A ventilation system has been designed for a large laboratory with a volume of 1100 m. The volumetric flow rate of ventilation air is 700 m/min_at_22C and 1 atm. (The latter two values may also be taken as the temperature and pressure of the room air.) A reactor in the is capable of emitting as much as 1.50 mol of sulfur dioxide into the room if a seal ruptures. An SO2 mole fraction in the room air greater than 1.0 106 (1 ppm) constitutes a health hazard.

Suppose the reactor seal ruptures at a time t=0 and the maximum amount of SO2 is emitted and spreads uniformly throughout the room almost instantaneously. Assuming that the air flow is sufficient to make the room air composition spatially uniform, write a differential SO2 balance, letting N be the total moles of gas in the room (assume constant) and x(t) the mole fraction of SO2 in the laboratory air. Convert the balance into an equation for dx/dt and provide an initial condition. (Assume that all of the SO emitted is in the room at t = 0.)

Draw a flow diagram.