ChE372:Fall 2014Homework 3

1. The reaction between ammonia and formaldehyde to give hexamine is

4 NH3 + 6 HCHO → (CH2)6 N4 + 6 H2O r = 1.42× 103 exp(−3090

T

)C2

ACB mol A/L.s

where A is ammonia and B is formaldehyde.

A 0.5 L CSTR is used for the reaction. Each reactant is fed to the reactor in separate stream, atthe rate of 1.5 × 10−3 L/s each. The ammonia concentration is 4 mol/L and the formaldehydeis 6.4 mol/L. The reactor temperature is 36 0C. Calculate the concentration of ammonia andformaldehyde in the effluent stream.

2. The liquid phase reaction

A + B ⇀↽ C + D r = k1CACB − k2CCCD

was tested in a laboratory CSTR with these results.

Residence time (hrs) 0.8 5.0% conversion of A 50 60

Feed concentrations were cA0 = 2 mol/L, cB0 = 1.5 mol/L and the others zero.

(a) Find the reaction rate constants k1 and k2. (Ans: k1 = 3.25; k2 = 0.375)

(b) Find the time for 90% of equilibrium conversion in a batch reactor. (Ans: 2 h)

3. Consider the gas-phase reaction

A → B + C r = kcA

in an isothermal plug flow reactor. The pressure is kept constant in the reactor. The feed consistsof A and an inert. The reactor is to be operated to give a conversion xA = 0.9. Study the effectof inert on the reactor volume:

Case I: The feed consist of 3 moles of A and one mole of inert.

Case II: The feed consist of 4 moles of A and one mole of inert.

By how much will the reactor volume change if the inlet is changed from case I to Case II?

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4. Consider a homogeneous gas phase reaction

A → 3B r = kc2A

For a feed rate of 4 m3/hr of pure A at 5 atm and 350 0C, a pilot reactor consisting of a 2.5 cmID pipe 2 m long gave 60% conversion of feed. A commercial plant is process 320 m3/hr of feedconsisting of 50% each of A and inerts at 25 atm and 350 0C, and 80% conversion is required.Find how many 2 meter lengths of 2.5 cm ID pipe are needed. Should they be placed in series orparallel?

5. Consider a system of two CSTR’s in series. The feed enters at a volumetric flow rate of 100 cfhand the feed is pure A with inlet concentration 1.5 lbmols/cuft. The effluent from the secondstage continues to react in the pipe line going to the storage unit. This line has 0.864 sq in crosssection and is 1000 feet long. The reaction is

2A ⇀↽ B + C r = 5(C2

A − CBCC

16

)lbmol/cuft-hr

It is required to have 80% approach to equilibrium at the storage tank. What is the volume ofthe CSTR if the residence time are the same in both CSTR’s.

CSTR - I

CSTR - II

CA2

CA3

CA0

CA1

Transfer Line (L = 1000 ft A = 0.864 in2)

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6. Consider the reversible, liquid-phase reaction

A ⇀↽ B r = k(CA − CB

K

)The equilibrium constant based on concentration for this reaction is 2 at temperature T1.

An ideal CSTR with volume of 1000 l is being operated at T1. The molar flow rate of A to theCSTR is 1500 mol/min. The Concentration of A in the feed is 2.5 mol/l; there is no B in thefeed.

(a) What is the lowest possible outlet concentration of A that can be obtained at T1.

(b) The actual concentration of A leaving the CSTR is 1.5 mol/L. What is the value of theforward rate constant k at T1?

(c) A second CSTR with volume of 1000 l is added in series with the first. The molar flow rateof A to the first reactor is increased so that the concentration of A leaving the second CSTRis 1.5 mol/l. The feed composition is unchanged. What is the new flow rate of A to the firstreactor?

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