Question

(C) A Pyrex spherical container is used to store Helium-gas (He) at 19.85 °C (293K). The outer diameter and the thickness of the container are 1.5 m and 0.05 m respectively. At the inner surface of the container, the molar concentration (Chei) is 7.3 x 10+ kmol/m while the concentration of He in Pyrex at the outer surface of the container is negligible. The binary-diffusion coefficient is 4.50 10-15 m2/s. The molar mass of He is 4.0 kg/kmol. Determine; (1) The diffusion resistance. (11) The molar flow rate by diffusion of the He through the container's shell. (111) The mass flow rate by diffusion of the He through the container's shell (in kg/s). Assumptions: • Steady-state, one dimensional mass diffusion. • No chemical reactions (1.e. no depletion or generation of He). • Total molar concentration can be assumed constant.

Answer 1

Given.

assuming steady state 1 D Diffusion through sphere.

inside He conc = C1 = 7.3 * 10 ^(-4) kmol/m³

​​​​​​outside He conc = 0 kmol/m³

D =diffusivity of He= 4.5 * 10^ (-15) m²/s.

surface area of sphere = 4*π*r1*r2

where r1 and r2 are inside and outside radius if sphere.

r1= 0.75-0.05=0.7 m

r2= 1.5/2 = 0.75 m

As=4πr1*r2=4*π*0.7*0.75=6.5973 m².

Molar of Diffusion by Ficks Law through sphere.

NA = 4πr1*r2*D *(C1-C2)/(r2-r1) ..units.....kmol/sec

Na = 6.5973*4.5 * 10^ (-15)*{(7.3 * 10 ^(-4)-0)}/(0.75-0.7)

thus molar flow.

ii)NA= 4.3343* 10^(-16) kmol/sec

iii)MA= 4*Na where Ma is mass flow rate of helium.

mass flow rate = 1.732*10^(-15) kg/sec.

i) Diffusional resistance = rate / conc diff

​​​​=D /(r2-r1)

=4.5 * 10^ (-15)/(0.75-0.7)

= 9 *10^( -14) m/sec .