---
title: "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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url: "https://nerd-notes.com/ubq/120041/"
date_modified: "2026-08-21T08:40:54+00:00"
---

# 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?

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?

- **A.** \(2.0\text{ min}\)
- **B.** \(7.3\text{ min}\)
- **C.** \(9.0\text{ min}\)
- **D.** \(16\text{ min}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120041/*