CHE 301 Problem set #4

1. The irreversible reaction

is carried out in a reactor that initially contains 1.5 m3 of solution with a concentration of 1 kmol of A per cubic meter of solution. A solution containing 0.50 kmol of A/m3 enters the tank at a rate of 10 m3/h and is mixed perfectly with the existing solution. If the resulting product solution leaves the reactor at 5.0 m3/h, obtain an expression for concentration of A as a function of time. The reaction is first order with k = 0.2 hr-1. Calculate the concentration of A after (a) 0.2 hr and (b) 1.0 hr. (Ref.2)

2. The elementary liquid phase reaction A + B --> C is carried out in a 500 liters batch reactor filled to the brim. The reaction rate is rA = - kCACB where k = 0.01 liter/(mol. min). Calculate the time to reach 90% conversion if the initial concentration of A and B are both 2.0 mol/liter. (Ref. 3)

3. Hexamethylene tetraamnie, N4(CH2)6, is to be produced in a well-stirred semibatch reactor by adding aqueous ammonia solution at a constant rate of 10 liters/min. to an initial charge of formalin solution [formaldehyde (HCHO) in water]:

6HCHO + 4NH3 --> N4(CH2)6 + 6H2O

The reaction is instantaneous, irreversible, and exothermic. The initial charge of formalin solution is 2000 liters with a formaldehyde (A) concentration, CAi, of 15.0 gmol/liter. The concentration of ammonia (B) in the solution is CB = 15.0 gmol/liter. Calculate the time required for complete consumption of formaldehyde. (Ref.3)

4. A positive displacement pump operates at 100 ft3/min. is connected to a 1,000 ft3 tank originally at 1 atm. Assume ideal gas prevails; determine the time it takes to pump the air out until the pressure reduces to 10 mmHg for

a. isothermal system

b. adiabatic system

5.Hydrogen is being supplied to customers in cylinders containing 220 ft3 of gas measured at 14.7 psia and 70oF. When the cylinders reach the users, the cylinders are guaranteed to be at least 2000 psia at 70oF. A customer complains that when the cylinders were received, they were not up to pressure. The supplier says that this is impossible because all cylinder valves were checked for leakage (it is agreed that leakage in valves or through cylinders does not exist), and to be absolutely sure that the user would receive full measure of gas, the cylinder were filled from a line in which the pressure never fell below 2100 psia, the temperature in the line always being 70oF  1oF.

Do you think the user's complaint could be justified or not? Why? (Ref.1)

6.(a) Solve + 2xy = x, y(0) = 1(b) Solve x+ y = 2 sin x

11.16, 11.17,11.18 (Text: Felder and Rousseau)

References

1. Thermodynamics and its Applications by Modell and Reid.

2. Mass Transfer by Hines and Maddox.

3. Elements of Chemical Reaction Engineering by Scott Fogler