Activity Volume fraction

Catalyst Surface area/ (m /g) Average pore diameter/ nm a — Fe crystallite size/nm Activity (volume fraction) % NH3... 

An equation algebraically equivalent to Eq. XI-4 results if instead of site adsorption the surface region is regarded as an interfacial solution phase, much as in the treatment in Section III-7C. The condition is now that the (constant) volume of the interfacial solution is i = V + JV2V2, where V and Vi are the molar volumes of the solvent and solute, respectively. If the activities of the two components in the interfacial phase are replaced by the volume fractions, the result is... 

Physical Properties. Physical properties of importance include particle size, density, volume fraction of intraparticle and extraparticle voids when packed into adsorbent beds, strength, attrition resistance, and dustiness. These properties can be varied intentionally to tailor adsorbents to specific apphcations (See Adsorption liquid separation Aluminum compounds, aluminum oxide (alumna) Carbon, activated carbon Ion exchange Molecular sieves and Silicon compounds, synthetic inorganic silicates). 

Consider fibers that all have the same strength and are relatively brittle in comparison to the matrix as studied by Kelly and Davies [3-26]. Moreover, both the fibers and matrix are active only in the linear elastic range (stage 1 in Figure 3-46). If the composite material has more than a certain minimum volume fraction of fibers, V, the ultimate strength is achieved when the fibers are strained to correspond to their maximum (ultimate) stress. That is, in terms of strains. 

It is conventional to take as the activation volume the value of AV when P = 0, namely —bRT. (This is essentially equal to the value at atmospheric pressure.) Pressure has usually been measured in kilobars (kbar), or 10 dyn cm 1 kbar = 986.92 atm. The currently preferred unit is the pascal (Pa), which is 1 N m 1 kbar = 0.1 GPa. Measurements of AV usually require pressures in the range 0-10 kbar. The units of AV are cubic centimeters per mole most AV values are in the range —30 to +30 cm moP, and the typical uncertainty is 1 cm moP. Rate constant measurements should be in pressure-independent units (mole fraction or molality), not molarity. ... 

Fig. 108.—The activity of benzene in solution with rubber plotted against the volume fraction of rubber. The solid curve represents smoothed experimental data of Gee and Treloar. The upper dashed curve represents the calculated ideal curve for an ideal solution of a solute with M = 280,000 dissolved in benzene. The diagonal dashed curve corresponds to ai — Vi. (From the data of Gee and Treloar. )...

Fig. 111.—Experimental values of the interaction parameter %i plotted against the volume fraction of polymer. Data for polydi-methylsiloxane M =3850) in benzene, A (New-ingi6). polystyrene in methyl ethyl ketone, (Bawn et aV ) and polystyrene in toluene, O (Bawn et alP) are based on vapor pressure measurements. Those for rubber in benzene, T (Gee and Orr ) were obtained using vapor pressure measurements at higher concentrations and isothermal distillation equilibration with solutions of known activities in the dilute range.

In order to minimize confusion, only the curves representing the smoothed results are shown for squalene-benzene, polyisoprene-ben-zene, and rubber-benzene. Calorimetric methods were applied to those polymers of comparatively low molecular weight temperature coefficients of the activity were used for the rubber-benzene mixtures. The ratio of the heat of dilution to the square of the volume fraction t 2, which is plotted against in Fig. 112, should be independent of the concentration according to the treatment of interactions... 

Feed concentration Active zone concentration Deadzone concentration Effluent concentration Ideal tank concentration Total flow rate Fractional by-pass flow By-pass flow rate Dead volume fraction Deadzone exchange flow Rate constant Fractional conversion Fractional deadzone flow... 

Dt and the mutual diffusion coefficient, D, are interconvertible by correcting for the penetrant activity in the polymer [12], For highly concentrated systems where the penetrant volume fraction, < >, is low,/can be approximated by... 

This monomer concentration Ma in the formalism of the quasi-homogeneous approximation, unlike M a, refers to the whole volume of the two-phase system. The aforementioned quantities are connected by the simple relationship Ma = flM a where y01 stands for the volume fraction of the a-th phase in miniemulsion. An analogous relation, Ra = sdaR a, exists between the concentrations Ra of the a-th type active centers in the entire system and those R a in the surface layer of the a-th phase. This layer thickness da has the scale of average spatial size of the a-th type block, which hereafter is presumed to be small as compared to the average radius of miniemulsion drops. Apparently, in this case, the curvature of the interphase surface can be neg-... 

Rate equation (1) indicates that ku should be inversely proportional to the activity of water for solvolysis by the AAil mechanism and independent of it if the bimo-lecular processes (pathways (i) and (ii)) pertain. Fig. 12 illustrates that acid independent rate constants at different volume fractions of D20 in CD3CN, /cH, were linearly dependent upon the inverse of ud2o in CD3CN as determined from the corresponding activities of H20 in CH3CN.142 This is in accord with the AA]1 mechanism (pathway (iii), Scheme 6). 

Remarkably, the use of a fluorous biphasic solvent system in combination with a [Rh(NBD)(DPPE)]+-type catalyst (NBD = norbornadiene) copolymerized into a porous nonfluorous ethylene dimethacrylate polymer, resulted in an increased activity of the catalyst relative to a situation when only toluene was used as solvent [30]. The results were explained by assuming that fluorophobicity of the substrate (methyl-trans-cinnamate) leads to a relatively higher local substrate concentration inside the cavities of the polymer when the fluorous solvent is used. That is, the polymer could be viewed as a better solvent than the fluorous solvent system. This interpretation was supported by the observations that (i) the increase in activity correlates linearly with the volume fraction of fluorous solvent (PFMCH) and (ii) the porous ethylene dimethacrylate polymer by itself lowers the concentration of decane in PFMCH from 75 mM to 50 mM, corresponding to a 600 mM local concentration of decane in the polymer. Gas to liquid mass transport limitation of dihydrogen could be mled out as a possible cause. 

Volume changes, by vitreous silica, 22 438 Volume flux, of droplets, 23 187 Volume fraction, in filtration, 11 328 Volume fraction calculation, in equivalent box model, 20 345—346 Volume mean diameter, 23 186 Volume of activation, 13 407-408... 

For a fast catalytic reaction, free access of gas, electrons, protons and water is needed. This leads to a best compromise of the volume fractions of protonconducting polymer, electron-conducting carbon, active sites and void space. 

As Beer s law in absorption spectroscopy has a path length dependence, the observe volume, Vobs, or active volume of an NMR probe is an important determinant of the sensitivity of NMR measurements. The observe volume is the fraction of the total sample volume, Vtot. that returns a signal when a sample is inserted in an NMR tube or is injected into a flow system. The relationship between chromatographic peak shape, peak volume and flow rate, and sensitivity in hyphenated NMR measurements is complex and is discussed in greater detail in Section 7.2. For the purpose of this discussion, the sample is assumed to be present at a uniform concentration in a sample volume, Vtot. The probe observe factor, /o, is calculated as shown in the following equation ... 

The mole fractions of labeled water at t = 0 and at equilibrium are noted as Xq and Xoo, respectively (Pig. 4). In the end, the signal of bound water becomes small and difficult to quantify. But, this does not influence the quality of the measured rate constant because the mole fraction at equilibrium, x, is known from the concentration of the metal ion and the coordination number. These experiments can be performed at variable temperature and at variable pressure to obtain activation enthalpies and entropies as well as activation volumes. 

Table V summarizes rate constants, and activation volumes for water exchange on [M(0H)(H20)5] together with those of [M(H20)6] . Accuracy of exchange rate constants /jqh and its activation parameters AH and AS relies on the knowledge of AHj , and ASa° (39,52). The hydrolysis of aqueous M " " ions is complicated by oligomerization and ranges of hydrolysis constants have been reported for example for Al (91,92) and Ga (93-95). As a general trend a strong increase in the lability of the coordinated water molecules is observed for the hydrolyzed species when compared to the hexa-aqua ions. Even at very low pH, where the mole fraction of the hydrolyzed species is extremely small, the water exchange observed by NMR on the bulk water can be dominated by the fast exchange on [M(0H)(H20)5] and not by the much slower exchange on...

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