Question

Problem 2: Fogler 6-6 (a-g), pg. 363 Consider the following system of gas-phase reactions: A X ??? 1/2 X A 1 r kC = 3 1/2 1 k = ? 0.004 (mol/dm ) min A B ??? B A 2 r kC = 1 2 k 0.3 min? = A ???Y 2 Y A 3 r kC = 3 3 k = ? 0.25 dm /mol min B is the desired product, and X and Y are foul pollutants that are expensive to get rid of. The specific reaction rates listed are at 27 ºC. The reaction system is to be operated at 27 ºC and 4 atm. Pure A enters the system at a volumetric flow rate of 10 dm3 /min. (a) Sketch the instantaneous selectivities ( / / , , B X BY S S and S rrr B XY B X Y / = + /( )) as a function of the concentration of CA. (b) Consider a series of reactors. What should be the volume of the first reactor? (c) What are the effluent concentrations of A, B, X, and Y from the first reactor? (d) What is the conversion of A in the first reactor? 2 (e) If 99% conversion of A is desired, what reaction scheme and sizes should you use to maximize B XY / S ? (f) Suppose that E1 = 20,000 cal/mol, E2 = 10,000 cal/mol, and E3 = 30,000 cal/mol. What temperature would you recommend for a single CSTR with a space of time of 10 min and an entering concentration of A of 0.1 mol/dm3 ? (g) If you could vary the pressure between 1 and 100 atm, what pressure would you choose?

Answer 1

a) Selectivity tells us how one product is favored over another when multiple reactions take place.

SB/X = rB/rX = k2CA/ k1CA1/2 = k2. CA1/2 / k1

SB/Y = rB/rY = k2CA / k3 CA2 = k2 CA-1/ k3

SB/XY = rB/rX + rY =

k2CA / k1CA1/2 +k3 CA2

b) PV = nRT

T = 300.5 K, P = 4 atm, V = ? n = 10 /22.4 = 0.446, R = 0.0821

4*V = 0.446 * 0.0821* 300.5

V = 2.75 L

C) Initial concentration CA = moles/volume = 0.446/2.75 = 0.1621 moles/L

rx = 0.004 * (0.1621)^1/2= 0.0016

rB = 0.3 * 0.1621 = 0.048

ry = (0.1621)^2 * 0.25 = 0.0065

net rate of disappearence of A = rx +rB +rY = 0.0016+0.048 +0.0065 = 0.056 mol/min

residence time = volume /velocity = 2.75 /10 = 0.275 min.

concentration of effluent A = 0.275 *0.056 = 0.0154, 0.1621 -0.0154 = 0.1467 mol

total B, X and Y = 0.0154 moles