Consider a long duct that spans from

$-$

to

$+$

$$

o

$.$

$$At x

$=$

$0$

$,$

$$two gases

$($

hydrogen and nitrogen

$)$

$$are separated by a membrane. H

$2$

$$spans from x

$=$

$-$

$$to x

$=$

$0$

$$and N

$2$

$$spans from x

$=$

$0$

$$to x

$=$

$+$

$$

o

$.$

$$Suddenly$,$ the membrane is removed and the gases diffuse into one another. It was derived in the class that the mass fraction of H

$2$

$$can be estimated from: Yu

$($

n

$)$

$=$

$[1$

$$erf

$($

n

$)]$

$,$

$$m

$(1)$

$$where n

$=$

$$x

$/$

V

$4$

Dt

$.$

$$t is time and D is the bi

$-$

molecular diffusivity of hydrogen and nitrogen. Assume D

$=$

$5$

$$x

$10$

$-$

$5$

$.$

$$a

$.$

$$Plot variation of H

$$

$$mass fraction with x at t

$=$

$10$

$,$

$102$

$,$

$103$

$,$

$104$

$$seconds and t

$=$

$0$

$.$

$$b

$.$

$$How long does it take for the hydrogen mass fraction at x

$=$

$-$

$0\mathrm{.}5$

$$m to decrease from about unity to

$0\mathrm{.}8$