Dependence upon particle concentration

These apply to a bimolecular reaction in which two reactant molecules become a single particle in the transition state. It is evident from Eqs. (6-20) and (6-21) that a change in concentration scale will result in a change in the magnitude of AG. An Arrhenius plot is, in effect, a plot of AG against 1/T. Because a change in concentration scale alters the intercept but not the slope of an Arrhenius plot, we conclude that the values of AG and A, but not of A//, depend upon the concentration scale employed for the expression of reactant concentrations. We, therefore, wish to know which concentration scale is the preferred one in the context of mechanistic interpretation, particularly of AS values. 

FIGURE 10.2 The passive diffusion of a charged species across a membrane depends upon the concentration and also on the charge of the particle, Z, and the electrical potential difference across the membrane, Ai/<. 

Smith, R. D., Campbell, J. A. Nielson, K. K. 1979. Concentration dependence upon particle size of volatilized elements in fly ash. Environmental Science and Technology, 13, 553-558. 

Several investigators have reported a particle concentration effect associated with the sorption of hydrophobic solutes. The decrease in the amount sorbed with increasing particle concentration is most pronounced for compounds characterized by large partitioning (Kd > 1000 mL/g). O Conner and Connolly (1980) reported observations that linear partition coefficients are inversely dependent upon the concentration of the solids in the system. Voice et al. (1983) also observed a significant increase in sorption as the solids concentration decreased and attributed it to the presence of microparticles contributed by the solids and not removed from suspension in the separation procedure. This suggests that sorption coefficients produced in studies using different techniques are not necessarily comparable. 

Particle Temperature Overshoot. The temperature of the burning char particles will run hotter than that of the bed by amounts that depend upon particle size, reactivity, bed temperature. It is determined in part by the heat released at the particle surface due to reaction and in part to the additional heat released by carbon monoxide oxidation near the particle surface (54-58). Measurements for 1.8 to 3.2 millimeter size coke particles burning in a fluidized band of sand at 1173 K increased from the bed temperature at low oxygen concentrations to values 150 to 200 K above the bed temperature for oxygen concentrations approaching that of air (72). Estimation of this temperature rise is important for purposes of evaluating the NO/C reaction and also for prediction of the burnout times of fines. 

At temperatures above the softening point, isotropic pitch often displays Newtonian flow characteristics (18,19), but this may well depend upon the concentration of any insoluble particles (i.e., primary QI in the case of coal tar based materials) present within the pitch. A high concentration of QI could lead to non-Newtonian character as a result of the particle-particle attractive forces. Figure 3 shows n -T curves for a variety of pitch materials and their pyrolysis products. Pyrolysis increases the Tg of the system and shifts the viscosity-temperature curve to higher temperatures. 

Denoyel and coworkers [61] used a thermodynamic adsorption method to study the adsorption of nonionic and anionic surfactants onto silica, kaolin, and alumina particles. The surfactants formed various structures depending upon their concentrations in the solution. It was found that 2D hemimicelles with low coverage were formed at very low surfactant concentrations. With... 

Acidic forms of zeolites are well suited as supports for metal functions which are employed for hydrogenation, since they can also withstand the presence of traces of sulfur compounds frequently found in feedstocks of petrochemical industry. It should be noted, however, that hydrogenation is a structure insensitive reaction so it will primarily depend upon the concentration of the accessible metal particles and the adsorption constant of the unsaturated hydrocarbon. This may offer an explanation as to why Pt catalysts, for example, are still active for hydrogenation, when their activity for dehydrocyclization or hydrogenolysis (i.e., for structure sensitive reactions) is completely lost (e.g., by poisoning). 

In Section 17.1, you learned how to calculate the average rate of a chemical reaction given the initial and final times and concentrations. The word average is important because most chemical reactions slow down as the reactants are consumed. To understand why most reaction rates slow over time, recall that the collision theory states that chemical reactions can occur only when the reacting particles collide and that reaction rate depends upon reactant concentration. As reactants are consumed, fewer particles collide and the reaction slows. Chemists use the concept of rate laws to quantify the results of the collision theory in terms of a mathematical relationship between the rate of a chemical reaction and the reactant concentration. 

It was mentioned in Chapter 4 that aerosol particles scatter and absorb solar radiation. These processes depend upon the concentration, size distribution, form, refractive index and absorption coefficient of the particles, as well as upon the wavelength of the radiation. In the case of water-soluble particles the extinction is also controlled by relative humidity (see Section 4.5). The energy absorbed by particles leads to an increase of temperature, while backscattering produces an energy loss for the system. Sines this energy loss may be characterized by the albedo, it is proposed to examine first the relation between albedo and temperature in surface air. 

Discussion When an electrolyte dissolves in water the solution contains, in addition to the undissociated compound, ions, the number of which depends upon the concentration of the solution. The number of particles present which affect the freezing point of the solution is, consequently, greater than in the case of a non-electrolyte. If a salt, sodium chloride for example, yields two ions when it dissociates, its effect upon the freezing point of water will be twice that of a non-electrolyte at the same concentration, provided it is completely dissociated if it is but partly dissociated the effect will be less. From this effect it is possible to calculate by the following method the extent of dissociation of the salt. 

Figure 4 Average particle diameter as a function of protein concentration for emulsions made using 20% soya oil and caseinate at different concentrations. Below a concentration of about 0.5% caseinate, the size of droplets is dependent upon the concentration of casein above this, the concentration depends on the conditions of homogenization.

The hexamminenickel(II) bromide and iodide separate in the form of face-centered cubic crystals that are isomor-phous with ammonium hexachloropIatinate(IV). Depending upon particle size, the color of the crystals varies from pale lavender to deep blue. The bromide is soluble in hot water and may be recrystallized from concentrated aqueous ammonia. These salts should be stored in tightly stop-... 

The allergic manifestations depend upon the concentration of antibody and antigen at a particular site and on the sensitivity of the tissues at that point to substances such as histamine. The differential deposition of inhaled antigens in various parts of the respiratory tract as a function of the particle size of the inhaled particles results in localised concentrations of... 

---