One oxidation treatment process uses light and hydrogen peroxide to generate the
highly reactive hydroxyl radical (OH•), which can be used to degrade certain PFAS
“forever compounds”, but not others. A very recent paper by Zhang (2023
Environmental Science and Technology: so recent no volume has been assigned) report a
second order rate constant between OH• and the PFAS, perfluoro(2-
ethoxyethane)sulfonic acid (PFSA with a k = 1.2 x 10 7 L/mole-second), while this radical is
less reactive with 4.8-dioxa-3H-perfluorononanoic acid (DPFA with a k = 5 x 10 5 L/mole-
second). Suppose your UV-hydrogen peroxide system generates a constant output
(steady-state) of this radical at a concentration of 3 x 10 -14 moles/L, please answer the
following.
a. What is the pseudo-first order rate constant for the degradation of both
compounds at this OH• concentration?
b. What are the half-lives for these two compounds?
c. Suppose you have to treat these two compounds such that they both must not
exceed the 50 nM water quality standard. If both compounds have a starting
concentration of 1µM how long (in hours) will it take each to reach this
concentration? For the slower reacting compound is the time needed to achieve
the water quality standard a reasonable time from a design perspective?
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a. The pseudo-first order rate constant (k') for the degradation of both compounds can be calculated by multiplying the second order rate constant (k) by the concentration of the hydroxyl radical ([OH•]).
For PFSA:
k' = k[OH•] = (1.2 x 10^7 L/mole-second)(3 x 10^-14 moles/L) = 0.36 second^-1
For DPFA:
k' = k[OH•] = (5 x 10^5 L/mole-second)(3 x 10^-14 moles/L) = 0.015 second^-1
b. The half-life (t1/2) of a reaction can be calculated using the formula t1/2 = 0.693/k'.
For PFSA:
t1/2 = 0.693/0.36 second^-1 = 1.93 seconds
For DPFA:
t1/2 = 0.693/0.015 second^-1 = 46.2 seconds
c. The time (t) it takes for a reaction to reach a certain concentration can be calculated using the formula t = ln([A]0/[A])/k', where [A]0 is the initial concentration and [A] is the final concentration.
For PFSA:
t = ln((1 x 10^-6 M)/(50 x 10^-9 M))/0.36 second^-1 = 3.22 x 10^4 seconds = 8.94 hours
For DPFA:
t = ln((1 x 10^-6 M)/(50 x 10^-9 M))/0.015 second^-1 = 8.64 x 10^5 seconds = 240 hours = 10 days
From a design perspective, the time needed to achieve the water quality standard for the slower reacting compound (DPFA) is not reasonable. A treatment process that takes 10 days to reduce the concentration of a compound to an acceptable level is not efficient. It would be necessary to find a more effective treatment method or to increase the concentration of the hydroxyl radical in the system.
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