Chemical reaction time constant

In other words, E is not a function of conversion or molar densities. The characteristic chemical reaction time constant is 25 min. The temperature is the same in each case. The following reactor configurations are employed. 

One liquid-phase chemical reaction occurs in an isothermal configuration of PFRs. The chemical kinetics are second order and irreversible [i.e., lEt = 2(Ca) ], and the characteristic chemical reaction time constant A. is 5 min. Rank the configurations listed in Table PI-3 from highest final conversion of reactant A in the exit stream of the last PFR in series to lowest final conversion in the exit stream of the last PFR. In each case, the volumetric flow rate is 10 L/min and Ca, miet is the same. Calcnlate the final conversion of reactant A in the exit stream of the third PFR in series for case 7. 

All reactors operate at the same temperature. The reactor types and configurations are described below. Notice that the total residence time for each configuration is 1 min, whereas the chemical reaction time constants are 1 minutes for the first reaction and 20 min for the second reaction. 

This expression for co is also appUcable for reversible chemical kinetics when the forward and backward reactions are both nth-order. In other words, it is acceptable to define the chemical reaction time constant for reversible reactions in terms of the kinetic rate constant for the forward step. The differential design equation given by (22-14) for one-dimensional convection and one chemical reaction in a plug-fiow tubular reactor reduces to... 

As expected, a shorter reactor is required to achieve the same final conversion when the characteristic chemical reaction time constant u> is smaller and the effectiveness factor E is larger. Since the integral in equation (22-27) that contains the dimensionless kinetic rate law reduces to a constant when the final conversion of... 

The effectiveness factor E is expressed in terms of the intrapellet Damkohler number, and the chemical reaction time constant co is the inverse of the best pseudo-first-order kinetic rate constant. The reactor design engineer employs an integral form of the design equation to predict the length of a packed catalytic tubular reactor Lpfr that will achieve a final conversion of CO specified by /final. The approximate analytical solution, vahd at high mass transfer Peclet numbers, is... 

At high-mass-transfer Peclet numbers, sketch the relation between average residence time divided by the chemical reaction time constant (i.e., r/co) for a packed catalytic tubular reactor versus the intrapeUet Damkohler number Aa, intrapeiiet for zeroth-, first-, and second-order irreversible chemical kinetics within spherical catalytic pellets. The characteristic length L in the definition of Aa, intrapeiiet is the sphere radius R. The overall objective is to achieve the same conversion in the exit stream for all three kinetic rate laws. Put all three curves on the same set of axes and identify quantitative values for the intrapeiiet Damkohler number on the horizontal axis. 

The overall requirement is 1.0—2.0 s for low energy waste compared to typical design standards of 2.0 s for RCRA ha2ardous waste units. The most important, ie, rate limiting steps are droplet evaporation and chemical reaction. The calculated time requirements for these steps are only approximations and subject to error. For example, formation of a skin on the evaporating droplet may inhibit evaporation compared to the theory, whereas secondary atomization may accelerate it. Errors in estimates of the activation energy can significantly alter the chemical reaction rate constant, and the pre-exponential factor from equation 36 is only approximate. Also, interactions with free-radical species may accelerate the rate of chemical reaction over that estimated solely as a result of thermal excitation therefore, measurements of the time requirements are desirable. 

Fig. 4. Variation of autocorrelation function with changes in the equilibrium constant in the fast reaction limit. A and B have the same diffusion coefficients but different optical (fluorescence) properties. A difference in the fluorescence of A and B serves to indicate the progress of the isomerization reaction the diffusion coefficients of A and B are the same. The characteristic chemical reaction time is in the range of 10 4-10-5 s, depending on the value of the chemical relaxation rate that for diffusion is 0.025 s. For this calculation parameter values are the same as those for Figure 3 except that DA = Z)B = lO"7 cm2 s-1 and QA = 0.1 and <9B = 1.0. The relation of CB/C0 to the different curves is as in Figure 3. 

Question (b) is a matter of chemical kinetics and reduces to the need to know the rate equation and the rate constants (customarily designated k) for the various steps involved in the reaction mechanism. Note that the rate equation for a particular reaction is not necessarily obtainable by inspection of the stoichiometry of the reaction, unless the mechanism is a one-step process—and this is something that usually has to be determined by experiment. Chemical reaction time scales range from fractions of a nanosecond to millions of years or more. Thus, even if the answer to question (a) is that the reaction is expected to go to essential completion, the reaction may be so slow as to be totally impractical in engineering terms. A brief review of some basic principles of chemical kinetics is given in Section 2.5. 

Early chemists thought that the beat of reaction, —AH. should be a measure of the "chemical affinity" of a reaction. With the introduction of the concepl of netropy (q.v.) and ihe application of the second law of thermodynamics lo chemical equilibria, it is easily shown that the true measure of chemical affinity and Ihe driving force for a reaction occurring at constant temperature and pressure is -AG. where AG represents the change in thermodynamic slate function, G. called Gibbs free energy or free enthalpy, and defined as the enthalpy, H, minus the entropy. S. times the temperature, T (G = H — TS). For a chemical reaction at constant pressure and temperature ... 

In order to extrapolate the laboratory results to the field and to make semiquantitative predictions, an in-house computer model was used. Chemical reaction rate constants were derived by matching the data from the Controlled Mixing History Furnace to the model predictions. The devolatilization phase was not modeled since volatile matter release and subsequent combustion occurs very rapidly and would not significantly impact the accuracy of the mathematical model predictions. The "overall" solid conversion efficiency at a given residence time was obtained by adding both the simulated char combustion efficiency and the average pyrolysis efficiency (found in the primary stage of the CMHF). 

Comparison of equations 3 and 10 shows the essential difference between the stationary states of closed and continuous, open systems. For the closed system, equilibrium is the time-invariant condition. The total of each independently variable constituent and the equilibrium constant (a function of temperature, pressure, and composition) for each independent reaction (ATab in the example) are required to define the equilibrium composition Ca- For the continuous, open system, the steady state is the time-invariant condition. The mass transfer rate constant, the inflow mole number of each independently variable constituent, and the rate constants (functions of temperature, pressure, and composition) for each independent reaction are requir to define the steady-state composition Ca- It is clear that open-system models of natural waters require more information than closed-system models to define time-invariant compositions. An equilibrium model can be expected to describe a natural water system well when fluxes are small, that is, when flow time scales are long and chemical reaction time scales are short. 

It is interesting to note that calculations of turbulent flows during fast chemical reactions, predicted that the chemical reaction rate constant influences the effective diffusion coefficient and accelerates micromixing, due to an increase of the local reactant concentration gradients [13]. The dependence of the lower boundaries of the reaction front macrostructure formation, in particular, the plane and the torch front, which characterise different scales of liquid flow mixing, on the values of the chemical reaction constants is experimental evidence of the correlation between the kinetic and diffusive parameters of the process. At the same time, one can suppose that the formation of the characteristic reaction front macrostructures is defined by the mixing at the macro- and microlevels. 

This can be accomplished by setting up appropriate kinetic equations arid subsequent integration of the resulting differential equations, from which the population of the various states in which the positrons exist o-Ps and PsM can be found as a function of time. From these values and the positron annihilation constants for these states, an equation for the time dependent two photon annihilation rate can be obtained, which in turn allows the determination of the chemical reaction rate constants by utilizing sophisticated nuclear chemical lifetime measurement techniques. 

Fig. 40. Calculated frequency dependence of fundamental harmonic peak current ratio ip.kinAp.d with preceding reversible chemical reaction. Equilibrium constant K = 0.1, drop-time Tj = 6 s, Tp d calculated according to equation...

As we have noted, potential step methods are particularly attractive for the determination of chemical rate constants in electrochemical mechanisms because the potential can be stepped to a potential at which the forward electron transfer is fast and irreversible, so that the current response depends only on the rates and mechanism of coupled chemical reactions. A complete quantitative evaluation of the mechanism was achieved by combining the potential step results with a series of simulations. The chemical reaction rate constants were determined by single-step experiments (the oxidation of NO2). Early in the step, the single-step response is determined by the equilibrium concentration of NO2. At later times, the response reflects the rate of conversion of N2O4 to NOj. Simulated potential step response curves could be compared to experimental data to extract the Ke, and k, and k, (see Figure 3-1). 

The effect of macromixing on the performance of chemical reactors is dealt with in standard text books [2] [4] [6] and will not be discussed here. Practical examples of micromixing effects are less known. From the discussion presented in Sec. 4 and influence of micromixing may be expected when a controlling step of the chemical process (time constant t ) competes with the micromixing process (time constant. This may happen especially in three domains fast and complex reaction systems, polymerization reactions, and precipitation (crystallization) reactions. Three examples of such micromixing effects are presented below. 

Mixing and reaction time constants are not readily calculated for pulp suspensions. Mixing rate is influenced by the complex suspension rheology. Bleaching rate is influenced by chemical diffusion into the fiber wall and can be controlled by mass transfer. Further, in laboratory experiments a net reaction rate is measured and may have been influenced by the mixing conditions during the test. Despite these concerns, a number of estimates can be made. 

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