MOL areas

The flux, JA, has units of mol/area-time, the concentration, c, in mol/volume, dif-fusivity, Dab, in length2/time, while the mole fraction, xA, is dimensionless naturally. Concentration can be calculated using from the ideal gas law. 

For unit total surface, mass transfer (mol/area time) = / kt 1 2(sQ st)dtACA... 

Reservoir Reservoir amount, A (mol x 10-12) Y Fluxes (mol area-1 x 10-12) Residence time (years)... 

Cas surface concentration of adsorbate, sites/area Cis surface concentration of i, typically molecules or mols/area Cl C3 constants defined in equation (ii). Illustration 3.4 c constant defined in equation (3-20a) biomass concentration, mass/volume culture... 

As a prelude to the development of kinetic rate expressions for heterogeneous chemical reactions, if A reacts with B, for example, then the next step in the mechanism is ha + Ba, forming an activated complex on the snrface. Each reversible step in the seqnence above is characterized by a forward rate constant adsoiption for adsoiption, with units of mol/area time atm, and a backward rate constant A ,desoiption for desorption, with units of mol/area time. The ratio of these rate constants adsorption/ h, desoiption defines the adsorption/desorption equi-... 

Total pressure analysis of the initial reactant product conversion rate can distinguish between these two mechanisms, provided that rates of conversion can be measured at sufficiently high pressure. The rate expressions given by equations (14-188) and (14-191) have units of mol/area-time for surface-catalyzed chemical reactions. However, rate data obtained from heterogeneous catalytic reactors are typically reported in units of mol/time per mass of catalyst. One obtains these units simply by multiplying the kinetic rate law (i.e., mol/area-time) by the internal surface area per mass of catalyst (i.e., S ), which is usually on the order of 100 m /g. If the feed stream to a packed catalytic reactor contains pure ethanol, then the initial reactant product conversion rate for the four-step mechanism is... 

The coefficient of the zeroth-order term in the polynomial model (i.e., the intercept o) is (FA forward. surf. with units of (mol/area-time atm) . ... 

The forward kinetic rate constant for chemical reaction on the catalytic surface, with units of mol/area time, is / forward,surf.Rx = l/(ao i). 

Now, it is necessary to discuss the mass transfer coefficient for component j in the boundary layer on the vapor side of the gas-liquid interface, fc ,gas, with units of mol/(area-time). The final expression for gas is based on results from the steady-state film theory of interphase mass transfer across a flat interface. The only mass transfer mechanism accounted for in this extremely simple derivation is one-dimensional diffusion perpendicular to the gas-liquid interface. There is essentially no chemical reaction in the gas-phase boundary layer, and convection normal to the interface is neglected. This problem corresponds to a Sherwood number (i.e., Sh) of 1 or 2, depending on characteristic length scale that is used to define Sh. Remember that the Sherwood number is a dimensionless mass transfer coefficient for interphase transport. In other words, Sh is a ratio of the actual mass transfer coefficient divided by the simplest mass transfer coefficient when the only important mass transfer mechanism is one-dimensional diffusion normal to the interface. For each component j in the gas mixture. 

In the design of a fixed bed reactor, it is necessary to know the rate of reaction encompassing mass and diffusion effects. These effects on the reaction rate can be represented by the effectiveness factor r), with pore diffusion, besides the effects of mass. This will be represented by an overall rate r" (mol mass h ) or r (mol/area h ). 

The balance mol/area at the inlet and outlet of the bed, considering the average concentration in the output and output superficial velocity, Us, is ... 

Figure 48.1 illustrates a typical Knudsen cell. The Knudsen cell provides a way to probe the vapor in equilibrium with the condensed sample of interest plus cell material. Under the low-pressure conditions used (<10 bar), the fugacities of real gases are equal to their partial pressure, and the behavior of the vapor phase is readily described by the kinetic theory of gases. There are several excellent texts on this subject [19,20]. The key relationship derived from kinetic theory to this technique is the Hertz-Knudsen-Langmuir (HKL) expression, which relates the flux of a molecular species striking a surface, Ja (mol area s ), to its equilibrium vapor pressure in a closed container ... 

From this, one can estimate the value of Ej (mol/area). This indicates that all SASs, will always have a higher concentration at the surface than in the bulk of the solution. This relation has been verified... 

Surface diffusion is a phenomenon accompanying adsorption of solutes onto the surface of the pores of the solid. It is an activated diffusion [see Eq. (4.14)], involving the jumping of adsorbed molecules from one adsorption site to another. It can be described by a two-dimensional analog of Pick s law, with surface concentration expressed, for example, as mol/area instead of mol/ volume. Surface diffusivities are typically of the order of 10 to 10 m s at ordinary temperatures for physically adsorbed gases [13] (see Chap. 11). For liquid solutions in adsorbent resin particles, surface diffusivities may be of the order of 10 mVs [9]. 

Consider that the gas rises at a rate G mol/(area)(time). Let the interfacial surface between gas and liquid be a area/volume of liquid-gas foam. As the gas rises a differential height dhj, the area of contact is a dh per unit area of tray. If, while of concentration y, it undergoes a concentration change in this... 

Similarly the liquid stream consists of L total mol/(area) (time), containing x mole fraction soluble gas, or mole ratio Xy and essentially nonvolatile solvent mol/(area) (time). 

The quantity of solute A in the gas passing the differential section of the tower under consideration is Gy mol/(area) (time), and the rate of mass transfer is therefore d Gy) mol A/(differential volume) (time). Since N = Q and N /... 

For packed towers, rates of flow are based on unit tower cross-sectional area, mol/(area)(time). As for absorbers, in the differential volume dZ, Fig. 9A9a, the interface surface is a dZ, where a is the of Chap. 6. The quantity of substance A in the vapor passing through the differential section is Gy mol/(area)(time), and the rate of mass transfer is d Gy) mol A/(differential volume)(time). Similarly, the rate of mass transfer is d Lx). Even where the usual simplifying assumptions are not strictly applicable, within a section of the column G and L are both sufficiently constant for equimolar counterdiffusion... 

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