Question

Consider an isothermal CSTR, with the liquid phase inlet feed of: Fao 61 mol/hr benzene Vo 10 L/min Diphenyl is synthesized by the following irreversible reaction 2benzene-» diphenyl H2 with the rate law: Tbenzene-kCbenzenek 0.2 L/(mol'min) a. Wirite the stoichiometric table for this reaction. b. What volume CSTR is required for the exit concentration of benzene to be 12 mM? c. What is the extent of reaction? d. What is the conversion of benzene?

Answer 1

1. A stoichiometric table allows to make a balance of matter of the reaction and to know the outflows of each species

Reaction: 2 benezene-->diphenyl H20 2 A-->B+C SpeciesInput flow |61 mol/hr Change Output flow A | -61mol/hr"XFA-61mol/hr-61mol/hr*X B01/261 mo/hr X FB-1/2 61mol/hr X 0 1/2 61mol/hr X FC 1/2 61mol/hr X
2. To know the volume first you must know the reaction speed according to the given expression, with the concentration of benzene (12mM) and the constant k (0.2L / molmin), are replaced in ra and in this way know the speed of reaction:

12mM * 1mol/1000mmol = 0.012M = Ca

-ra = 0.2 L/molmin * (0.012M)2 * 60 min/1h = 2.88 * 10-5 L / molmin

The volume is defined by the design equation of a continuous stirred tank reactor is as follows:

V = Fao * X / -ra                     (1)

This can be rewritten as follows:

V = (Fa - Fao) / -ra                  (2)

And likewise take them to terms of concentration:

V = [(Cao * ro) - (Ca * ro)] / - ra   (3)

From this last equation we do not know Cao, which is defined by dividing the molar flow between the volumetric flow:

Cao = Fao / ro
Fao = 61 mol/hr * (1 hr/60min) = 1.016 mol/min
Cao = (1.016 mol/min) / (10 L/min)
Cao = 1.02 mol/L

The concentrations, reaction rate and volumetric flow are substituted in equation 3 to finally know the volume:

V = [(1.02 mol/L * 10 L/min) - (0.012 mol/L * 10 L/min] / 2.88 * 10-5V = 35000L

3. The conversion of benzene is cleared from equation 1 (raised in part 2)

X = (V * -ra) / Fao
X = (35000L * 2.88 * 10-5 L / mol min) / 1.016 mol/L
X = 0.9921