Water is held at the bottom of a narrow metal tube at a constant temperature of 318 K. The dry ambient air outside the tube is at 1 atm and 318 K. Water evaporates and diffuses through the air in the tube, and the diffusion path $z_2 - z_1$ is 30 cm long (from the water surface at $z_1$ to the open top at $z_2$). Calculate the rate of evaporation at steady state in $\mathrm{mol/(s\,cm^2)}$. The diffusivity of water vapour (A) in air (B) at 1 atm and 318 K is $0.282\ \mathrm{cm^2/s}$. Vapour pressure of water at 318 K is 9.5 kPa. Assume that air is insoluble in water.

At 298 K and total pressure of 1 atm, methane (A) is diffusing at a steady state through non-diffusing argon (B) and helium (C). At position $z_1 = 0$, the partial pressures of the gases (in atm) are $p_{A1} = 0.4$, $p_{B1} = 0.4$ and $p_{C1} = 0.2$, and at position $z_2 = 0.005$ m, $p_{A2} = 0.1$, $p_{B2} = 0.6$ and $p_{C2} = 0.3$. The binary diffusivities are $D_{AB} = 2.02 \times 10^{-5}\ \mathrm{m^2/s}$, $D_{AC} = 6.75 \times 10^{-5}\ \mathrm{m^2/s}$ and $D_{BC} = 7.29 \times 10^{-5}\ \mathrm{m^2/s}$. Calculate the flux of methane $N_A$ ($\mathrm{kmol/(m^2\,s)}$).