Rate laws Liquid phase reactions

Material and energy balances are based on the conservation law, Eq. (7-69). In the operation of liquid phase reactions at steady state, the input and output flow rates are constant so the holdup is fixed. The usual control of the discharge is on the liquid level in the tank. When the mixing is adequate, concentration and temperature are uniform, and the effluent has these same properties. The steady state material balance on a reacdant A is... 

Ordinary or bulk diffusion is primarily responsible for molecular transport when the mean free path of a molecule is small compared with the diameter of the pore. At 1 atm the mean free path of typical gaseous species is of the order of 10 5 cm or 103 A. In pores larger than 1CT4 cm the mean free path is much smaller than the pore dimension, and collisions with other gas phase molecules will occur much more often than collisions with the pore walls. Under these circumstances the effective diffusivity will be independent of the pore diameter and, within a given catalyst pore, ordinary bulk diffusion coefficients may be used in Fick s first law to evaluate the rate of mass transfer and the concentration profile in the pore. In industrial practice there are three general classes of reaction conditions for which the bulk value of the diffusion coefficient is appropriate. For all catalysts these include liquid phase reactions... 

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 liquid-phase reaction A - B + C takes place in a single-stage CSTR The rate law for... 

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. 

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... 

This irreversible reaction has an elementary rate law and is carried out in aqueous ethanol. Therefore, like almost all liquid-phase reactions, the density remains almost constant throughout the reaction. It is a general principle that for most liquid-phase reactions, the volume V for a batch reaction system and the volumetric flow rate v for a continuous-flow system will not change appreciably during the course of a chemical reaction. 

To obtain a plot of heat generated, G(T), as a function of temperature, we must solve for X as a function of T using the CSTR mole balance, the rate law, and stoichiometry. For example, for a first-order liquid-phase reaction, the CSTR mole balance becomes... 

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. 

The production of methyl bromide is an iireversible liquid-phase reaction that follows an elementary rate law. The reaction... 

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 summarize for liquid-phase reactions (or as we will soon see for isoiherma and isobaric gas-phase reactions with no change in the total number of moles) we can use a rate law for reaction (2-2) such as -r - k/,jC,, Cs obtait - A t iat is,... 

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. 

Lumping of species for hydrocarbon mixtures. [3rd Ed. P5-16] Prepare an experimental plan to find the rate law. (3rd Ed. P5-J7] Batch data on the liquid phase reaction... 

Isothermal reactor. This example concerns an elementary, exothermic, second-order reversible liquid-phase reaction in a tubular reactor with a parabolic velocity distribution. Only the mole, rate law, and stoichiometry balance in the tubular reactor are required in ihi.s FEMLAB chemical engineering module. 

Simple homogeneous liquid-phase reactions can be described with the help of formal kinetic rate laws in which the reaction rate r depends on the concentrations of the reactants, on the temperature and possibly on the homogeneous catalyst only. Examples of such formal kinetic rate laws are presented in Table 4-1. 

For the purpose of illustration of the relations developed above, RD of an ideal mixture of three components being subject to the reversible liquid-phase reaction A + B o C is considered. The rate of reaction is given by the power law expression... 

The reactor operates at 40 bar and 120°C and its volume is 1200 ft (75% liquid). For the liquid-phase reaction, the inlet streams have the specifications, shown in table given below Pure aniline and hydrogen enters the reactor with a flow rate of 45 and 160 kmol/h at 43 and 230°C, respectively, and 41 bar. Reaction kinetic data for Arrhenius law are given as ... 

Hyperbolic equations were used in Chapter 6 to represent reactions catalyzed by solid surfaces. They are referred to as LHHW models and they can be empirically extended to homogeneous catalysis in liquid phase reactions. The actual rate equation to be used for a given reaction will depend on the regime of that reaction. Methods of discerning the controlling regimes for catalytic gas-liquid reactions described in the gas-liquid chapter were based on simple power law kinetics. Extension of these methods to gas-Uquid reactions catalyzed by homogeneous catalysts involves no new principles, but the mathematics becomes more... 

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