Question

Ammonia gas is diffusing at constant rate through a layer of stagnant air 1 mm thick. Conditions are fixed so that the gas contains 50% by volume of ammonia at one boundary of the stagnant layer. The ammonia at the other boundary is quickly absorbed and the concentration is zero. The temperature is 295 K and the pressure is 1 atm. If the diffusivity of ammonia in air is 0.18 cm2/s calculate the rate of diffusion of ammonia through the layer.

Answer 1

The convective flux NA= XA*(NA+NB)+JA

where JA= flux due to diffusion =-DAB*dC_A/dZ

given NB=0 ( stagnant film), CA=C*XA= Overall concentration*mole fraction

NA*(1-XA) =- DAB*dCA/dX =-DAB*C*dXA/dZ

which on integration gives

NA= DAB*C ln {(1-XA2)/(1-XA1)}/z

XA1 and XA2 are mole fractinos at point 1 and 2 respectively

where DAB= 0.18 cm²/s C=P/RT= 1/82.06cm3.atm/mole.K*298=4.089*10-5 moles/cm³

z= 1mm =0.1cm XA2= O and XA1=0.5 ( volume fraction =mole fraction)

N = 0.18cm²/s*4.089*10-5 moles/cm³*ln{(1/0.5)}/ 0.1= 5.101*10^-5moles/cm2.sec