Quantitation expressing concentration

In all cases the reaction of the solution can be quantitatively expressed by the magnitude of the hydrogen ion (or hydroxonium ion) concentration, or, less frequently, of the hydroxide ion concentration, since the following simple relations between [H + ] and [OH-] exist ... 

Spiro [27] has derived quantitative expressions for the catalytic effect of electron conducting catalysts on oxidation-reduction reactions in solution in which the catalyst assumes the Emp imposed on it by the interacting redox couples. When both partial reaction polarization curves in the region of Emp exhibit Tafel type kinetics, he determined that the catalytic rate of reaction will be proportional to the concentrations of the two reactants raised to fractional powers in many simple cases, the power is one. On the other hand, if the polarization curve of one of the reactants shows diffusion-controlled kinetics, the catalytic rate of reaction will be proportional to the concentration of that reactant alone. Electroless metal deposition systems, at least those that appear to obey the MPT model, may be considered to be a special case of the general class of heterogeneously catalyzed reactions treated by Spiro. 

The concept of mole fraction of a component used in Equation (4.1) is a convenient measure of concentration when dealing with trace quantities and dilute solutions, often experienced in environmental systems. This is especially the case with transport phenomena and equilibrium between phases, where it results in simple quantitative expressions. The phenomena of interest when dealing with the exchange of odorous compounds and oxygen between wastewater and a sewer atmosphere are, in this respect, relevant examples. 

The amount of solute and solvent in a solution can be quantitatively expressed using numerous concentration units. The choice of a particular concentration unit depends largely on practice and convenience. We have probably all made solutions using recipes or directions that tell us to add so much water to a substance. In the field of chemistry, the most common concentration units are molarity, molality, percent by mass, and parts per. Each of these is defined here ... 

Effect ofNOa- on G(Ce+8). There is a striking effect (43) of NO on Ce+4 reduction in sulfuric acid solutions. T1 + increases (44) G(Ce+s) from 2Gh o, + GH — G0Hto 2Gh,o, + Gh + G0h. N08 at concentrations greater than 0.01 M markedly enhances G(Ce +a) both in the presence and absence of T1 +, the effect being approximately equal in both cases. Mahlman (24) confirmed this effect and extended the study from 0.5M to 5.0M. The enhancement, AG(Ce+3), for NOs concentrations from O.lilf to 5.0M is quantitatively expressed by Equation 1 as shown in Figure 1. 

Radiation. The decrease in GH, for N03 concentrations from 0.01 M to 1.0M is quantitatively expressed for Co60 7-radiation by Equation 2 as shown in Figure 2. 

The decrease in GH, for H202 and UO2SO4 concentrations from O.OlAf to l.Oikf is quantitatively expressed for Co00 7-radiation by Equations 3 and 4 as also shown by Figure 2. 

Equation 3 is based on the data of Ghormley and Hochanadel (12) and Anderson and Hart (3). Equation 4 is based on the data of Boyle, Kieffer, Hochanadel, Sworski, and Ghormley (6). Similarly, though not shown in Figure 2, the decrease in Gh, for N02 and Cu+2 concentrations from 0.01M to 1.0M is quantitatively expressed for Co00 7-radiation by Equations 5 and 6. 

The sum of G(H2) and G(C1 ) at moderately low concentrations of chlorinated compounds indicates (17) that all reducing species react to yield either H2 or Cl . The enhancement, AG(H2 + Cl-), at concentrations of CH2ClCOOH from 0.1 M to 2.5Af is quantitatively expressed for Co00 7-radiation by Equation 14 as shown in Figure 5. 

Since the shape of the curves in diffusion kinetics is invariant with respect to most of the pertinent parameters (19), the conclusion is reached that diffusion kinetics can not quantitatively express the dependence of Gh,° on solute concentration. Therefore, the question arises as to whether a... 

Equations 1-14 demonstrate that some effects of solute which are commonly attributed to reaction with eaq can be quantitatively expressed by a reaction mechanism in which bimolecular reaction of the precursor with solute is in competition with precursor disappearance by a first-order process. The first observation that such a reaction mechanism may be applicable in water was made by Dainton and Peterson (9) who proposed H20 and its reaction with H +aq to explain the increase in radical pair yield for Co60 7-radiation with increase in sulfuric acid concentration. Dainton and Watt (10) proposed the alternative hypothesis that H+aq makes available to solutes isolated radical pairs [H + OH] which would otherwise revert to water. Hayon (18), however, has normalized the increase in radical pair yield by a wide variety of solutes with reference to H +aq on the basis of their reactivity towards eaq and concluded that the increase in radical pair yield is caused by reduction of the back reaction to form water in the spur. 

Nomura and Harada already reported an experimental and theoretical study on the effect of lowering the amount of monomer initially charged on the number of polymer particles formed in a batch reactor(14). Under usual conditions in batch operation, micelles disappear and the formation of particles terminates before the disappearance of monomer droplets in the water phase. However, if the initial monomer concentration is extremely low, micelles would exist even after the disappearance of monomer droplets and hence, particle formation will continue until all emulsifier molecules are adsorbed on the surfaces of polymer particles. This condition is quantitatively expressed by the following emulsifier balance equation., ... 

Changes in biomass concentration throughout the fermentation process were followed by optical density (OD) measurement at 580 nm using an Ultrospec 2000 Spectrophotometer. Quantitative biomass concentration was assayed applying microbiuret cell protein determination (16). Biomass concentration was expressed in grams of dry matter per liter of fermentation broth by assuming a twofold multiplication constant for microbial protein to cell mass. For carbon balance calculations, the elemental composition of C. saccharolyticus was assumed to be CH1 8O0 5N0 2 (24.6 mg/mmol). 

As observed, it becomes possible to quantitatively express the degree of the mixing state based on the spatial distribution of the concentration of tracer in the equipment. Accordingly, the evaluation of the mixing capacity of the operation/equipment becomes possible by using the change in mixedness with time. 

To obtain quantitative expressions for the corrosion current and the corrosion potential, one has to substitute the proper expression for the metal-dissolution- and electronation-current densities. If no oxide films form on the surface of the corroding metal and neither of the current densities is controlled by mass transport, i.e., there is no concentration overpotential, one can insert the Butler-Volmer expression for the deelectronation- and electronation-current densities. Thus,... 

In the simplest and most important cases, two general reasons responsible for ion mobility in solids are (i) the presence of ions or groups of ions with a relatively weak bonding with respect to the neighborhood, and (ii) the existence of a network of positions available for ion jumps. These factors may be quantitatively expressed in terms of ionic -> charge carrier - concentration, and their - diffusion coefficient. 

To provide a quantitative expression for the diffusion flux 7 one cannot use the Nernst-Planck flux equation (4.231) because the latter describes the independent flow of one ionic species and in the case under discussion it has been shown that the migration current of the H ions is profoundly affected by the concentration of the K" ions. A simple modification of the Nernst-Planck equation can be argued as follows. 

Although quahtative descriptions of concentration can be useful, solutions are more often described quantitatively. Some commonly used quantitative descriptions are percent by either mass or volume, molarity, and molality. These descriptions express concentration as a ratio of measured amounts of solute and solvent or solution. Table 15-3 lists each ratio s description. 

Research in the field of combustion toxicology is primarily concerned with items 1, all of which are related to the toxic potency of the fire gas effluent. Toxic potency is defined by ASTM as a quantitative expression relating concentration (of smoke or combustion gases) and exposure time to a particular degree of adverse physiological response, for example, death on exposure of humans or animals. This definition is followed by a discussion, which states, The toxic potency of smoke from any material or product or assembly is related to the composition of that smoke which, in turn, is dependent upon the conditions under which the smoke is generated. One should add that the LCso is a common end point used in laboratories to assess toxic potency. In the comparison of the toxic potencies of different compounds or materials, the lower the LC50 (i.e., the smaller the amount of material necessary to reach the toxic end point), the more toxic the material is. 

As approximate formulas are available for Get and G, quantitative expressions for Gj(H) can also be created and used to derive expressions for the coagulation concentration (the latter is the concentration that causes every encounter between two coUoidal particles to lead to destabilisation). Verwey and Overbeek [10] introduced... 

To express counterion distributions more quantitatively, counterion concentration c+ profiles for a 64 base-pair DNA at various polymer concentrations are plotted in Figure 4 as functions of the radial coordinate r measured from the axis of the DNA cylinder at its center and in Figure 5 as functions of the z coordinate along the surface of the cylinder. The very high counterion concentration ( 3 M) on the surface of the polyion rapidly decreases in both radial and longitudinal directions, and dilution of the polymer concentration has the slightest effect on these profiles. 

Three ways of quantitatively expressing the concentration of a solution will be presented here Mass/mass percent, %(m/m), mass/volume percent, %(m/v), and molarity, M. A fourth, molality, will appear later in this chapter. You should know an interesting fact about concentrations. No matter what size sample of a solution you have, be it a teaspoonful or a bucketful, the concentration is the same for both. This is because concentrations are stated in terms of the amount of solute in a fixed amount of solvent 100 g, 100 mL, or 1.00 L. It s like density. The density of mercury is 13.6 g/mL. If I have 100 mL or three drops of mercury, the density of mercury is still 13.6 g/mL. Neither density nor concentration depends on the size of the sample. 

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