Surface area, collision theory

Case B Radicals enter both micelles and polymer particles at rates that are proportional to their surface areas (collision theory), so that the rate of new particle formation is given by... 

Complete the following concept map using the following terms surface area, collision theory, temperature, reaction rates, concentration, reactivity, catalyst. 

Summarize the collision theory and how surface area applies to reaction rates. 

The BET surface area equation is based on Langmuir s kinetic theory of monolayer gas adsorption on surfaces [6], Langmuir theorized that the collision... 

You can also use simple collision theory to explain why increasing the surface area of a solid-phase reactant speeds up a reaction. With greater surface area, more collisions can occur. This explains why campfires are started with paper and small twigs, rather than logs. Figure 6.8 shows an example of the effect of surface area on collision rate. 

Use collision theory and transition state theory to explain how concentration, temperature, surface area, and the nature of reactants control the rate of a chemical reaction. 

In your own words, describe how collision theory explains why increased surface area increases the rate of a reaction. 

Collision theory can be used to define rate constants for adsorption processes in terms of the number of gas-phase molecules colliding with a surface per unit area per unit time, F" ... 

A related matter concerns the physical mechanism by which radicals (primary or oligomeric) are acquired by the reaction loci. One possibility, first proposed by Garden (1968) and subsequently developed by Fitch and Tsai (1971), is that capture occurs by a collision mechanism. In this case, the rate of capture is proportional to, inter alia, the surface area of the particle. Thus, if the size of the reaction locus in a compartmentalized free-radical polymerization varies, then a should be proportional to r, where r is the radius of the locus. A second possibility (Fitch, I973) is that capture occurs by a diffusion mechanism. In this case, the rate of capture is approximatdy proportional to r rather than to r. A fairly extensive literature now exists concerning this matter (see, e.g., Ugelstad and Hansen, 1976, 1978. 1979a, b). The consensus of present opinion seems to favor the diffusion theory rather than the collision theory. The nature of the capture mechanism is not. however, relevant to the theory discussed in this chapter. It is merely necessary to note that both mechanisms predict that the rate of capture will depend on the size of the reaction locus constancy of a therefore implies that the size of the locus does not change much as a consequence of polymerization. 

Now suppose you were to lower a red-hot chunk of steel instead of steel wool into a flask of oxygen gas. The oxygen would react with the steel much more slowly than it would with the steel wool. Using what you know about the collision theory, can you explain why You are correct if you said that, for the same mass of iron, steel wool has much more surface area than the chunk of steel. The greater surface area of the steel wool allows the oxygen molecules to collide with many more iron atoms per unit of time. 

Aerosols are unstable with respect to coagulation. The reduction in surface area that accompanie.s coalescence corresponds to a reduction in the Gibbs free energy under conditions of constant temperature and pressure. The prediction of aerosol coagulation rates is a two-step process. The first is the derivation of a mathematical expression that keeps count of particle collisions as a function of particle size it incorporates a general expression for tlie collision frequency function. An expression for the collision frequency based on a physical model is then introduced into the equation Chat keep.s count of collisions. The collision mechanisms include Brownian motion, laminar shear, and turbulence. There may be interacting force fields between the particles. The processes are basically nonlinear, and this lead.s to formidable difficulties in the mathematical theory. 

Reinhard Schinke received his Ph.D. in physics in 1976 at the University of Kaiserslautern, Germany, working in the held of molecular collision theory. In 1980, after 1 year at the IBM research laboratory in San Jose, California, as a postdoc, he entered the department of molecular interactions at the Max-Planck Institute for Fluid Dynamics in Goettingen where he has remained since. His research switched from collisions to the area of photodissociation and more recently to unimolecular reactions. Currently he studies the recombination of ozone with particular emphasis on a dynamical explanation of the pronounced isotope effect, which has been observed both in the atmosphere and in the laboratory. Throughout his scientihc career, he has tried to understand experimental observations on the basis of accurate potential energy surfaces and exact dynamics calculations. 

In the case of the condensation of a vapor with pressure p", the frequency of the attachment of molecules to a unit of surface area of the critical nucleus may be considered to be equal to the collision frequency of molecules with the surface. The latter, in agreement with molecular-kinetic theory, is given by... 

While the paramagnetic substances hemin, hematin, and copper phthalocyanine catalyze the conversion at room temperature, the diamagnetic hematoporphyrin and metal-free phthalocyanine are inactive (67). No catalysis was found for the H2-fD2 reaction. Since the surface area of the hemin crystals could be estimated, the collision efficiency of the conversion could be calculated. The value of 10 ° so determined is in reasonable agreement with Wigner s theory (59). 

At this time it had become possible to determine experimentally total surface area and the distribution of sizes and total volume of pores. Wheeler set forth to provide the theoretical development of calculating the role of this pore structure in determining catalyst performance. In a very slow reaction, reactants can diffuse to the center of the catalyst pellet before they react. On the other hand, in the case of a very active catalyst containing small pores, a reactant molecule will react (due to collision with pore walls) before it can diffuse very deeply into the pore structure. Such a fast reaction for which diffusion is slower than reaction will use only the outer pore mouths of a catalyst pellet. An important result of the theory is that when diffusion is slower than reaction, all the important kinetic quantities such as activity, selectivity, temperature coefficient and kinetic reaction order become dependent on the pore size and pellet size with which a pellet is prepared. This is because pore size and pellet size determine the degree to which diffusion affects reaction rates. Wheeler saw that unlike many aspects of heterogeneous catalysis, the effects of pore structure on catalyst behavior can be put on quite a rigorous basis, making predictions from theory relatively accurate and reliable. 

But the rate of collision of gas molecules with a surface is a familiar result of the kinetic theory of gases the number of molecules striking a unit of surface area per unit time is proportional to the mean molecular velocity v and to the number density c of molecules in the gas ... 

It should be noted that the derivation of Eq. (3.5) is based on the assumption that free radicals are captured by monomer-swollen micelles or particle nuclei at a rate that is proportional to their surface area (termed the collision theory [15]). In this case, there is no free radical concentration gradient surrounding the colloidal particle. It would be more appropriate to use the diffusion theory [17,18] to calculate the rate of entry of free radicals into micelles or particle nuclei if this concentration gradient does exist. The diffusion theory proposes that the rate of entry of free radicals into a colloidal particle is equal to 2ndpDy R y, where dp is the diameter of the particle, D is the diffusion coefficient of free radicals in water, and [R ] , is the bulk concentration of free radicals in water. It is generally accepted that the diffusion theory is more realistic to describe the absorption of free radicals by micelles or particle nuclei [19]. The detailed reaction mechanisms involved in the entry of free radicals into monomer-swollen micelles or particle nuclei will be discussed in Chapter 4. 

Boyle s Law Boyle s law states that for a constant number of particles at constant temperature, the volume of a gas is inversely proportional to its pressure. According to kinetic molecular theory, if you decrease the volume of a gas, you force the gas particles to occupy a smaller space. As long as the temperature remains the same, the number of collisions with the surrounding surfaces (per unit surface area) must necessarily increase, resulting in a greater pressure. 

When we explain the effects of concentration, temperature, surface area and catalysts on rates of reaction, we use the collision theory. Collision theory states that in order to react with each other, particles must collide in the correct orientation and with sufficient energy. The particles might be atoms, ions or molecules. 

In chemical kinetics a reaction rate constant k (also called rate coefficient) quantifies the speed of a chemical reaction. The value of this coefficient k depends on conditions such as temperature, ionic strength, surface area of the adsorbent or light irradiation. For elementary reactions, the rate equation can be derived from first principles, using for example collision theory. The rate equation of a reaction with a multi-step mechanism cannot, in general, be deduced from the stoichiometric coefficients of the overall reaction it must be determined experimentally. The equation may involve fractional exponential coefficients, or may depend on the concentration of an intermediate species. 

Contamination from the gas phase will be proportional to the number of collisions a surface undergoes. Hence, from kinetic theory, the number of collisions per unit time and unit area, Zc, is given by ... 

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