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Question

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 mol/L, and a 10-cm-diameter circular plastic plug with a thickness of 2 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 mg/s. If the diffusion coefficient of ammonia through the plug is $1.3 \times 10^{-10} m^2/s,$ determine whether or not the plug can safely contain the ammonia inside the vessel.

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\textbf{Known:}

*  concentration of ammonia in vessel $C_A= 30 \dfrac{\text{ mol}}{\text{ L}}$
*  diameter of circular plastic plug of vessel $D$=10 cm= 0.01 m
*  thickness of circular plastic plug of vessel $L$=2 mm= 0.002 m
*  capable concentration of the ammonia in room $\dot{ m}_{diff, capable}= 0.2 \dfrac{\text{ mg}}{\text{ s}}$
*  diffusion coefficient of ammonia through the plug $D_{AB}= 1.3 \cdot 10^{-10} \dfrac{\text{ m}^2}{\text{ s}}$