Reaction fractional conversion

A (desired) liquid-phase dimerization 2A -> A2, which is second-order in A0"a2 = for a), is accompanied by an (undesired) isomerization of A to B, which is first-order in A(rB = 1 Ca). Reaction is to take place isothermally in an inert solvent with an initial concentration Ca0 = 5 mol L-1, and a feed rate (q) of 10 L s 1 (assume no density change on reaction). Fractional conversion (/a) is 0.80. 

For single reactions, fractional conversion is normally the preferred measure of the extent of reaction. However, for multiple reactions the reaction coordinate is the method of choice. The relationship that exists between conversion and the reaction coordinate is... 

Design equation— ideal hatch reactor— homogeneous reaction (fractional conversion)... 

Only the concentrations of reactants and products appear in the final rate equation. The concentrations of active centers were eliminated in Step 3. All of the concentrations in the final rate equation are related through stoichiometry. For a single reaction, each concentration in the rate equation can be expressed in terms of one stoichiometric variable, e.g., extent of reaction, fractional conversion of a reactant, or the concentration of a single species, e.g., the concentration of the limiting reactant. 

Fig. 6.3 Determining fractional conversion of one-step reaction fractional conversion = released partial/released total amount of heat...

In fact, the fractional conversion of the waste s nitrogen to NO decreases with increa sing nitrogen content (see Fig. 8) (29), as can be understood from the reaction pathway (see Fig. 7). 

Oxidation of cumene to cumene hydroperoxide is usually achieved in three to four oxidizers in series, where the fractional conversion is about the same for each reactor. Fresh cumene and recycled cumene are fed to the first reactor. Air is bubbled in at the bottom of the reactor and leaves at the top of each reactor. The oxidizers are operated at low to moderate pressure. Due to the exothermic nature of the oxidation reaction, heat is generated and must be removed by external cooling. A portion of cumene reacts to form dimethylbenzyl alcohol and acetophenone. Methanol is formed in the acetophenone reaction and is further oxidized to formaldehyde and formic acid. A small amount of water is also formed by the various reactions. The selectivity of the oxidation reaction is a function of oxidation conditions temperature, conversion level, residence time, and oxygen partial pressure. Typical commercial yield of cumene hydroperoxide is about 95 mol % in the oxidizers. The reaction effluent is stripped off unreacted cumene which is then recycled as feedstock. Spent air from the oxidizers is treated to recover 99.99% of the cumene and other volatile organic compounds. 

Equimolal proportions of the reactants are used. Thermodynamic data at 298 K are tabulated. The specific heats are averages. Find (1) the enthalpy change of reaction at 298 and 573 K (2) equilibrium constant at 298 and 573 K (3) fractional conversion at 573 K. 

This case includes most liquid reactions and also those gas reactions that operate at both constant temperature and pressure with no change in the number of moles during reaction. The relationship between concentration C and fractional conversion is as follows ... 

Nc = 0.0 gmol, Nq = 0.0 gmol, respectively. A mixture of A and B is charged into a 1-liter reactor. Determine the holding time required to achieve 90% fractional conversion of A (X = 0.9). The rate constant is k = 1.0 X 10 [(liter) /(gmoP min)] and the reaction is first order in A, second order in B and third order overall. 

For a cascade of N CFSTRs of equal volume, Vr, in which the first order forward reaction A—occurs with a throughput u, show that the system fractional conversion is... 

In the above reactions, the fractional conversion is defined as loss of reactant... 

The first order reaction is represented by (-r ) = kC, and applying the mass balance Equation 6-120 and the heat balance Equation 6-121, respectively, gives the fractional conversion in terms of the mass balance equation ... 

Using the same values of the kinetic parameters as in Type 1, and given C o = 0-1 mo 1/1, it is possible to solve Equation 6-155 with Equations 6-127 and 6-128 simultaneously to determine the fractional conversion X. A computer program was developed to determine the fractional conversion for different values of (-iz) and a temperature range of 260-500 K. Eigure 6-30 shows the reaction profile from the computer results. 

Fig ure 6-32. Fractional conversion versus T pt for a first order reversible reaction A R. 

Consider the reversible first order reaction A R. It is possible to determine the minimum reactor volume at the optimum temperature Tgp( that is required to obtain a fractional conversion X, if the feed is pure A with a volumetric flowrate of u. A material balance for a CESTR is... 

Figure 6-35. Fractional conversion versus Tg t for reaction type A R + S.

These results have been fit to experimental data obtained for the reaction between a diisocyanate and a trifunctional polyester polyol, catalyzed by dibutyltindilaurate, in our laboratory RIM machine (Figure 2). No phase separation occurs during this reaction. Reaction order, n, activation energy, Ea, and the preexponential factor. A, were taken as adjustable parameters to fit adiabatic temperature rise data. Typical comparison between the experimental and numerical results are shown in Figure 7. The fit is quite satisfactory and gives reasonable values for the fit parameters. Figure 8 shows how fractional conversion of diisocyanate is predicted to vary as a function of time at the centerline and at the mold wall (remember that molecular diffusion has been assumed to be negligible). 

Peller. (14) These reaction probabilities can easily be calculated from any of the fractional conversions of A,B, and G endgroups p, q and q respectively, if the reaction order is known. For example, it is obvious that Pj J P m stoichiometry. 

Solution The first-order rate constant is 0.693/2.1=0.33 so that the fractional conversion for a first-order reaction will be 1 — exp(—0.227) where f is in seconds. The inlet and outlet pressures are known so Equation (3.27) can be used to And t given that [L/Mom ] = 57/9.96 = 5.72s. The result is f = 5.91 s, which is 3.4% higher than what would be expected if the entire reaction was at Pout- The conversion of the organic compound is 86 percent. 

No systematic studies of a number of compoimds have yet appeared to discover correlations suggestive of mechanism. This paper presents the fractional conversions and reaction rates measured under reference conditions (50 mg contaminants/m ) in air at 7% relative humidity (1000 mg/m H2O), for 18 compounds including representatives of the important contaminant classes of alcohols, ethers, alkanes, chloroethenes, chloroalkanes, and aromatics. Plots of these conversions and rates vs. hydroxyl radical and chlorine radical rate constants, vs. the reactant coverage (dark conditions), and vs. the product of rate constant times coverage are constructed to discern which of the proposed mechanistic suggestions appear dominant. 

For nth-order reaction in terms of fraction conversion, Xa for a tank... 

Set the volumetric flow rate and feed concentration for the tank and tubular reactors to desired values. Set also the order of reaction to n = 1.01. Run for a range of fraction conversions from 0 to 0.99. Compare the required volumes for the two reactor types. 

Cross-sectional area Volumetric flow rate Reaction rate Stoichiometric constant Molar flow rate Molar feed flow rate A Molar feed flow rate B Molar inert flow rate Pressure Gas constant Temperature Fraction conversion Mole fraction Length... 

For a simple A -t- B —> C reaction in a continuous stirred-tank reactor, as shown in Fig. 5.134, in terms of fraction conversion of the reactant A, the balance... 

Oin experimental technique of choice in many cases is reaction calorimetry. This technique relies on the accurate measurement of the heat evolved or consumed when chemical transformations occur. Consider a catalytic reaction proceeding in the absence of side reactions or other thermal effects. The energy characteristic of the transformation - the heat of reaction, AH i - is manifested each time a substrate molecule is converted to a product molecule. This thermodynamic quantity serves as the proportionality constant between the heat evolved and the reaction rate (eq. 1). The heat evolved at any given time during the reaction may be divided by the total heat evolved when all the molecules have been converted to give the fractional heat evolution (eq. 2). When the reaction under study is the predominant source of heat flow, the fractional heat evolution at any point in time is identical to the fraction conversion of the limiting substrate. Fraction conversion is then related to the concentration of the limiting substrate via eq. (3). 

The conversion to equilibrium is effected in the presence of a catalyst at a pressure of 300 bar. Assuming the behavior to remain ideal, calculate the fractional conversion for each reaction and hence the volume composition of the equilibrium mixture. 

The fraction conversion / is an intensive measure of the progress of a reaction, and it is... 

The variable / depends on the particular species chosen as a reference substance. In general, the initial mole numbers of the reactants do not constitute simple stoichiometric ratios, and the number of moles of product that may be formed is limited by the amount of one of the reactants present in the system. If the extent of reaction is not limited by thermodynamic equilibrium constraints, this limiting reagent is the one that determines the maximum possible value of the extent of reaction ( max). We should refer our fractional conversions to this stoichiometrically limiting reactant if / is to lie between zero and unity. Consequently, the treatment used in subsequent chapters will define fractional conversions in terms of the limiting reactant. 

One can relate the extent of reaction to the fraction conversion by solving equations 1.1.4 and 1.1.7 for the number of moles of the limiting reagent nlim and equating the resultant expressions. 

---