Ozone is sometimes used as a disinfectant for drinking water. Ozone is nag y rea
ID: 914788 • Letter: O
Question
Ozone is sometimes used as a disinfectant for drinking water. Ozone is nag y 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 percent 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 predisinfect 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 pipes exit into the plant? The pipe may be realistically assumed to act as an ideal PFR.Explanation / Answer
Step 1 - Calculate rate constant k,as
k = 0.693 / 12
.. = 0.05775 min-1
Step 2 , -
Apply the first orderr rate equation to get the desired initial concentration of ozone [Ro ], using first order rate equation ie.
k = 2.303 / t { log [ [Ro ] / [ R ] } given t ( time = 1 min , ) , [ R ] ie final concentration = 1.0 mg. / L
So, 0.05775 = 2.303 /1 { log [Ro] - log (1.0) }
log [R0 ] = 0.05775 / 2.303
........... = 0.025076
....... [Ro] = 1.0594 mg / L
Thus the initial concentration of ozone should be 1.06 mg / litre , partcularly when the pipe is considered to act as an ideal PFR.
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