A ventilation system has been designed for a large laboratory with a volume of 1100 m3. The volumetric flow rate of ventilation air is 700 m3/min at 22째C and 1 atm. (The latter two values may also be taken as the temperature and pressure of the room air.) A reactor in the laboratory 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 x 10-6 (1 ppm) constitutes a health hazard.
(a) 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 SO2 emitted is in the room at t = 0.)
(b) Predict the shape of a plot of x versus t. Explain your reasoning, using the equation of part (a) in your explanation.
(c) Separate variables and integrate the balance to obtain an expression for x(t). Check your solution.
(d) Convert the expression for x(r) into an expression for the concentration of SO2 in the room, CSO2 (mol SO2/L). Calculate (i) the concentration of SO2 in the room two minutes after the rupture occurs, and (ii) the time required for the SO2 concentration to reach the ?osafe?? level.
(e) Why would it probably not yet be safe to enter the room after the time calculated in part (d)?