Ozone is sometimes used as a disinfectant for drinking water. Ozone is highly reactive. It will react with many benign species found in water, as well as the pathogens it is intended to kill. It is found that ozone reaction in water nearly follows first-order kinetics in ozone concentration, such that its concentration decreases by 50 % in 12 minutes (t_1/2 = 12 min.). A water supplier wants to inject ozone into a pipe bringing water to the water treatment plant to pre-disinfect the influent. The 3.0 ft diameter pipe is 3,400 feet long with a steady flow rate of 10,000 gal/min. 

What concentration of ozone (in mg/L) should be injected at the head of the pipe so that there will be an ozone concentration of 1.0 mg/L at the pipe’s exit into the plant? 

The pipe may be realistically assumed to act as an ideal PFR.

3 ft 3,400 ft Q-10,000 gal/min Half-life of O3 (1/2) = 12 min Water treatment plant C= 1 mg/L 1 ft = 0.305 m I gal-3.785 L