1.ii Methane and hydrogen diffuse through a porous membrane 4.0 x 10 m thick and

Question

1.ii Methane and hydrogen diffuse through a porous membrane 4.0 x 10 m thick and 1 atm as shown in Figure 1-2. For each mole of methane diffusing through the membrane into the hydrogen, an equal amount of hydrogen diffuses into the methane olar counter diffusion). The partial pressures of methane on either side of the membrane are maintained a 2.66 x 104 and 1.33 x 10 N/m2, respectively. Calculate the molar flux of methane into the hydrogen. An effective diffusivity of 1.0 x 10-5 m2/s may be assumed. Figure 1-2 Problem 1.11 Diffusion Pure methane Pure hydrogen through a Porous Membrane.

Explanation / Answer

The flux equation can be written as

NA= XA*(NA+NB)+ JA

but for equimolar counter diffusion NA=-NB and JA= -DAB*dCA/dZ

NA= JA= -DABdCA/dZ for gases CA=PA/RT

NA*RT =-DAB*dPA/dZ

when intetgrated NA= DAB*(P2-P1)/RT(Z2-Z1)=1*10-3*(2.66-1.33)*104/ (8314*273.15*4*10-3)=0.001464 Kmol/m2.sec

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