Insulation degrades (experiences an increase in thermal conductivity) if it is subjected to water vapor condensation. The problem may occur in home insulation during cold periods, when vapor in a humidified room diffuses through the drywall (plaster board) and condenses in the adjoining insulation. Estimate the mass diffusion rate for a \(3 \mathrm{~m} \times 4 \mathrm{~m}\) wall, under conditions for which the vapor pressure is 0.035 bar in the room air and 0.0 bar in the insulation. The drywall is \(15 \mathrm{~mm}\) thick, and the solubility of water vapor in the wall material is approximately \(5 \times 10^{-3} \mathrm{kmol} / \mathrm{m}^{3} \cdot\) bar. The binary diffusion coefficient for water vapor in the drywall is approximately \(10^{-9} \mathrm{~m}^{2} / \mathrm{s}\).