Example $5$

Two tanks are connected by a tube, $5mm$ in diameter and $0\mathrm{.}5m$ long. One tank contains nitrogen and one tank contains $C{O}_2.$ The pressure and temperature are maintained at $200$kPa and $25C.$ The diffusivity is $0\mathrm{.}08c\frac{m^2}{s}.$ At some initial time, $t=0,$ diffusion occurs between two tanks. After a while, the mole fraction of the nitrogen reaches $0\mathrm{.}7$ on one end and $0\mathrm{.}25$ at the other end. Determine

a$)$ The rates and direction of mass transfer of $C{O}_2$ and nitrogen

b$)$ The velocities of each compound

c$)$ The molar average velocities of the mix