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Chapter 5, Problem 1DP (I Bookmark) Show all steps : OOMD It is desired to enric

ID: 701902 • Letter: C

Question

Chapter 5, Problem 1DP (I Bookmark) Show all steps : OOMD It is desired to enrich the partial pressure of hydrogen in a hydrogen-nitrogen gas mixture for which the partial pressures of both gases are 0.1013 MPa (1 atm) It has been proposed to accomplish this by passing both gases through a thin sheet of some metal at an elevated temperature; inasmuch as hydrogen diffuses through the plate at a higher rate than does nitrogen, the partial pressure of hydrogen will be higher on the exit side of the sheet. The design calls for partial pressures of 0.051 MPa (0.5 atm) and 0.01013 MPa (0.1 atm), respectively, for hydrogen and nitrogen. The concentrations of hydrogen and nitrogen (CH and CN, in mol/m3) in this metal are functions of gas partial pressures (pH2 and pN2, in MPa) and absolute temperature and are given by the following expressions: G+ 2.5 × 102exp (-27A 27,800J/mol PH, exp 37.600J/mol Furthermore, the diffusion coefficients for the diffusion of these gases in this metal are functions of the absolute temperature, as follows: D1t(m 2/s) = 1.4 × 10-7exp 13,400 J/mol RT Dn(/s) = 3.0 × 10-7 exp 76.150J/mol RT Is it possible to purify hydrogen gas in this manner? If so, specify a temperature at which the process may be carried out, and also the thickness of metal sheet that would be required. If this procedure is not possible, then state the reason(s) why.

Explanation / Answer

Since, diffusion is at steady state, we employ Fick's 1st Law.
The partial pressures on the highPressure side of the sheet are the same, and the pressure of hydrogen on the low pressure side is5 times that of nitrogen, and concentrations are proportional to the square root of the partial pressure, the diffusion flux of hydrogen JH is the square root of 5 times the diffusion flux of nitrogen

2.5*10^3*((.1013)^.5-(.051)^.5)*exp(-27.8/R/T)*(1.4*10^-7)*exp(-13.4/R/T)=(5)^.5*2.75*10^3*((.1013)^.5-(.0103)^.5)*exp(-37.6/R/T)*(3*10^-7)*exp(-76.15/R/T)

T = ~3000K

which value is extremely high (surely above the melting point of the metal).  Thus, such a diffusion process is not possible.

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