Two bulbs are connected by a tube, $0\mathrm{.}002$ m in diameter and $0\mathrm{.}20$ m in length. Initially, bulb $1$ contains argon, and bulb $2$ contains xenon. The pressure and temperature are maintained at $1$ atm and $105\backslash$deg C$,$ at which the diffusivity is $0\mathrm{.}180$ cm$2/$s$.$ At time t $=0,$ diffusion is allowed to occur between the two bulbs. At t$=0,$ the argon mole fraction in the gas at end $1$ of the tube is $0\mathrm{.}75,$ and $0\mathrm{.}20$ at the other end.

Consider the problem above with a tube that is $10$ cm long. At t$=0,$ the argon mole fraction in the gas at end $1$ of the tube is $1,$ and $0$ at the other end. Assume that the bulbs have a diameter of $15$ cm$.$ Other conditions remain the same.

a$.)$ Determine the time at which the argon mole fraction in the left bulb is $0\mathrm{.}6,$ and the time when the argon mole fraction in the right bulb is $0\mathrm{.}3.$

b$.)$ USE EXCEL: After $90$ hours, plot in excel the argon and xenon velocities vs the tube distance $($z$),$ and report the value of vargon and vxenon at z $=$ L$.$