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AP Chemistry
5.3 Concentration Changes Over Time
AdvancedMCQMathematicalProportional Analysis16k
A student studies the first-order decomposition of a pollutant, \(\text{P}\), in a water-treatment reactor at constant temperature. The student obtains the following data.

Time elapsed (\(\text{min}\))\([\text{P}]\) (\(\mu\text{mol/L}\))
\(0.0\)\(8.00\)
\(7.0\)\(4.00\)
\(14.0\)\(2.00\)

In a full-scale treatment system operating under identical conditions, a parcel of water has already spent \(5.0\text{ min}\) in an upstream chamber before entering a polishing chamber. What minimum additional residence time in the polishing chamber is required for \(87.5\%\) of the amount of \(\text{P}\) initially present before upstream treatment to decompose?

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