Walter, Jesse, and Mike Ehrmantraut stole 1000 gallons of methylamine. Afterwards, however, Jesse and Mike decided to get out of the meth-cooking business and sell their shares of methylamine. Walter wanted to keep all of the methylamine for future meth cooks and not let Jesse and Mike have their shares. Now, let’s suppose Jesse and Mike decided to sabotage Walter’s cooking operation by ruining the methylamine by performing the following gas phase reaction:
2 CH3NH2⇄(CH3)2NH + NH3
This reaction converts the methylamine to dimethylamine, using a silica-alumina catalyst. The molar flow rate into a packed-bed reactor is 12 mol/s and the entering pressure is 9 atm. Assume there is no pressure drop or temperature change in the reactor. Suppose that the reaction rate follows an elementary rate law in terms of partial pressure, with: kf= 4 × 10-6mol atm-2g_catalyst-1s-1and Keq= 3.0
a)[2 points] Write the mole balance for this PBR The reaction above can be written as: 2 A ⇄B + C For a PBR the mole balance (in terms of conversion) results in: =−′
b)[3 points] Write the rate law in terms of partial pressures First we should note that the units of the rate constant are in terms of pressure: k = 4.25×10-6mol atm-2 g_cat-1 s-1As usual, the rate expression should have units of mol g_cat-1 s-1, therefore the rate expression for this elementary reaction can be written as: ′=PP2− =PP2�1−2�′=� −�
c)[4 points] Set-up a stoichiometric table for this reaction Assuming that initially we have pure A, and taking A as the limiting reactant, we can rewrite the reaction as: A ⇄½ B + ½ C Then, =0(1− )=120=120
ENCH 421 – 2017 Winter – Dr. Hector De la Hoz Siegler2 TT=0= 0 ∴= 0
d)[3 points] Write the partial pressures in terms of conversion Note that: PP=Then, PP=As the volumetric flow rate is constant [i. e. no increase in the number of moles, constant pressure, and constant temperature], we can write: PP=0=