Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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![**Title: Determination of Rate Constant of a First-Order Reaction**
**Introduction:**
In this experiment, a student is tasked with identifying the reaction order of the oxidation of a purple dye. The reaction is determined to be first-order, and the half-life observed is 420 seconds.
**Objective:**
To calculate the rate constant \( k \) for the first-order reaction using the given half-life.
**Problem Statement:**
A student conducts an experiment to determine the order of reaction for the oxidation of a purple dye. The reaction is determined to be first-order and the half-life is 420 seconds. What is the rate constant, \( k \)?
**Formula:**
The rate constant \( k \) for a first-order reaction can be calculated using the formula:
\[ k = \frac{\ln(2)}{t_{1/2}} \]
where:
- \( \ln(2) \) is the natural logarithm of 2 (approximately 0.693).
- \( t_{1/2} \) is the half-life of the reaction.
**Calculation:**
Given that the half-life \( t_{1/2} \) is 420 seconds, we can substitute this value into the formula.
\[ k = \frac{0.693}{420 \text{ s}} \]
**Rate Constant:**
After performing the calculation, the rate constant \( k \) is determined to be approximately:
\[ k = 1.65 \times 10^{-3} \text{ s}^{-1} \]
**Interactive Element:**
Below this problem description, there may be an interactive element on the educational website where students can input their calculated values:
\[ k = \]
\[ [ \text{Enter your coefficient (green)} ] \times 10^{ [ \text{Enter your exponent (yellow)} ]} \text{ s}^{-1} \]
\[ \text{Enter} \]
**Conclusion:**
Understanding the rate constant of a reaction provides insight into the reaction kinetics and how the concentration of reactants decreases over time. This experiment helps students to practically apply the integrated rate law for first-order reactions and reinforces the concept of half-life in the context of chemical kinetics.](https://content.bartleby.com/qna-images/question/a6113e33-e853-450e-898f-bcbb2a6fb476/0bf176cd-a4a1-48a9-b49d-628b62daf7d7/cwqsskh_processed.jpeg)
Transcribed Image Text:**Title: Determination of Rate Constant of a First-Order Reaction**
**Introduction:**
In this experiment, a student is tasked with identifying the reaction order of the oxidation of a purple dye. The reaction is determined to be first-order, and the half-life observed is 420 seconds.
**Objective:**
To calculate the rate constant \( k \) for the first-order reaction using the given half-life.
**Problem Statement:**
A student conducts an experiment to determine the order of reaction for the oxidation of a purple dye. The reaction is determined to be first-order and the half-life is 420 seconds. What is the rate constant, \( k \)?
**Formula:**
The rate constant \( k \) for a first-order reaction can be calculated using the formula:
\[ k = \frac{\ln(2)}{t_{1/2}} \]
where:
- \( \ln(2) \) is the natural logarithm of 2 (approximately 0.693).
- \( t_{1/2} \) is the half-life of the reaction.
**Calculation:**
Given that the half-life \( t_{1/2} \) is 420 seconds, we can substitute this value into the formula.
\[ k = \frac{0.693}{420 \text{ s}} \]
**Rate Constant:**
After performing the calculation, the rate constant \( k \) is determined to be approximately:
\[ k = 1.65 \times 10^{-3} \text{ s}^{-1} \]
**Interactive Element:**
Below this problem description, there may be an interactive element on the educational website where students can input their calculated values:
\[ k = \]
\[ [ \text{Enter your coefficient (green)} ] \times 10^{ [ \text{Enter your exponent (yellow)} ]} \text{ s}^{-1} \]
\[ \text{Enter} \]
**Conclusion:**
Understanding the rate constant of a reaction provides insight into the reaction kinetics and how the concentration of reactants decreases over time. This experiment helps students to practically apply the integrated rate law for first-order reactions and reinforces the concept of half-life in the context of chemical kinetics.
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