For the following three questions, state if you would solve the problem as being in equilibrium, steady state, or neither.

A 20 m thick membrane of Pd is exposed to a hydrogen atmosphere with pH2 = 0.5 atm at T = 600C for 24 hours. The diffusion coefficient of H in Pd is 1.4 103 cm2/s.

Neither steady state nor equilibrium

Steady state, not equilibrium

Equilibrium

A cube with an edge length of 1 cm of Pd is exposed to a hydrogen atmosphere with pH2 = 1 atm at T = 600C for 30 sec. The diffusion coefficient of H in Pd is 1.4 103 cm2/s.

Equilibrium

Neither steady state nor equilibrium

Steady state, not equilibrium

A 10 m thick membrane of Pd separates two compartments. One compartment contains hydrogen gas with pH2 = 0.7 atm. The other contains no hydrogen. The whole setup is held at a temperature of T = 600C. The diffusion coefficient of H in Pd is 1.4 103 cm2/s.

Equilibrium

Steady state, not equilibrium

Neither steady state nor equilibrium

For the following two questions, consider the experimental scenarios and decide which Ficks law is more appropriate to solve the problem.

A 12 mm thick sheet of tin is exposed to nitrogen at pN2 = 4 atm. What is nitrogen concentration in the tin sample as a function of position and time?

Fick's 2nd law

Fick's 1st law

Neither of the two laws

Hydrogen gas with a pressure of pH2 = 2 atm flows through the interior of a steel tube, while an inert gas streams along the outside of the tube. What is the number of hydrogen molecules lost per minute from the gas streaming through it?

Neither of the two laws

Fick's 2nd law

Fick's 1st law

For the following two questions consider the diffusion of oxygen through two iron membranes with thicknesses of 1 and 2 m.

An experiment observes that after a long time, the flux of O2 through the two Fe membranes of thickness 1 and 2 m is 2.7 mol/(m2s). Which of the following statement is true?

The concentration profile follows the error function solution

The kinetics is diffusion controlled

The kinetics is interface controlled

The concentration profile follows the thin-film solution

The system is in equilibrium

What happens to the amount of oxygen diffusing through the membrane per second if the area of the 1 m thick membrane is doubled?

Increases by a factor of two

Increases by a factor of four

Decreases by a factor of four

Unchanged

Decreases by a factor of two

For the following three questions, identify which of the solutions to the diffusion equation applies?

A 5 mm thick sheet of carburized iron is annealed for one hour in an inert atmosphere. The diffusion coefficient of carbon in iron is 6105 cm2/s

Steady-state solution

Thin-film solution

Trigonometric series

Error function solution

Thick-film solution

A 10 m thin film of a radioactive Ag tracer is deposited on the end of a 10 cm Cu cylinder and annealed for 2 weeks. The diffusion coefficient of Ag is 3107 cm2/s.

Steady-state solution

Trigonometric series

Thin-film solution

Error function solution

Thick-film solution

A 5mm thick sheet of titanium is exposed to nitrogen gas for 1 minute. The diffusion coefficient of nitrogen is 4108 cm2/s.

Trigonometric series

Error function solution

Thin-film solution

Steady-state solution

Thick-film solution

For the following two questions consider the diffusion of cobalt in an fcc cobalt-iron alloy, which is experimentally investigated at 1,000C by tracer diffusion experiments with radioactive 60Co and 59Fe tracers. The tracer is applied as a very thin film to one of the two planar surfaces of a long cylindrical sample. All samples have the shape of cylinders and their lengths are large compared to the penetration depths occurring in the experiment.

Consider the concentration profile c(x, t) of 60Co as a function of position for two different times t1 > 0 and t2 = 4t1. How does the maximum concentration change for the two different times?

Decrease by factor 2

Decrease by factor 4

Increase by factor 4

Unchanged

Increase by factor 2

How does the width of the concentration profile change for the two different times?

Decrease by factor 2

Decrease by factor 4

Unchanged

Increase by factor 2

Increase by factor 4

A 10 m thick metal sheet of size 10 cm 10 cm is annealed in a pure nitrogen atmosphere with pN2 = 10 atm, until a uniform concentration of N atoms is established within the sheet. Then the sheet is quenched and subsequently annealed in a nitrogen-free stream of argon for different times until equilibrium is reached. Which equation would you use to describe the concentration profile as a function of time?

In an experiment at elevated temperatures, the noble gas He slowly permeates a 0.5 mm glass membrane. The partial pressure of He on one side of the membrane is pHe = 2 atm, and on the other side pHe = 0.6 atm. The solubility of He in the specific glass of the membrane is 105 mol/cm3 at a He pressure of pHe = 1 atm and the temperature at which the experiment is performed. The flux of He through the membrane is measured to be 108 mol/(cm2s). Assuming that the He diffusion coefficient, DHe, is independent of the He concentration in the membrane, calculate the value of DHe in units of 106 cm2/s.

For the following two questions, consider a metal sheet that is 2 mm thick and has an area of 500 cm2 separating two chambers containing different gas atmospheres. One chamber contains a 1:9 nitrogen/argon mixture, and the other contains pure argon. The total pressure at both sides of the metal sheet is 1 atm. The metal is at a temperature of 1,000C. At this temperature and at a partial pressure of nitrogen of 1 atm, the solubility of nitrogen atoms is 2106 mol/cm3. It has been found that the number of moles of nitrogen molecules leaking from the nitrogen/argon mixture through the metal sheet denoted above into the pure argon atmosphere is 1104 mol/hour. The partial pressure of N2 in the pure argon atmosphere is all the time practically zero. Assume that the diffusion coefficient of nitrogen atoms diffusing through the metal sheet is independent of the nitrogen concentration in the metal sheet.

What is the concentration of nitrogen dissolved in the metal in equilibrium with the chamber containing the 1:9 nitrogen/argon mixture in units of 108 mol/cm3?

What is the diffusion coefficient of nitrogen atoms in the metal at 1,000C in units of 106 cm2/s?

For the following two questions, consider pure helium gas passing through a 1 meter long plastic pipe. The outer radius of the pipe is 1 cm, and the inner radius is 0.8 cm. The pipe has a temperature of 80C and is surrounded by air. Chemical analysis of the air surrounding the pipe shows that in steady state, 1105 mol of helium diffuses through the pipe each second. When the pipe is replaced, a microprobe analysis shows the helium concentration at r = 0.8 cm, cHe = 0.012 mol/cm3, and at r = 1.0 cm, cHe = 0.0002 mol/cm3.

Calculate the flux of He through the plastic pipe at the outer surface in units of 1010 mol/cm2/s

Calculate the diffusion coefficient of He in the plastic pipe in units of 108 cm2/s.