reactions and catalysis, we will calculate the rate of collisions between a gas and a surface. For a surface of area A (see Fig. 3.8) the molecules that will be able to hit this surface must have a velocity component orthogonal to the surface v. All molecules with velocity Vx, given by the Max-well-Boltzmann distribution f(v ) in Cartesian coordinates, at a distance v At orthogonal to the surface will collide with the surface. The product VxAtA = V defines a volume and the number of molecules therein with velocity Vx is J vx) V Vx)p where p is the density of molecules. By integrating over all Vx from 0 to infinity we obtain the total number of collisions in time interval At on the area A. Since we are interested in the collision number per time and per area, we calculate... 

The rate of adsorption of a gas on a surface is determined by the rate of collision between the gas and the surface and by the sticking coefficient ... 

In Lab 17.1, you learned about the effect of temperature and concentration on reaction rate. Another factor that affects reaction rate is the amount of surface area of the reactants. If a chemical reaction is to take place, the molecules of reactants must collide. Changing the amount of surface area modifies the rate of collision, and, thus, the rate of reaction. If surface area increases, collision frequency increases. If surface area decreases, so does the number of collisions. In this lab, you will examine the effect of surface area on rate of reaction. You will also determine how a combination of factors can affect reaction rate. 

Approximation refers to the bringing together of the substrate molecules and reactive functionalities of the enzyme active site into the required proximity and orientation for rapid reaction. Consider the reaction of two molecules, A and B, to form a covalent product A-B. For this reaction to occur in solution, the two molecules would need to encounter each other through diffusion-controlled collisions. The rate of collision is dependent on the temperature of the solution and molar concentrations of reactants. The physiological conditions that support human life, however, do not allow for significant variations in temperature or molarity of substrates. For a collision to lead to bond formation, the two molecules would need to encounter one another in a precise orientation to effect the molecular orbitial distortions necessary for transition state attainment. The chemical reaction would also require... 

An evaluation of the number of moon craters per unit area (differentiated according to the diameter of the craters) as a function of the time at which the collisions leading to their formation occurred indicates that the processes involved were similar to those which could have occurred on Earth. It is likely that the bombardment reached a maximum around four billion years ago and dropped after about another billion years to the present rate of collision (Neukum, 1987). 

Which of the following changes will decrease the rate of collisions between gaseous molecules of type A and B in a closed container ... 

With all other factors held constant, decreasing the number of molecules decreases the chance of collision. Adding an accelerating catalyst has no effect on the rate of collisions. It lowers the activation energy, thereby increasing the chance for effective molecular collisions. Furthermore, it increases the rate of production. 

The rate of collision of gas molecules is given by gas kinetic theory. Molecules have an average kinetic energy given by the expression... 

Now putting all these together, we obtain a rate of collision of A with B... 

The rate of collision a) is determined by the rate of diffusion of the ions to the surface, and by the electrostatic attraction between the ions. The former is equivalent to the action of a force equal BT... 

Since N and Wj are constants for the same surfe.ce we may write this expression as (1 — di) n, where is a constant. In comparison with the enormous electrostatic field the diffusive force is negligible. Under these conditions the rate of collision is given by... 

The condensation of low-volatility vapors on preexisting particles depends on a number of factors, including the rate of collisions of the gas with the surface, the probability of uptake per collision with the surface, i.e., the mass accommodation coefficient (see Chapter 5.E.1), the size of existing particles, and the difference in partial pressure of the condensing species between the air mass and the particle surface. While some of these parameters are reasonably well known, others are not. For example, mass accommodation coefficients for the complex surfaces found in the atmosphere are not well known. Indeed, the exact nature of the surfaces themselves, which determines the uptake and the partial pressures of gases at the surface, remains a research challenge. 

Assuming only that the rate of reaction depends directly on the rate of collisions between CO and 02, an initial rate can be calculated and then compared with an experimental reaction rate. The calculated value overestimates the reaction rate... 

It is interesting to examine Eq. 9.138 in the limits of very high and very low pressure. At very high pressure the rate of collision of the excited intermediate C with other species M is very high. Thus the stabilization process is expected to be much faster than the decomposition and reaction rates ... 

Eq. 10.20. We want to derive the rate of collisions with one of the walls perpendicular to the x axis, for example. 

In a simple view, the rate of surface reaction is just the rate of collision with the surface times the probability that a collision results in a reaction. We denote the later term as the sticking coefficient (probability) y. 

The primary characteristic frequency of an ordinary gas is the rate of collision f = V / A = ttVtiD2 y where V is the mean particle velocity, and V = (8 kT I KWifl2 for particles of mass m. Among the special frequencies associated with plasmas, the most notable is the plasma frequency ... 

To set up a quantitative theory based on this qualitative picture, we need to know the rate at which molecules collide and the fraction of those collisions that have at least the energy min. The rate of collisions (the number of collisions per second) between A and B molecules in a gas at a temperature T can be calculated from the kinetic model of a gas ... 

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