Mass transfer molar concentration

Applying mass transfer theory to a component / in the liquid, assumint good mixing and neglecting atmospheric concentrations, the evaporation molar rate of a single component can be expressed as... 

On the basis of each of the theories discussed, the rate of mass transfer in the absence of bulk flow is directly proportional to the driving force, expressed as a molar concentration difference, and, therefore ... 

In distillation, equimolecular counterdiffusion takes place if the molar latent heats of the components are equal and the molar rate of flow of the two phases then remains approximately constant throughout the whole height of the column. In gas absorption, however, the mass transfer rate is increased as a result of bulk flow and, at high concentrations of soluble gas, the molar rate of flow at the top of the column will be less than that at the bottom, At low concentrations, however, bulk flow will contribute very little to mass transfer and, in addition, flowrates will be approximately constant over the whole column. 

The term Csm/Cr (the ratio of the logarithmic mean concentration of the insoluble component to the total concentration) is introduced because hD(CBm/Cr) is less dependent than hD on the concentrations of the components. This reflects the fact that the analogy between momentum, heat and mass transfer relates only to that part of the mass transfer which is not associated with the bulk flow mechanism this is a fraction Cum/Cr of the total mass transfer. For equimolecular counterdiffusion, as in binary distillation when the molar latent heats of the components are equal, the term Cem/Cj- is omitted as there is no bulk flow contributing to the mass transfer. 

A similar argument can be applied to the mass transfer process when a concentration gradient exists. Thus, if the molar concentration of A remote from the surface is Ca, and at the surface it is Caw, the moles of A transferred to the surface will be (M/pHC — Cam ), if the density (p) can be assumed to be constant over the range of concentrations encountered, Thus the moles of A transferred to the surface per unit area and unit time (-/V Ov-o is given by ... 

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 ... 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

Carbon dioxide is absorbed in alkaline water from a mixture consisting of 30% CO2 and 70% Nj and the mass transfer rate is 0.1 kmobs. The concentration of CO2 in the gas in contact with the water is effectively zero. The gas is then mixed with an equal molar quantity of a second gas stream of molar composition 20% CO2, 50%, N2 and 30% H2. What will be the new mass transfer rate, if the surface area, temperature and... 

Fig. 4.18 represents a countercurrent-flow, packed gas absorption column, in which the absorption of solute is accompanied by the evolution of heat. In order to treat the case of concentrated gas and liquid streams, in which the total flow rates of both gas and liquid vary throughout the column, the solute concentrations in the gas and liquid are defined in terms of mole ratio units and related to the molar flow rates of solute free gas and liquid respectively, as discussed previously in Sec. 3.3.2. By convention, the mass transfer rate equation is however expressed in terms of mole fraction units. In Fig. 4.18, Gm is the molar flow of solute free gas (kmol/m s), is the molar flow of solute free liquid (kmol/m s), where both and Gm remain constant throughout the column. Y is the mole ratio of solute in the gas phase (kmol of solute/kmol of solute free gas), X is the mole ratio of solute in the liquid phase (kmol of...

The difference in mole fractions is most significant in the case of S02 where this difference is 15% of the bulk phase level. This result indicates that external mass transfer limitations are indeed significant, and that this difference should be taken into account in the analysis of kinetic data from this system. Note that there is a difference in nitrogen concentration between the bulk fluid and the external surface because there is a change in the number of moles on reaction, and there is a net molar flux toward... 

In this section, we have examined how the coupling between mass transfer and the chemical reaction defines the concentration profile of the limiting reagent (i.e., hydrogen), and how the mass or molar flow between the gas and the liquid phase can be computed. In the next section, the estimation of the overall rate of reaction (i.e., the reactor productivity) will be reviewed for different gas-liquid reactors. 

We will now describe the application of the two principal methods for considering mass transport, namely mass-transfer models and diffusion models, to PET polycondensation. Mass-transfer models group the mass-transfer resistances into one mass-transfer coefficient ktj, with a linear concentration term being added to the material balance of the volatile species. Diffusion models employ Fick s concept for molecular diffusion, i.e. J = — D,v ()c,/rdx, with J being the molar flux and D, j being the mutual diffusion coefficient. In this case, the second derivative of the concentration to x, DiFETd2Ci/dx2, is added to the material balance of the volatile species. 

For mass transfer in the gas phase, the molar flux of a particular component N (in kmolm s ) is related to the concentration difference in the gas phase AC, expressed in terms of molar concentration (kmol m ), by... 

The film (individual) coefficients of mass transfer can be defined similarly to the film coefficient of heat transfer. A few different driving potentials are used today to define the film coefficients of mass transfer. Some investigators use the mole fraction or molar ratio, but often the concentration difference AC (kg or kmol m ) is used to define the liquid phase coefficient (m while the partial pressure difference A/i (atm) is used to define the gas film coefficient (kmolh m 2 atm ). However, using and A gp of different dimensions is not very convenient. In this book, except for Chapter 15, we shall use the gas phase coefficient (m h" ) and the liquid phase coefficient ki (m h ), both of which are based on the molar concentration difference AC (kmol m ). With such practice, the mass transfer coefficients for both phases have the same simple dimension (L T" ). Conversion between k and is easy, as can be seen from Example 2.4. 

A gas component A in air is absorbed into water at latm and 20 °C. The Henry s law constant of A for this system is 1.67 X 10 Pa m kmol h The liquid film mass transfer coefficient and gas film coefficient I(q are 2.50x10 and 3.00 X10" ms respectively, (i) Determine the overall coefficient of gas-liquid mass transfer (ms ). (ii) When the bulk concentrations of A in the gas phase and liquid phase are 1.013 X 10 Pa and 2.00 kmol m , respectively, calculate the molar flux of A. 

The mass-transfer coefficients, by definition, are equal to the ratios of the molar mass flux to the concentration driving forces. The mass-transfer coefficients are related to each other as follows ... 

Classical treatment of mass transfer is to consider a unit, of mass transfer as a measure of the interphase equilibrium changes needed to produce a desired degree of diffusion [13], This concept is best applied to the concept of a theoretical plate in distillation [4], Defining Gm as the gas superficial molar velocity (mole/hr/ft2 of tower cross section) and dy as the change of concentration of the diffusing species, then... 

Rate Measures for Interfacial Processes Terminology used for reporting rate data can be confusing. Normally rate data are reported on a volumetric basis with transfer rate and effective area combined. For example, kLa denotes mass-transfer data per unit volume. The L subscript means it is referenced to the molar concentration difference between the interface and the bulk liquid. This is commonly used on data involving a sparingly soluble (high relative volatility) component. Note that the lowercase k means the data deal only with the resistance in the liquid phase. 

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