WORKSHEET $1-$ Molecular Diffusion

EN$7700$T

Mass

Transfer

Operations $-1$

Solve the following problems.

Ammonia diffuses through nitrogen gas under equimolarcounter diffusion at a total pressure of $1\mathrm{.}013x{10}^{5}Pa$ and at a temperature of $298K.$ The diffusion path is $0\mathrm{.}15m.$ The partial pressure of ammonia at one point is $1\mathrm{.}5{10}^{4}Pa$ and at the other point is $5{10}^{3}Pa.$ Diffusivity under the given condition is $2\mathrm{.}3{10}^{-5}\frac{m^2}{s}.$ Calculate the flux of ammonia.

Ans: $N_A=6\mathrm{.}19{10}^{-7}$kmo$\frac{l}{m^2}-s$

In an oxygen$-$nitrogen gas mixture at $1$atm$\mathrm{.}25C,$ the concentrations of oxygen at two planes $0\mathrm{.}2cm$ apart are $10\%$ and $20\%($by volume$)$ respectively. Calculate the flux of oxygen when

a$.$ nitrogen is non$-$diffusing

b$.$ there is equimolar counter diffusion.

Diffusivity of oxygen in nitrogen is $0\mathrm{.}215c\frac{m^2}{s}.$

Ans.

a$.N_A=5\mathrm{.}18{10}^{-5}$kmo$\frac{l}{m^2}-s$

b$.N_A=4\mathrm{.}395{10}^{-5}$kmo$\frac{l}{m^2}-s$

The diffusivity of carbon tetrachloride, $CC{l}_4$ through oxygen $O_2,$ was determined in a steady state Arnold evaporating cell. The cell, having a cross sectional area of $0\mathrm{.}82c{m}^2,$ was operated at $273K$ and $755mmHg$ pressure. The average length of the diffusion path was $17\mathrm{.}1cm.$ If $0\mathrm{.}0208c{m}^3$ of $CC{l}_4$ was evaporated in $10$ hours of steady state operation, determine the value of the diffusivity of $CC{l}_4$ through oxygen?

Ans. $D_{AB}=6\mathrm{.}355{10}^{-6}\frac{m^2}{s}$

Ethanol vapor is diffusing through a layer of water vapor under equimolar counter diffusion at $35C$ and $1$atm. pressure. The molal concentration of alcohol on the two sides of the gas film $($water vapor$)0\mathrm{.}3mm$ thick are $80\%$ and $10\%$ respectively. Assuming the diffusivity of ethanol$-$water vapor to be $0\mathrm{.}18c{m}^2/$s$.$

a$.$ Calculate the rate of diffusion of ethanol in water vapor in $k\frac{g}{h}$ through an area of $100c{m}^2$

b$.$ If the water vapor layer is stagnant, estimate the rate of diffusion of alcohol vapor.

Ans.

a$.$ Rate ${?}_{ettanol}=2\mathrm{.}75k\frac{g}{h}$

b$.$ Rate thanol $=1\mathrm{.}6425{10}^{-3}k\frac{g}{s}$