### First-Order Reaction AnalysisConsider the first-order reaction of ethane (\(C_2H_6\)) dissociating into two methyl radicals (\(2 \cdot CH_3\)) at a temperature of 500°C. The half-life of this reaction is given as 21 minutes. The following problems explore various aspects of this reaction:#### (a) Concentration Decrease- **Problem 1:** Calculate the time required for the concentration of \(C_2H_6\) to decrease from 6.6 mM to 3.1 mM.- **Problem 2:** Calculate the time required for the concentration to decrease from 3.1 mM to 1.8 mM.Both problems ask for results in minutes.#### (b) Concentration After a Specific Time- **Problem:** Given that the initial concentration of ethane is 4.5 mM, determine its concentration after 2.5 hours.Provide the concentration in mM.#### (c) Reaction Completion- **Problem:** Calculate the time needed for the reaction to be 94% complete.Express the time in minutes. ---These calculations require understanding of first-order reaction kinetics, particularly the use of the half-life formula and integrated rate laws.

It is known as a first-order reaction when the rate of the reaction is proportional to the reactant…

Consider the first-order reaction C₂H6 2 CH3 at 500°C where its half-life is 21 minutes. (a) How long does it take for the concentration of C₂H6 to drop from 6.6 mM to 3.1 mm? 4.0 min From 3.1 mM to 1.8 mm? 4.0✔ min (b) If the original concentration of ethane is 4.5 mm, what is the concentration after 2.5 hours? 4.0 MM (c) How long will it take for the reaction to be 94% complete? 4.0 min

Consider the first-order reaction C₂H6 2 CH3 at 500°C where its half-life is 21 minutes. (a) How long does it take for the concentration of C₂H6 to drop from 6.6 mM to 3.1 mm? 4.0 min From 3.1 mM to 1.8 mm? 4.0✔ min (b) If the original concentration of ethane is 4.5 mm, what is the concentration after 2.5 hours? 4.0 MM (c) How long will it take for the reaction to be 94% complete? 4.0 min

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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