Reactant fractional conversion

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. 

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

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. 

The fractional conversion of a given reactant, Xa, is defined for a batch system as... 

Reactant A is consumed, so tA is negative, and the fractional conversion will increase with Z. 

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... 

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. 

If nonstoichiometric amounts of reactants are present in the initial system, the presence of excess reactants tends to increase the equilibrium fractional conversion of the limiting re-... 

The accumulation term is just the time derivative of the number of moles of reactant A contained within the reactor (dNJdt). This term also may be written in terms of either the extent of reaction ( ) or the fraction conversion of the limiting reagent (fA). (A is presumed to be the... 

At any point the molal flow rate of reactant A can be expressed in terms of the fraction conversion fA and the molal flow rate corresponding to zero conversion FA0. 

Fa o may also be written as the product of a volumetric flow rate and a reactant concentration where both are measured at some reference temperature and pressure and correspond to zero fraction conversion. Thus... 

For semibatch operation, the term fraction conversion is somewhat ambiguous for many of the cases of interest. If reactant is present initially in the reactor and is added or removed in feed and effluent streams, the question arises as to the proper basis for the definition of /. In such cases it is best to work either in terms of the weight fraction of a particular component present in the fluid of interest or in terms of concentrations when constant density systems are under consideration. In terms of the symbols shown in Figure 8.20 the fundamental material balance relation becomes ... 

Equation 2.2-2 may appear in various forms, if nA is related to other quantities (by normalization), as follows (1) If A is the limiting reactant, it may be convenient to normalize nA in terms of /A, the fractional conversion of A, defined by ... 

For a reaction represented by A - products, in which the rate, ( — rA), is proportional to cA, with a proportionality constant kA, show that the time (t) required to achieve a specified fractional conversion of A (/A) is independent of the initial concentration of reactant cAo. Assume reaction occurs in a constant-volume batch reactor. 

A useful tool for dealing with reaction stoichiometry in chemical kinetics is a stoichiometric table. This is a spreadsheet device to account for changes in the amounts of species reacted for a basis amount of a closed system. It is also a systematic method of expressing the moles, or molar concentrations, or (in some cases) partial pressures of reactants and products, for a given reaction (or set of reactions) at any time or position, in terms of initial concentrations and fractional conversion. Its use is illustrated for a simple system in the following example. 

A second-order reaction may typically involve one reactant (A -> products, ( -rA) = kAc ) or two reactants ( pa A + vb B - products, ( rA) = kAcAcB). For one reactant, the integrated form for constant density, applicable to a BR or a PFR, is contained in equation 3.4-9, with n = 2. In contrast to a first-order reaction, the half-life of a reactant, f1/2 from equation 3.4-16, is proportional to cA (if there are two reactants, both ty2 and fractional conversion refer to the limiting reactant). For two reactants, the integrated form for constant density, applicable to a BR and a PFR, is given by equation 3.4-13 (see Example 3-5). In this case, the reaction stoichiometry must be taken into account in relating concentrations, or in switching rate or rate constant from one reactant to the other. 

Fractional conversion of a reactant, /A for reactant A, say, is the ratio of the amount of A reacted at some point (time or position) to the amount introduced into the system, and is a measure of consumption of the reactant. It is defined in equation 2.2-3 for a batch system, and in equation 2.3-5 for a flow system. The definition is the same whether the system is simple or complex. 

The process design of a batch reactor may involve determining the time (t) required to achieve a specified fractional conversion (/A, for limiting reactant A, say) in a single batch, or the volume (V) of reacting system required to achieve a specified rate of production on a continual basis. The phrase continual basis means an ongoing operation,... 

For a constant-density system, several simplifications result. First, regardless of the type of reactor, the fractional conversion of limiting reactant, say fA, can be expressed in terms of molar concentration, cA ... 

Calculate the ratio of the volumes of a CSTR and a PFR ( Vst pf) required to achieve, for a given feed rate in each reactor, a fractional conversion (/A) of (i) 0.5 and (ii) 0.99 for the reactant A, if the liquid-phase reaction A - products is (a) first-order, and (b) second-order with respect to A. What conclusions can be drawn Assume the PFR operates isothermally at the same T as that in the CSTR. 

For exothermic, reversible reactions, the existence of a locus of maximum rates, as shown in Section 5.3.4, and illustrated in Figures 5.2(a) and 18.3, introduces the opportunity to optimize (minimize) the reactor volume or mean residence time for a specified throughput and fractional conversion of reactant. This is done by choice of an appropriate T (for a CSTR) or T profile (for a PFR) so that the rate is a maximum at each point. The mode of operation (e.g., adiabatic operation for a PFR) may not allow a faithful interpretation of this requirement. For illustration, we consider the optimization of both a CSTR and a PFR for the model reaction... 

In Example 21-1 above, the effects on equilibrium of changing P (at constant T and r, initial molar ratio of inert species to limiting reactant) and changing r (at constant P and T) are examined. Here, we focus on the effect of T (at constant P, r) through the dependence of fractional conversion on T. For the reaction A +. . . products (at equilibrium), we examine the behavior of fA (7), where represents /A at equilibrium. 

The fractional conversion across the bed is given in terms of the fractions of reactant in the bubble and emulsion regions ... 

A batch reactor and a single continuous stirred-tank reactor are compared in relation to their performance in carrying out the simple liquid phase reaction A + B —> products. The reaction is first order with respect to each of the reactants, that is second order overall. If the initial concentrations of the reactants are equal, show that the volume of the continuous reactor must be 1/(1 — a) times the volume of the batch reactor for the same rate of production from each, where a is the fractional conversion. Assume that there is no change in density associated with the reaction and neglect the shutdown period between batches for the batch reactor. 

Reactor volume was 0.276 liters. Data are presented of P in torr, na0 mols/sec of entering reactant, y = nd/na0 mols carrier gas per mol of reactant, and x fractional conversion. Check a first order rate equation. 

The aqueous second order reaction, 2A 2B, has the specific rate k = 1.0 liter/mol-hr and the initial concentration Ca0= 1 mol/liter. Downtime is 1 hr/batch. Cost of fresh reactant is 100/batch and the value of the product is 200xa/batch, where xa is the fractional conversion of A. What is the daily profit for each of these modes of operation ... 

Carothers next step was to move from polyesters to nylons and to increase the fractional conversion (p) by making salts using the equivalent reaction of 1,6-hexanediamine (hexamethylenediamine) and adipic acid. These salts were recrystallizable from ethanol giving essentially a true 1 1 ratio of reactants. Thus, a high molecular weight polyamide, generally known as simply a nylon, in this case nylon-6,6, was produced from the thermal decomposition of this equimolar salt as shown in structure 4.55. This product has a melting point of 265°C. 

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