Two bulbs are connected by a straight tube of diameter \(0.001 \mathrm{~m}\) and length \(0.15 \mathrm{~m}\). Initially one bulb contains nitrogen and the bulb at the other end contains hydrogen. The system is maintained at a temperature of \(298 \mathrm{~K}\) and a total pressure of \(1 \mathrm{~atm}\). The volume of each bulb is \(8 \times 10^{-6} \mathrm{~m}^{3}\).

Calculate and plot the mole-fraction profile of nitrogen in the first bulb as a function of time. Verify the validity of the quasi-steady-state approximation by calculating the diffusion time and the process time constants.