Constant-volume batch systems

The rate equation for a constant volume batch system is ... 

Assuming a constant volume batch system, from the stoichiometric coefficients of Equation 5-22... 

Assuming the reaction is first order in a constant volume batch system, the rate equations of A, B, and C, respectively, are ... 

If the rate of the reaction is independent of the concentration of the reacting substance A, then the amount dCA by which the concentration of A decreases in any given unit of time dt is constant throughout the course of the reaction. The rate equation for a constant volume batch system (i.e., constant density) can be expressed as ... 

Consider the reaction A+B——> products. The rate equation for a constant volume batch system (i.e., constant density) is ... 

With the restrictions that CAO = CBO and Cco = CDO = 0 in Equation 3-170, the rate equation for a constant volume batch system becomes... 

Br2 + CH3CHO + H20 -> CH3COOH + 2H+ + 2Br (3-191) The rate equation of the reaction for a constant volume batch system is... 

For constant-pressure batch systems we would simply substitute Nj for F in the equations above. For constant-volume batch systems we woulduseconcentrations ... 

However this "definition" is wrong It is simply a mole balance that is only valid for a constant volume batch system. Equation (1-1) will not apply to any continuous-flow reactor operated at steady state, such as the tank tCSTR) reactor where the concentration does not vary from day to day (i.c.. the concentration is not a function of time). For amplification on this point, see the section "Is Sodium Hydroxide Reacting " in the Summary Notes for Chapter 1 on the CD-ROM or on the web. 

P3-14. Reinforces the point that the equilibrium conversion will be different fori flow system and a constant volume batch system. 

The information required here is not concentration versus time, but rate of reaction versus concentration. As will be seen later, some types of chemical reactors give this information directly, but the constant-volume, batch systems discussed here do not [ What does it profit you, anyway —F. Villon], In this case it is necessary to determine rates from conversion-time data by graphical or numerical methods, as indicated for the case of initial rates in Figure 1.25. In Figure 1.27 a curve is shown representing the concentration of a reactant A as a function of time, and we identify the two points Cai and Ca2 for the concentration at times q and t2- The mean value for the rate of reaction we can approximate algebraically by... 

Initiation Thermal scission of an initiator is the most common means of generating radicals in FRP (see Section 4.2). This unimolecular reaction is characterized by a first-order rate coefficient (k, s ) so that, for a constant-volume batch system, Eq. (2) may be integrated to yield Eq. (15), with t = 0. 

To summarize for constant volume batch systems and for liquid-( ase reactions, we can use a rate law for reaction (2-2) such as -r = AaCaQ to obtain —r =f[X). that is,... 

As expected, the dependence of reaction rate on conversion for a constant-volume batch system [t.e.. Equation (E4-5.I0)) is different than that for a flow system [Equation (E4-5.1 i)] for gas-phase reactions. 

Aaglvsis The purpose of (his example was to calculate the equilibrium conversion lirst for a constant volume batch system in pan (a), and then for a constant pressure flow reaction in pan (b). One notes that there is a change in the total number of moles in this reaction and, as a result, these two equilibrium conversions are not the same We next showed how to express =fiX) for a reversible-ga-s-phase reaction. Finally, in Pan (d) having -r = j X), we specified a molar flow rate of A (e.g., 3.0 mol A/min) and calculated the CSTR volume necessary to achieve 40% conversion, We did this calculation to give insight to the types of analyses we as chemical reaction engineers will carry out as we move into similar but more complex calculations in Chapters 5 and 6. 

Example 4-5. Why is the equilibrium conversion lower for the batch system than the flow system Will this always be the case for constant volume batch systems For the case in which the total concentration Ctd is to remain constant as the inerts are varied, plot the equilibrium conversion as a function of mole fraction of inerts for both a PFR and a constant-volume batch reactor. The pressure and temperature are constant at 2 atm and 340 K. Only N 04 and inert 1 are to be fed. 

Suppose by chance the reaction is elementary with k(j =40 dmVmol/s. Write the rate of reaction solely as a function of conversion for (t) a how system and for (2) a constant volume batch system. 

---