Question

In order to prepare Lithium nitride, air is passed gently over a reactor. Suppose that Nitrogen diffuse to a length 5cm before getting reacted with Lithium. Nitrogen reacts with lithium quickly so that partial pressure of Nitrogen at that point is 0. Reactor is a cylinder of length 10cm and diameter 2cm. Assume air to be a mixture of Nitrogen and Oxygen only. The temperature is 298K and total pressure 1atm. Diffusivity of N2 in O2 is 2*10^-5m^2/s. Calculate the Molar flux (mol/m^2.s) of N2 at a distance of 2.5cm from the top with respect to an observer moving with twice the mass average velocity a direction towards the liquid surface. (R=8.205*10^-5m^3atmK^-1mol^-1). Assume z=0 at the top of the reactor.

(a) 4.242*10^-4

(b) 4.242*10^-5

(c) 4.242*10^-3

(d) 4.242*10^-2

I have been asked this question in an interview.

The origin of the question is Diffusion in a Binary Gas Mixture in chapter Diffusion in Solids and Molecular Diffusion in Fluids of Mass Transfer

Answer 1

Correct choice is (a) 4.242*10^-4

The best I can explain: Case: Diffusion of A through non-diffusing B

                           N2 in air= 79%

                           O2 in air= 21%

              Molar flux of N2, NA=0.025mol/m^2.s

             Pressure of N2 at the point z=2.5cm=

(  DAB*P ln⁡[(P-P5)/(P-P0)])/RTl=(DAB*P ln⁡[(P-P5)/(P-P2.5)])/RTl

P2.5=0.542atm

Velocity of N2= NART/P2.5=112.78*10^-5m/s

Molar flux of O2-=0

Velocity of O2=0

Average molar mass=0.542*28+0.458*32=29.832

Mass average velocity= (0.542*28*112.78*10-5)/29.832=57.37*10^-5m/s

Required molar flux at the distance of z=5, is

                                               CA(uA-2V)= NA-2PAV/RT=4.242*10^-4mol/m^2.s.