The following liquid-phase reaction is to be carried out in an isothermal batch
ID: 707533 • Letter: T
Question
The following liquid-phase reaction is to be carried out in an isothermal batch reactor. A +3 B R k 106 m/mol-s The initial concentration of species A is 1000 mol/m3, and a stoichiometric ratio of the two reactants is used. No species R is present initially. Express the reaction rate, -ra, in terms of the concentration of species A (i.e. eliminate the concentration of species B from the reaction rate equation). Detemice how long i requiedeieninety purent peies A comenion. Also determine how long is required to achieve ninety percent species B conversion. What is the product concentration when the species A conversion is ninety percent? Is this reaction elementary?Explanation / Answer
Since we always have a stoichiometric ratio,
CAO = 1000 mol/m3
CBO = 3000 mol/m3
CA = CAO (1 - X)
CB = CBO - CAO * 3X = 3CAO (1-X) since CBO = 3CAO
Thus, -rA = kCACB = 3k[ CAO (1-X)]2
For a batch reactor, the design equation is: dCA/dt = rA
In liquid phase, CAO dX/dt =- rA
Thus, CAO dX/dt = 3*k* CAO2 (1-X)2
dX/(1-X)2 = 3kCAOdt
Integrating X from 0 to 0.95,
19 = 3 * 10-6 * 1000 * t
t = time req for 95 % conversion of A = 6333.33 s = 1.76 hrs
Since everything occurs stoichiometrically, B will require the same to get converted by 95%.
At 95% conversion,
R = CAO X = 950 mol/m3
Reaction is not elementary, since the rate law does not follow the stoichiometric coefficients in the chemical equation.
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