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 $0\mathrm{.}8$