Rate equation Liquid phase reactions

We call Equation (2-6) the differential form of the design equation for a batch reactor because we have written the mole balance in terms of conversion. The differential forms of the batch reactor mole balances. Equations (2-5) and (2-6), are often used in the interpretation of reaction rate data (Chapter 7) and for reactCHS with heat effects (Chapters 11-13), respectively. Batch reactors are frequently used in industry for both ga.s-phase and liquid-phase reactions. The lidmratory bomb calorimeter reactor is widely used for ol ning reaction rate data Liquid-phase reactions are frequently carried out in batch reactors when small-scale production is desired or operating difficulties rule out the use of continuous Row systems. 

When reactants are distributed between several phases, migration between phases ordinarily will occur with gas/liquid, from the gas to the liquid] with fluid/sohd, from the fluid to the solid between hquids, possibly both ways because reactions can occur in either or both phases. The case of interest is at steady state, where the rate of mass transfer equals the rate of reaction in the destined phase. Take a hyperbohc rate equation for the reaction on a surface. Then,... 

Measurements Using Liquid-Phase Reactions. Liquid-phase reactions, and the oxidation of sodium sulfite to sodium sulfate in particular, are sometimes used to determine kiAi. As for the transient method, the system is batch with respect to the liquid phase. Pure oxygen is sparged into the vessel. A pseudo-steady-state results. There is no gas outlet, and the inlet flow rate is adjusted so that the vessel pressure remains constant. Under these circumstances, the inlet flow rate equals the mass transfer rate. Equations (11.5) and (11.12) are combined to give a particularly simple result ... 

For a liquid-phase reaction, or gas-phase reaction at constant temperature and pressure with no change in the total number of moles, the density of the system may be considered to remain constant. In this circumstance, the system volume (V) also remains constant, and the equations for reaction time (12.3-2) and production rate (12.3-6) may then be expressed in terms of concentration, with cA = nAlV ... 

Since this is a liquid-phase reaction, we assume density is constant The quantity V in the material-balance equation (14.3-5 or 15) is the volume of file system (liquid) in the reactor. The reactor (vessel) volume is greater than this because of file 75%-capacity requirement. From file specified rate law,... 

The composition of a liquid phase reaction, 2 A => B, was followed as a function of time by a spectrographic method with the tabulated results. The initial concentration was A0 = 1.0 mol/liter. Check first and second orders. The rate equation is... 

A liquid phase reaction with rate equation r = kA2 takes place with 50/ conversion in a CSTR. (a) What will be the conversion if this reactor is replaced by one six times as large ... 

A liquid phase reaction with rate equation r = kC is to be carried out to 90% conversion, starting with a concentration of 2 lbmol/cuft. The starting temperature is 550 R. It is to be raised 2°F/min for 60 minutes, then kept at 670 R until the desired conversion is reached. The specific rate is given by k = exp(3.322-5000/T)... 

The reversible liquid phase reaction, 2A B, has the rate equation... 

The endothermic liquid phase reaction, 2A => B + C, is to be conducted in a heated CSTR. Feed rate is F = 20 cuft/min at 310 F. The reaction temperature is maintained at 400 F by heat lbmol/cuft. The rate equation is... 

As with homogeneous aldol reactions, simple power-type rate equations have been frequently used to describe the kinetics of solid-catalysed condensations. For several liquid phase reactions, second-order kinetics was established, viz. 

The law of mass action, the laws of kinetics, and the laws ol distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equilibrium values otherwise, hydrolysis must occur The equations governing the rate of the reaction and the variation of the rale constant (as a function of such variables as temperature, catalyst strength, and proponion of reactants) describe Ihe kinetics of the liquid-phase reaction. The usual distillation laws must he modified, since must esterifications arc somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after Ihe extent of conversion has been determined. See also Distillation. 

When the liquid-phase reactions are extremely slow, the gas-phase resistance can be neglected and one can assume that the rate of reaction has a predominant effect upon the rate of absorption. In this case the differential rate of transfer is given by the equation... 

The removal of the acid components H2S and CO2 from gases by means of alkanolamine solutions is a well-established process. The description of the H2S and CO2 mass transfer fluxes in this process, however, is very complicated due to reversible and, moreover, interactive liquid-phase reactions hence the relevant penetration model based equations cannot be solved analytically [6], Recently we, therefore, developed a numerical technique in order to calculate H2S and CO2 mass transfer rates from the model equations [6]. 

The atomic processes that are occurring (under conditions of equilibrium or non equilibrium) may be described by statistical mechanics. Since we are assuming gaseous- or liquid-phase reactions, collision theory applies. In other words, the molecules must collide for a reaction to occur. Hence, the rate of a reaction is proportional to the number of collisions per second. This number, in turn, is proportional to the concentrations of the species combining. Normally, chemical equations, like the one given above, are stoichiometric statements. The coefficients in the equation give the number of moles of reactants and products. However, if (and only if) the chemical equation is also valid in terms of what the molecules are doing, the reaction is said to be an elementary reaction. In this case we can write the rate laws for the forward and reverse reactions as Vf = kf[A]"[B]6 and vr = kr[C]c, respectively, where kj and kr are rate constants and the exponents are equal to the coefficients in the balanced chemical equation. The net reaction rate, r, for an elementary reaction represented by Eq. 2.32 is thus... 

Here, rate equations are given in terms of concentrations C , in units of moles per unit volume. This is the most convenient choice for liquid-phase reactions. For gas-phase reactions, partial pressures p, suggest themselves as an alternative and can be substituted without loss of generality. However, the dimensions and numerical values of the rate coefficients change accordingly. 

Liquid Phase. For liquid-phase reactions in which there is no volume change, concentration is the preferred variable. The mole balances are shown in Table 4-5 in terms of concentration for the four reactor types we have been discussing. We see from Table 4-5 that we have only to specify the parameter values for the system (CAo,Uo,etc.) and for the rate law (i.e., ifcyv. .3) to solve the coupled ordiaaiy differential equations for either PFR, PBR, or batch reactors or to solve the coupled algebraic equations for a CSTR. 

A Second-Order Reaction in a CSTR. For a second-order liquid-phase reaction being carried out in a CSTR, the combination of the rate law and the design equation yields... 

We now insert rate laws written in terms of molar flow rates [e.g., Equation (3-45)] into the mole balances (Table 6-1). After performing this operation for each species we arrive at a coupled set of first-order ordinary differential equations to be solved for the molar flow rates as a function of reactor volume (i.e., distance along the length of the reactor). In liquid-phase reactions, incorporating and solving for total molar flow rate is not necessary at each step along the solution pathway because there is no volume change with reaction. 

To derive the overall kinetics of a gas/liquid-phase reaction it is required to consider a volume element at the gas/liquid interface and to set up mass balances including the mass transport processes and the catalytic reaction. These balances are either differential in time (batch reactor) or in location (continuous operation). By making suitable assumptions on the hydrodynamics and, hence, the interfacial mass transfer rates, in both phases the concentration of the reactants and products can be calculated by integration of the respective differential equations either as a function of reaction time (batch reactor) or of location (continuously operated reactor). In continuous operation, certain simplifications in setting up the balances are possible if one or all of the phases are well mixed, as in continuously stirred tank reactor, hereby the mathematical treatment is significantly simplified. 

All processes are modeled as series of countercurrent equilibrium cells. Parameters were determined experimentally (section 3). A liquid-phase reaction is accounted for by Da = (rate constant)x(cell volume)/(solid flow rate). Adsorption is described by the bi-Langmuir model. All equations were implemented in the simulation environment DIVA [3] details on the implementation of a largely analogous model can be found in [1,4]. The following set of performance parameters were used to evaluate each process ... 

The main difficulty in using Eq. 7.2.11 is that the extent is not a measurable quantity. Therefore, we have to derive a relationship between Zout and an appropriate measured quantity. We do so by using the design equation and relevant stoichiometric relations. In most applications, we measure the concentration of a species at the reactor outlet and calculate the extent by either Eq. 7.2.5 for liquid-phase reactions or Eq. 7.2.6 for gas-phase reactions. We can then determine the orders of the individual species for power rate expressions. 

C )n.reqiU nr/v. using any one of the rate laws in Part I of this chapter, n-e can now find -r = f(X for liquid-phase reactions. However, for gas-phase reactions the volumetric flow rate most often changes during the course of the reaction because of a change in the total number of moles or in temperature or pressure. Hence, one cannot always use Equation (3-29) to express concentration as a function of conversion for gas-phase reactions. 

For liquid-phase reactions and for gas-phase reactions with no pressure drop (F = Pq), one can combine the information in levels and , to express the rate of reaction as a function of conversion and arrive at level . It is now possible to detemiine either the time or reactor volume necessary to achieve the desired conversion by substituting the relationship linking conversion and rate of reaction into the appropriate design equation (level ). 

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