We are measuring the diffusivity of water in air at \(42^{\circ} \mathrm{C}\). A tube is placed with one end in the water and the other end in a stream of dry air. The air column in the tube is 22\(\mathrm{cm}\) long, and we assume mole fraction of water is zero at the end in the air stream, \(\mathrm{y}_{\text {water }}(\mathrm{z}=22)=0\). System pressure \(=0.95 \mathrm{~atm}\) and is constant. At \(42^{\circ} \mathrm{C}\), vapor pressure of water is \(0.1098 \mathrm{~atm}\), and diffusivity of water in air is \(D_{\mathrm{W} \text {-air }}=2.88 \times 10^{-5}\) \(\mathrm{m}^{2} / \mathrm{s}\). Assume ideal gases. Use the Maxwell-Stefan theory in difference equation form to determine flux of water at steady state.