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I am looking to irradiate water containing some amounts of iron and would like to measure the amount of hydroperoxyl and hydroxyl radicals produced in real time as a result of the irradiation. Is there any way to do so without very expensive equipment such as an EPR machine?

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There are various colorimetric methods to measure peroxide production, and since you plan to have iron in solution, "the chromogenic $\ce{Fe+++}$-xylenol orange reaction, in which a purple complex is formed when $\ce{Fe++}$ provided in the reagent is oxidized to $\ce{Fe+++}$ by peroxides present in the sample," would seem to be ideal for your purpose, as suggested by BioAssay System. Another test uses Amplex™ Red reagent (10-acetyl-3,7-dihydroxyphenoxazine) and a peroxidase to create easily detected light -- but during irradiation, it might be confused with Cherenkov radiation.

As for hydroxyl measurement, if offset by hydronium production, then pH would not change -- but conductivity might. However, measuring such a small change in an otherwise conductive solution with dissolved salts might be tricky. You might test pH indicators to see if there is any noticeable change, but I'd not be sanguine about that.

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