An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 137

PROBLEMS

3.1. Our ancestors have learned to make vinegar by aerobic bacterial fermentation of
alcohol, which is derived by anaerobic fermentation of sugar. Vinegar can also be made
by carbonylation of methanol, which is derived by reaction of synthesis gas, which can
be obtained by steam reforming of methane. Write out these reactions.
3.2. What is an elementary reaction?
3.3. What is an approximate reaction? In what sense an approximate reaction should
stoichiometry be held? How does approximate reaction differ from coupled reaction?
3.4. For the complex reaction with stoichiometry A þ 3B / 2R þ P and with second-order

rate expression: r P ¼ kC A C B are the reaction rates related by r A ¼ r B ¼ r R ¼ r P ? If the

rates are not so related, then how are they related?
3.5. Given the reaction 2 NO 2 þ N 2 O 5 , what is the relationship between the

rates of formation of N 2 O 5 and disappearance of the two reactants?
3.6. We have a process that reacts 67% CH 4 in O 2 at 10 atm to form syngas
( D H R ¼

½O 2 ¼¼¼¼

8.5 kcal/mol-CH 4 ).
(a) Estimate the adiabatic reactor temperature at completion if we produce 100%
syngas with a feed temperature of 400 C. Assume C p ¼

7 cal/(mol $ K).
(b) Estimate the adiabatic reactor temperature if we suddenly begin producing 100%
total combustion products ( D H R ¼

7/2 and R ¼

192 kcal/mol).
(c) What do we have to be concerned with regarding reactor construction materials and
pressure relief capabilities to design for this possibility?
3.7. Methanol is synthesized commercially from CO and H 2 by the reaction
CO

OH
over a Cu/ZnO catalyst at ~350 Cat50 e 100 atm. The standard-state thermodynamic
data on this reaction are D H R, 298 ¼

þ 2 H

2 #

CH 3

90.64 kJ/mol and D G R,298 ¼

24.2 kJ/mol.
(a) What is the equilibrium conversion of a stoichiometric mixture of CO and H 2 to
methanol at 298 K at 1 atm?
(b) Assuming D H R independent of T, what are K eq and the equilibrium conversion at
1 atm and 350 C?
(c) K eq at 350 C is measured to be 1.94 10 4 . How large is the error assuming

constant D H R ?
(d) At what pressure will the equilibrium conversion be 50% at 350 C?
3.8. The maximum allowable temperature for a reactor to maintain integrity is 800 K.
At present, our operating set point is 780 K, the 20-K margin of safety to guard
against fluctuating feed, sluggish controls, etc. With a more sophisticated control
system, we could be able to raise our set point to 792 K without sacrificing the safety
limits we have now. By how much can the reaction rate, hence, production rate, be
raised by this change if the reaction taking place in the reactor has an activation
energy of 200 kJ/mol?
3.9. The pyrolysis of ethane proceeds with an activation energy of about 300 kJ/mol. How
much faster is the decomposition at 625 C than at 525 C?
3.10. At 1100 K n-nonane thermally cracks 20 times as rapidly as at 1000 K. Find the
activation energy for this decomposition.