Mass transfer rate molar flux

A solute diffuses from a liquid surface at which its molar concentration is C, into a liquid with which it reads. The mass transfer rate is given by Fick s law and the reaction is first order with respect to the solute, fn a steady-state process the diffusion rate falls at a depth L to one half the value at the interface. Obtain an expression for the concentration C of solute at a depth z from the surface in terms of the molecular diffusivity D and the reaction rate constant k. What is the molar flux at the surface ... 

Mass Transfer Rate. The molar flux, NA = /cl(( cioiis — cc10h8 ), assuming the concentration of naphthalene in the bulk of the liquid phase is negligible, i.e. cc10hSl = 0, becomes... 

Henry constant for absorption of gas in liquid Free energy change Heat of reaction Initiator for polymerization, modified Bessel functions, electric current Electric current density Adsorption constant Chemical equilibrium constant Specific rate constant of reaction, mass-transfer coefficient Length of path in reactor Lack of fit sum of squares Average molecular weight in polymers, dead polymer species, monomer Number of moles in electrochemical reaction Molar flow rate, molar flux Number chain length distribution Number molecular weight distribution... 

Given the binary mass transfer coefficients and the mole fractions and there are three unknown quantities in these equations the molar fluxes, N-, N2, However, there are only two independent mass transfer rate equations. Thus, one more equation is needed this will be the bootstrap relation ... 

The mass transfer rates can be evaluated from a model of mass and energy transfer in distillation such as those developed in Chapters 11 and 12. We review the necessary material here for convenience. The molar fluxes in each phase are given by... 

In Section 12.2.2 we derived an expression that allows us to calculate the average molar fluxes in a vertical slice of froth on a tray under the assumptions that the vapor rises through the froth in plug flow and the liquid in the vertical slice is well mixed. Extend the treatment and derive an expression for the average mass transfer rates for the entire tray if the liquid is in plug flow. Some clues as to how to proceed may be found in Section 13.3.3. 

Assuming constant molar overflow, LjV is constant and the assumption of equimolar counterdiffusion is valid, so that the flux of one component across the vapor-liquid interface is equal and opposite to the flux of the other component = -Nb)-For a diffeential height dz in a packed column, the mass transfer rate is ... 

N,j are the interfacial mass-transfer rates the product of the molar fluxes and the net interfacial area. The overall molar balances are obtained by summing Eqs. (9.8) and (9.9) over the total number (c) of components in the mixture. At the vapor-U-quid interface we have the continuity equations... 

Fig. 9. The molar flux of component A at the vapour-liquid interface (°) and at the boundary between mass transfer film and liquid bulk (S) as function of reaction rate constant in case (a) the mass transfer coefficients are equal and (b) the mass transfer coefficients are different.

Chemical equilibrium constant for dimerization Liquid-liquid distribution ratio Liquid flow rate Number of equilibrium stages Number of relationships Number of design variables Minimum number of equilibrium stages Number of phases Number of repetition variables Number of variables Rate of mass transfer Molar flux... 

Revise the analysis of Example 11.5.3 and show how a method based on the film models of Chapter 8 could be used to compute the rates of mass transfer. Then use the Krishna-Standart method (of Sections 8.3 and 8.8.3) and compute the molar fluxes. Binary pair mass transfer coefficients may be estimated using the Chilton-Colburn analogy. 

Another possible scenario is that as a consequence of mass transfer only the number of primary particles changes, whereas their size remains more or less constant. This hypothesis seems to be realistic in the case of negative molar flux, J <0, or, in other words, in the case of shrinking particles. In fact, in this case it is more likely that the external particles will be consumed before the internal ones. The resulting expressions for the continuous rate of change of the two internal coordinates therefore read as... 

Closure. After completing this chapter, the reader should be able to define and describe molecular diffusion and how it varies with temperature and pressure, the molar flux, bulk flow, the mass transfer coefficient, the Sherwood and Schmidt numbers, and the correlations for the mass transfer coefficient. The reader should be able to choose the appropriate correlation and calculate the mass transfer coefficient, the molar flux, and the rate of reaction. The reader should be able to describe the regimes and conditions under which mass transfer-limited reactions occur and when reaction rate limited reactions occur and to make calculations of the rates of reaction and mass transfer for each case. One of die most imponant areas for the reader apply the knowledge of this (and other chapters) is in their ability to ask and answer "What if. , questions. Finally, the reader should be able to describe the shrinking core model and apply it to catalyst regeneration and pharmacokinetics. 

Step 11. Write all the boundary conditions that are required to solve this boundary layer problem. It is important to remember that the rate of reactant transport by concentration difhision toward the catalytic surface is balanced by the rate of disappearance of A via first-order irreversible chemical kinetics (i.e., ksCpJ, where is the reaction velocity constant for the heterogeneous surface-catalyzed reaction. At very small distances from the inlet, the concentration of A is not very different from Cao at z = 0. If the mass transfer equation were written in terms of Ca, then the solution is trivial if the boundary conditions state that the molar density of reactant A is Cao at the inlet, the wall, and far from the wall if z is not too large. However, when the mass transfer equation is written in terms of Jas, the boundary condition at the catalytic surface can be characterized by constant flux at = 0 instead of, simply, constant composition. Furthermore, the constant flux boundary condition at the catalytic surface for small z is different from the values of Jas at the reactor inlet, and far from the wall. Hence, it is advantageous to rewrite the mass transfer equation in terms of diffusional flux away from the catalytic surface, Jas. 

A gas-phase mass balance can be written for each component because all four components are volatile and exist in both phases. In each case, the control volnme contains all gas bubbles in the CSTR. The units of each term in all of the gas-phase mass balances are moles per time. At steady state, the inlet molar flow rate of component j is balanced by the outlet molar flow rate and the rate at which component j leaves the gas phase via interphase mass transfer. The inlet and outlet molar flow rates represent convective mass transfer. Interphase transport is typically dominated by diffusion, but convection can also contribute to the molar flux of component j perpendicular to the gas-liquid interface. All of the gas-phase mass balances can be written generically as... 

Overall heat transfer coefficient Overall mass transfer coefficient Mass mass flow rate Number of moles molar flux Total pressure... 

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