**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.

The half-life of a first-order reaction can be determined by using the following formula:…

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? k = [?] x 10 [?] S-1 exponent (yellow) coefficient (green) Enter

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? k = [?] x 10 [?] S-1 exponent (yellow) coefficient (green) Enter

Chemistry

10th Edition

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

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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