Mass transfer molar rate

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... 

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... 

When the mass transfer rates of the two components are equal and opposite the process is said to be one of equimolecular counterdiffusion. Such a process occurs in the case of the box with a movable partition, referred to in Section 10.1. It occurs also in a distillation column when the molar latent heats of the two components are the same. At any point in the column a falling stream of liquid is brought into contact with a rising stream of vapour with which it is not in equilibrium. The less volatile component is transferred from... 

Thus, the diffusional process in a liquid gives rise to a situation where the components are being transferred at approximately equal and opposite mass (rather than molar) rates. 

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. 

When the mass transfer process deviates significantly from equimolecular counterdiffusion, allowance must be made for the fact that there may be a very large difference in the molar rates of transfer of the two components. Thus, in a gas absorption process, there will be no transfer of the insoluble component B across the interface and only the soluble component A will be transferred. This problem will now be considered in relation to the Reynolds Analogy. However, it gives manageable results only if physical properties such as density are taken as constant and therefore results should be applied with care. 

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 ... 

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 balance is made with respect to a control volume which may be of finite (V) or of differential (dV) size, as illustrated in Figure 1.3(a) and (b). The control volume is bounded by a control surface. In Figure 1.3, m, F, and q are mass (kg), molar (mol), and volumetric (m3) rates of flow, respectively, across specified parts of the control surface,6 and Q is the rate of heat transfer to or from the control volume. In (a), the control volume could be the contents of a tank, and in (b), it could be a thin slice of a cylindrical tube. 

The Hatta criterion compares the rates of the mass transfer (diffusion) process and that of the chemical reaction. In gas-liquid reactions, a further complication arises because the chemical reaction can lead to an increase of the rate of mass transfer. Intuition provides an explanation for this. Some of the reaction will proceed within the liquid boundary layer, and consequently some hydrogen will be consumed already within the boundary layer. As a result, the molar transfer rate JH with reaction will be higher than that without reaction. One can now feel the impact of the rate of reaction not only on the transfer rate but also, as a second-order effect, on the enhancement of the transfer rate. In the case of a slow reaction (see case 2 in Fig. 45.2), the enhancement is negligible. For a faster reaction, however, a large part of the conversion occurs in the boundary layer, and this results in an overall increase of mass transfer (cases 3 and 4 in Fig. 45.2). 

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. 

Mass transfer Peclet number (PeMT), 25 270, 279, 280, 281, 283, 285, 311, 316. See also Peclet numbers (Pe) critical value of, 25 283-285 effect on dimensionless reactant molar densities, 25 289t, 294-295 particle-based, 25 291 Mass-transfer rate, in liquid-bquid extraction, 10 751... 

On the basis of the simplified view of the flow patterns just described, a model for predicting mass transfer rates can be developed using penetration theory and the fact that mass is transferred simultaneously from both the nip and the wiped film. We can therefore write that the total molar mass transfer rate from an element of fluid over a length dk in the extruder is... 

The variation of efficiencies is due to interaction phenomena caused by the simultaneous diffusional transport of several components. From a fundamental point of view one should therefore take these interaction phenomena explicitly into account in the description of the elementary processes (i.e. mass and heat transfer with chemical reaction). In literature this approach has been used within the non-equilibrium stage model (Sivasubramanian and Boston, 1990). Sawistowski (1983) and Sawistowski and Pilavakis (1979) have developed a model describing reactive distillation in a packed column. Their model incorporates a simple representation of the prevailing mass and heat transfer processes supplemented with a rate equation for chemical reaction, allowing chemical enhancement of mass transfer. They assumed elementary reaction kinetics, equal binary diffusion coefficients and equal molar latent heat of evaporation for each component. 

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.

The dependence of kobsd on stirring speed for Br-I exchange reactions with polymer-supported crown ethers 34 and 35 has been determined under the same conditions as with polymer-supported phosphonium salts 1 and 4149). Reaction conditions were 90 °C, 0.02 molar equiv of 100-200 mesh catalyst, 16-17% RS, 2% CL, 20 mmol of 1-bromooctane, 200 mmol of KI, 20 ml of toluene, and 30 ml of water. Reaction rates with 34 and 35 increased with increased stirring speed up to 400 rpm, and were constant above that value. This result resembles that with polymer-supported onium ion catalysts and indicates that mass transfer as a limiting factor can be removed in experiments carried out at stirring speeds of 500-600 rpm, whatever kind of polymer-supported phase transfer catalyst is used. 

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