Chapter 14

A thin plastic membrane separates hydrogen from air. The molar concentrations of hydrogen in the membrane at the inner and outer surfaces are determined to be \(0.045\) and \(0.002 \mathrm{kmol} / \mathrm{m}^{3}\), respectively. The binary diffusion coefficient of hydrogen in plastic at the operation temperature is \(5.3 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{s}\). Determine the mass flow rate of hydrogen by diffusion through the membrane under steady conditions if the thickness of the membrane is (a) \(2 \mathrm{~mm}\) and (b) \(0.5 \mathrm{~mm}\).

Exposure to high concentration of gaseous ammonia can cause lung damage. The acceptable shortterm ammonia exposure level set by the Occupational Safety and Health Administration (OSHA) is 35 ppm for 15 minutes. Consider a vessel filled with gaseous ammonia at \(30 \mathrm{~mol} / \mathrm{L}\), and a 10 -cm- diameter circular plastic plug with a thickness of \(2 \mathrm{~mm}\) is used to contain the ammonia inside the vessel. The ventilation system is capable of keeping the room safe with fresh air, provided that the rate of ammonia being released is below \(0.2 \mathrm{mg} / \mathrm{s}\). If the diffusion coefficient of ammonia through the plug is \(1.3 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{s}\), determine whether or not the plug can safely contain the ammonia inside the vessel.

The solubility of hydrogen gas in steel in terms of its mass fraction is given as \(w_{\mathrm{H}_{2}}=2.09 \times 10^{-4} \exp (-3950 / T) P_{\mathrm{H}_{2}}^{0.5}\) where \(P_{\mathrm{H}_{2}}\) is the partial pressure of hydrogen in bars and \(T\) is the temperature in \(\mathrm{K}\). If natural gas is transported in a 1-cm-thick, 3-m-internal-diameter steel pipe at \(500 \mathrm{kPa}\) pressure and the mole fraction of hydrogen in the natural gas is 8 percent, determine the highest rate of hydrogen loss through a 100 -m-long section of the pipe at steady conditions at a temperature of \(293 \mathrm{~K}\) if the pipe is exposed to air. Take the diffusivity of hydrogen in steel to be \(2.9 \times 10^{-13} \mathrm{~m}^{2} / \mathrm{s}\).

Helium gas is stored at \(293 \mathrm{~K}\) in a 3 -m-outer-diameter spherical container made of 5 -cm-thick Pyrex. The molar concentration of helium in the Pyrex is \(0.00073 \mathrm{kmol} / \mathrm{m}^{3}\) at the inner surface and negligible at the outer surface. Determine the mass flow rate of helium by diffusion through the Pyrex container.

Hydrogen can cause fire hazards, and hydrogen gas leaking into surrounding air can lead to spontaneous ignition with extremely hot flames. Even at very low leakage rate, hydrogen can sustain combustion causing extended fire damages. Hydrogen gas is lighter than air, so if a leakage occurs it accumulates under roofs and forms explosive hazards. To prevent such hazards, buildings containing source of hydrogen must have adequate ventilation system and hydrogen sensors. Consider a metal spherical vessel, with an inner diameter of \(5 \mathrm{~m}\) and a thickness of \(3 \mathrm{~mm}\), containing hydrogen gas at \(2000 \mathrm{kPa}\). The vessel is situated in a room with atmospheric air at \(1 \mathrm{~atm}\). The ventilation system for the room is capable of keeping the air fresh, provided that the rate of hydrogen leakage is below \(5 \mu \mathrm{g} / \mathrm{s}\). If the diffusion coefficient and solubility of hydrogen \(\mathrm{gas}\) in the metal vessel are \(1.5 \times 10^{-12} \mathrm{~m}^{2} / \mathrm{s}\) and \(0.005 \mathrm{kmol} / \mathrm{m}^{3}\).bar, respectively, determine whether or not the vessel is safely containing the hydrogen gas.

Pure \(\mathrm{N}_{2}\) gas at \(1 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\) is flowing through a 10-m-long, 3-cm-inner diameter pipe made of 2 -mm-thick rubber. Determine the rate at which \(\mathrm{N}_{2}\) leaks out of the pipe if the medium surrounding the pipe is \((a)\) a vacuum and \((b)\) atmospheric air at \(1 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\) with 21 percent \(\mathrm{O}_{2}\) and 79 percent \(\mathrm{N}_{2}\).

You probably have noticed that balloons inflated with helium gas rise in the air the first day during a party but they fall down the next day and act like ordinary balloons filled with air. This is because the helium in the balloon slowly leaks out through the wall while air leaks in by diffusion. Consider a balloon that is made of \(0.1\)-mm-thick soft rubber and has a diameter of \(15 \mathrm{~cm}\) when inflated. The pressure and temperature inside the balloon are initially \(110 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\). The permeability of rubber to helium, oxygen, and nitrogen at \(25^{\circ} \mathrm{C}\) are \(9.4 \times 10^{-13}, 7.05 \times 10^{-13}\), and \(2.6 \times 10^{-13} \mathrm{kmol} / \mathrm{m} \cdot \mathrm{s} \cdot\) bar, respectively. Determine the initial rates of diffusion of helium, oxygen, and nitrogen through the balloon wall and the mass fraction of helium that escapes the balloon during the first \(5 \mathrm{~h}\) assuming the helium pressure inside the balloon remains nearly constant. Assume air to be 21 percent oxygen and 79 percent nitrogen by mole numbers and take the room conditions to be \(100 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\).

What are the adverse effects of excess moisture on the wood and metal components of a house and the paint on the walls?

How does the condensation or freezing of water vapor in the wall affect the effectiveness of the insulation in the wall? How does the moisture content affect the effective thermal conductivity of soil?

Moisture migration in the walls, floors, and ceilings of buildings is controlled by vapor barriers or vapor retarders. Explain the difference between the two, and discuss which is more suitable for use in the walls of residential buildings.