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 m and a thickness of 3 mm, containing hydrogen gas at 2000 kPa. The vessel is situated in a room with atmospheric air at 1 atm. The ventilation system for the room is capable of keeping the air fresh, provided that the rate of hydrogen leakage is below 5 mg/s. If the diffusion coefficient and solubility of hydrogen gas in the metal vessel are 1.5 × 10-12 m2/s and 0.005 kmol/m3∙bar, respectively, determine whether or not the vessel is safely containing the hydrogen gas.