Consider the design or a spherical glass flask or inner diameter d_in = 5 cm and

Question

Consider the design or a spherical glass flask or inner diameter d_in = 5 cm and outer diameter d_out = 5.4 cm (i.e., 0.2 em-thick glass) carrying mostly Nitrogen = 0.98) and a small amount of Helium (y_A = 0.02) at 0.5 atm pressure and 25 degree C temperature. The glass wall of the flask is made up Silica (density 2.35 g/cm^3 and molecular weight 60 g/mol) and it contains small pores that allow. Helium to dissolve and leak out from the other side, but the pores are too small for the Nitrogen gas to leak out. The concentration c_A of dissolved Helium in glass is related to its partial pressure P_A in the gas phase via the relationship c_A = S P_A, where the partition coefficient S = 0.5 mol/m^3/atm. Assuming that the atmosphere does not contain any Helium and that the diffusion coefficient of Helium in glass is D_AB = 4.2 middot 10^-12 m^2/s, determine: (a) Amount of Helium leaking out of the flask in mol/s;

Explanation / Answer

Partial pressure of He inside flask = 0.5*0.02 = 0.01 atm

So concentration of He in glass (inner surface): cA = S.PA = 0.5*0.01 = 0.005 mol/m3

concentration of He outside = 0

Concentration gradient = (0.005mol/m3)/(0.4cm) = 1.25 mol/m4

Flux of He going out = DAB*Concentration Gradient = 4.2*10-12 m2/s * 1.25mol/m4 = 5.25*10-12 mol/m2.s

Outer surface area of flask = 3.14*(5.4*10-2)2 = 9.16*10-3m2

So He leaking out = 5.25*10-12*9.16*10-3 = 4.803*10-14 mol/s (answer)

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