Practice Problems

Instructions

• Divide yourselves into groups of three (3).

• Write your names and your complete solution into your answer sheet, and box/encircle your final answer. Any group who does not comply shall not be given points for that particular problem.

• No communicating with the other groups.

• The group who garners the highest number of points will be given a perfect grade for their classwork.

Question 1 (10 pts, 10 min)

Helium and nitrogen gas are contained in a conduit 5.0 mm in diameter and 0.10 m long at 298 K and a uniform constant pressure of 1.0 atm abs. The partial pressure of He at one end of the tube is 0.060 atm and 0.020 atm at the other end. The diffusivity of He in N2 is 0.687 cm2/s at 298 K. Calculate the steady-state molar flux of N2 assuming ideal gas behavior.

TIME IS UP!!!

Question 2 (10 pts, 10 min)

Water in the bottom of a narrow metal tube 2.50 cm in diameter is held at a constant temperature of 293 K. The total pressure of dry air is 101.325 kPa and the temperature is also 293 K. Water evaporates and diffuses isothermally through the air in the tube and the diffusion path is 0.1524 m long. Calculate the steady rate of evaporation if the diffusivity of the water vapor at 293 K is 0.250 × 10-4 m2/s.

TIME IS UP!!!

Question 3 (30 pts, 15 min)

Diffusion and chemical reaction in a liquid. A solid sphere of substance A with radius R is suspended in a liquid B in which it is slightly soluble, and with which A undergoes a first-order chemical reaction with rate constant k. At steady-state the diffusion is exactly balanced by the chemical reaction. Derive the differential equation that would describe the concentration profile of A for this system.

TIME IS UP!!!

Question 4 (20 pts, 15 min)

Diffusion of water vapor to air in a narrow tube is occurring at a constant temperature T and total pressure P. At any given time, the water level is z meter from the top. As diffusion proceeds, the level drops very slowly. Derive the equation for the time tF for the level to drop from a starting point z0 at t = 0 to zF at t = tF seconds. Assume a steady state diffusion since the level change is very slow and that the ideal gas equation is valid for the water vapor. Let r be the density of water vapor, D its diffusivity in air and M its molar mass.TIME IS UP!!!

Question 5 (50 pts, 5 min)

Consider a catalytic reactor, wherein each catalyst particle is surrounded by a stagnant film gas of thickness through which substance A has to diffuse in order to arrive at the catalytic surface, where the polymerization reaction nA An occurs instantaneously. The product An then diffuses back out through the gas film to the main turbulent gas stream composed of A and An. Let xA0 be the concentration of surface at the main gas stream. Using shell balance, derive an expression for the diffusion flux of A across the gas film, NA. TIME IS UP!!!

GOOD LUCK!!!