Gas Constant in Different Unit Systems

The adsorption equilibrium constants Ka c a.c will be in different units for liquid systems than for gas systems. Equilibrium constants for several systems are listed in Table 18-2. 

So far, so good. The situation is really no different, say, than the ideal gas law, in which the gas constant is numerically different and has different units depending on the units chosen for p and V, The unit change in Example 10.1 is analogous to changing the gas constant from liter-atmospheres to calories it is apparent that one system is physically more meaningful than another in specific problems. Several considerations interfere with this straightforward parallel, however, and cause confusion ... 

At integrating (305) for the conditions of a flow system (93, 98), it proved to be convenient to introduce a constant k proportional to k. The value of k was also calculated from data obtained in circulation flow systems (4, 96, 99-103). If the volume of ammonia reduced to 0°C and 1 atm, formed in unit volume of catalyst bed per hour, is accepted as a measure of reaction rate, then k = (4/3)3 1 m)k (101). The constancy of k at different times of contact of the gas mixture with the catalyst and different N2/H2 ratios in the gas mixture can serve as a criterion of applicability of (305). Such constancy was obtained for an iron catalyst of a commercial type promoted with A1203 and K20 at m = 0.5 (93) from our own measurements at atmospheric pressure in a flow system and literature data on ammonia synthesis at elevated pressures up to 100 atm. A more thorough test of applicability of (305) to the reaction on a commercial catalyst at high pressures was done by means of circulation flow method (99), it confirmed (305) with m = 0.5 for pressures up to 300 atm. Similar results were obtained in a large number of investigations by different authors in the USSR and abroad. These authors, however, have obtained for some promoted iron catalysts m values differing from 0.5. Thus, Nielsen et al. (104) have found that m 0.7. 

Figure 12.5 depicts schematically the gas- and aqueous-phase concentrations of A in and around a droplet. The aqueous-phase concentrations have been scaled by HART, to remove the difference in the units of the two concentrations. This scaling implies that the two concentration profiles should meet at the interface if the system satisfies at that point Henry s law. In the ideal case, described by (12.45), the concentration profile after the scaling should be constant for any r. However, in the general case the gas-phase mass transfer resistance results in a drop of the concentration from cA(oo) to cA(Rp) at the air-droplet interface. The interface resistance to mass transfer may also cause deviations from Henry s law equilibrium indicated in Figure 12.5 by a discontinuity. Finally, aqueous-phase transport limitations may result in a profile of the concentration of A in the aqueous phase from [A(/ ,)J at the droplet surface to [A(0)] at the center. All these mass transfer limitations, even if the system can reach a pseudo-steady state, result in reductions of the concentration of A inside the droplet, and slow down the aqueous-phase chemical reactions. 

Fig. 17. 4f-derived specific heat for crystal-field-split doublet-doublet system in units of the gas constant, CJR, as a function of TIT (on a logarithmic scale) for different ratios For... 

Here Vq is the standard electrode potential of the redox system (with respect to the hydrogen reference electrode at 1 mol concentration), n is the number of electrons in the unit reaction, R is not resistance but the universal gas constant, and F is the Faraday constant (see Section 7.8). aox and area are activities, a = yc, where c is the concentration and y is the activity coefficient. Y = 1 for low concentrations (no ion interactions), but <1 at higher concentrations. The halfcell potentials are referred to standardized conditions, meaning that the other electrode is considered to be the standard hydrogen electrode (implying the condition pH = 0, hydrogen ion activity 1 mol/L). The Nernst concept is also used for semipermeable membranes with different concentration on each side of the membrane (see Section 7.6.4). 

The constant of proportionality D which appears in (5.9) and (5.10) is called the diffusion coefficient. In general it will be a function of the nuclear properties of the medium (and therefore a spatially dependent function in nonhomogeneous systems) and of the neutron speed. If we define the net neutron current in the units neutrons per unit area per unit time, it follows that the diffusion coefficient D has the units of length. This definition differs from the one customarily used in gas-diffusion problems. In the gas problems the coefficient D has the units length squared divided by time." Thus if the current of gas particles is defined analogously to the neutron problem, D = vD. Evidently the particle speed v is absorbed into the definition of the proportionality constant in the gas problem. 

Note that Henry s constant is expressed in various other units, for example, in conjunction with kinetic equations for gas-liquid systems (Section 4.4). If the gas phase concentration is denoted in pressure units (Pa) and the liquid phase concentration in molarity (mol m ), a different unit for Henry s constant is obtained (Ha,c = Pa/ca, Pam mol ). If both the liquid and the gas phase concentrations are expressed as molar fractions, a dimensionless value is obtained for Henry s constant. Therefore, be careful in noting the correct units obtained from the literature. In addition, note that in older literature an absorption coefficient is frequently used, for example, the Bunsen absorption coefficient bu (in ni m bar ) defined as the volume of gas (at 1.013 bar and 0°C) absorbed by one volume of liquid at a certain pressure, for example, 1 bar. Thus bu is inversely proportional to and equivalent to the term /Omoi,iiq 0.0224 m morVWx-... 

As in the case of gas-liquid systems, the reader is referred to Chapter 12 and the text by Nagata (1975) for additional discussion. Scale-up from laboratory data on the same system can be predicted to some extent. Constant power per unit volume is a good guide, but care must be taken with large tanks and density differences, as mentioned above. 

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