Iodic Table Environmental scientists calculating pollutant half-lives often define a transport rate constant that is analogous to a reaction rate constant and describes how a pollutant moves out of an ecosystem. In a study of the gasoline additive MTBE in Donner Lake, California, scientists from the University of California, Davis, found that in the summer the half-life of MTBE in the lake was 29.02 days. Assume that the transport process is first order. What was the transport rate constant of MTBE out of Donner Lake during the study? Express your answer in reciprocal days. days-

Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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**Title:** Understanding Pollutant Transport Rate Constants in Environmental Science

**Introduction:**
Environmental scientists calculating pollutant half-lives often define a transport rate constant that is analogous to a reaction rate constant and describes how a pollutant moves out of an ecosystem. This concept is crucial in understanding the behavior of pollutants in environmental systems.

**Case Study: MTBE in Donner Lake, California**
In a study of the gasoline additive MTBE (methyl tert-butyl ether) in Donner Lake, California, scientists from the University of California, Davis, investigated the behavior of this pollutant during the summer. They determined that the half-life of MTBE in the lake was 29.02 days.

**Calculating the Transport Rate Constant:**
Assume that the transport process is first order, which means the rate at which MTBE moves out of the lake is directly proportional to its concentration.

**Question:**
What was the transport rate constant of MTBE out of Donner Lake during the study? Express your answer in reciprocal days (days⁻¹).

**Interactive Component:**
An input box is provided for students to calculate and enter the transport rate constant in days⁻¹. 

**Understanding the Calculation:**
This exercise involves converting the half-life of a pollutant into a transport rate constant using the formula for first-order kinetics: 

\[ k = \frac{0.693}{t_{\frac{1}{2}}} \]

Where \( k \) is the rate constant and \( t_{\frac{1}{2}} \) is the half-life. By inputting the given half-life of 29.02 days, students can find the rate constant that governs the pollutant's decrease over time.
Transcribed Image Text:**Title:** Understanding Pollutant Transport Rate Constants in Environmental Science **Introduction:** Environmental scientists calculating pollutant half-lives often define a transport rate constant that is analogous to a reaction rate constant and describes how a pollutant moves out of an ecosystem. This concept is crucial in understanding the behavior of pollutants in environmental systems. **Case Study: MTBE in Donner Lake, California** In a study of the gasoline additive MTBE (methyl tert-butyl ether) in Donner Lake, California, scientists from the University of California, Davis, investigated the behavior of this pollutant during the summer. They determined that the half-life of MTBE in the lake was 29.02 days. **Calculating the Transport Rate Constant:** Assume that the transport process is first order, which means the rate at which MTBE moves out of the lake is directly proportional to its concentration. **Question:** What was the transport rate constant of MTBE out of Donner Lake during the study? Express your answer in reciprocal days (days⁻¹). **Interactive Component:** An input box is provided for students to calculate and enter the transport rate constant in days⁻¹. **Understanding the Calculation:** This exercise involves converting the half-life of a pollutant into a transport rate constant using the formula for first-order kinetics: \[ k = \frac{0.693}{t_{\frac{1}{2}}} \] Where \( k \) is the rate constant and \( t_{\frac{1}{2}} \) is the half-life. By inputting the given half-life of 29.02 days, students can find the rate constant that governs the pollutant's decrease over time.
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