### Example Problem: Determining the Rate Constant for a Reaction#### Problem StatementThe rate constant for the reaction below was determined to be \( 3.241 \times 10^{-5} \, \text{s}^{-1} \) at 800 K. The activation energy of the reaction is 225 kJ/mol. What would be the value of the rate constant at 930 K?\[ \text{N}_2\text{O}(g) \rightarrow \text{N}_2(g) + \text{O}(g) \]#### Steps to SolveTo determine the new rate constant at a different temperature, we can use the Arrhenius equation shown below:\[ k = Ae^{-\frac{E_a}{RT}} \]However, since we are comparing two temperatures, we can use the following form of the Arrhenius equation:\[ \ln \left( \frac{k_2}{k_1} \right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \]Where:- \( k_1 \) and \( k_2 \) are the rate constants at temperatures \( T_1 \) and \( T_2 \) respectively,- \( E_a \) is the activation energy,- \( R \) is the gas constant (8.314 J/mol·K),- \( T_1 \) and \( T_2 \) are the absolute temperatures (in Kelvin).Using the given values:- \( k_1 = 3.241 \times 10^{-5} \, \text{s}^{-1} \)- \( T_1 = 800 \, \text{K} \)- \( T_2 = 930 \, \text{K} \)- \( E_a = 225 \, \text{kJ/mol} = 225000 \, \text{J/mol} \)Calculate:\[ \ln \left( \frac{k_2}{3.241 \times 10^{-5}} \right) = \frac{225000}{8.314} \left( \frac{1}{800} - \frac{1}{930} \right) \]Calculate inside the parenthesis first:\[ \frac{1}{800} - \frac{

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The rate constant for the reaction below was determined to be 3.241x10-5 s-1 at 800 K. The activation energy of the reaction is 225 kJ/mol. What would be the value of the rate constant at 9.30×10² K? N₂O(g) → N₂(g) + 0(g)

The rate constant for the reaction below was determined to be 3.241x10-5 s-1 at 800 K. The activation energy of the reaction is 225 kJ/mol. What would be the value of the rate constant at 9.30×10² K? N₂O(g) → N₂(g) + 0(g)

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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