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For the sequential reaction A → B → C, the rate constants are kA = 0.41 /sec and kB = 0.051 /sec. (a)Determine the time at which [B] is maximum. (b) Which one of the following graphs would represent this reaction?

For the sequential reaction A → B → C, the rate constants are kA = 0.41 /sec and kB = 0.051 /sec. (a)Determine the time at which [B] is maximum. (b) Which one of the following graphs would represent this reaction?

Chemistry
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
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For the sequential reaction A → B → C, the rate constants are kA = 0.41 /sec and kB = 0.051 /sec.

(a)Determine the time at which [B] is maximum.

(b) Which one of the following graphs would represent this reaction?

### Reaction Kinetics: Changes in Concentration Over Time #### Overview The series of graphs illustrate the concentration changes of substances over time in a chemical reaction, focusing on the role of rate constants (\( k_A \) and \( k_I \)). These graphs are essential for understanding reaction kinetics, specifically for reactions where intermediates are present. #### Graph Descriptions Each graph shows the concentration of different species involved in the reaction as functions of time (\( t \)). ##### Graph (a) - **Rate Comparison**: \( k_A = 2k_I \) - **Axes**: - Vertical: \([X]/[A]_0\) (normalized concentration) - Horizontal: Time (s) - **Curves**: - [A] (Reactant): Blue, decreases rapidly. - [I] (Intermediate): Grey, forms and then decays. - [P] (Product): Red, increases. ##### Graph (b) - **Rate Comparison**: \( k_A = 8k_I \) - **Axes**: - Vertical: \([X]/[A]_0\) (normalized concentration) - Horizontal: Time (s) - **Curves**: - [A] (Reactant): Blue, decreases very rapidly. - [I] (Intermediate): Grey, sharp formation and rapid decay. - [P] (Product): Red, increases steeply and reaches a plateau. ##### Graph (c) - **Rate Comparison**: \( k_A = 0.25k_I \) - **Axes**: - Vertical: \([X]/[A]_0\) (normalized concentration) - Horizontal: Time (s) - **Curves**: - [A] (Reactant): Blue, decreases gradually. - [I] (Intermediate): Grey, forms slowly and decays gradually. - [P] (Product): Red, increases slowly. #### Key Takeaways 1. **Rate Constants Effect**: - When \( k_A \) is much greater than \( k_I \), the product forms rapidly (graph b). - When \( k_A \) is much smaller than \( k_I \), the product forms slowly (graph c). 2. **Intermediate Concentrations**: The peak of the intermediate [I] is highest when the rate constants \( k_A
Transcribed Image Text:### Reaction Kinetics: Changes in Concentration Over Time #### Overview The series of graphs illustrate the concentration changes of substances over time in a chemical reaction, focusing on the role of rate constants (\( k_A \) and \( k_I \)). These graphs are essential for understanding reaction kinetics, specifically for reactions where intermediates are present. #### Graph Descriptions Each graph shows the concentration of different species involved in the reaction as functions of time (\( t \)). ##### Graph (a) - **Rate Comparison**: \( k_A = 2k_I \) - **Axes**: - Vertical: \([X]/[A]_0\) (normalized concentration) - Horizontal: Time (s) - **Curves**: - [A] (Reactant): Blue, decreases rapidly. - [I] (Intermediate): Grey, forms and then decays. - [P] (Product): Red, increases. ##### Graph (b) - **Rate Comparison**: \( k_A = 8k_I \) - **Axes**: - Vertical: \([X]/[A]_0\) (normalized concentration) - Horizontal: Time (s) - **Curves**: - [A] (Reactant): Blue, decreases very rapidly. - [I] (Intermediate): Grey, sharp formation and rapid decay. - [P] (Product): Red, increases steeply and reaches a plateau. ##### Graph (c) - **Rate Comparison**: \( k_A = 0.25k_I \) - **Axes**: - Vertical: \([X]/[A]_0\) (normalized concentration) - Horizontal: Time (s) - **Curves**: - [A] (Reactant): Blue, decreases gradually. - [I] (Intermediate): Grey, forms slowly and decays gradually. - [P] (Product): Red, increases slowly. #### Key Takeaways 1. **Rate Constants Effect**: - When \( k_A \) is much greater than \( k_I \), the product forms rapidly (graph b). - When \( k_A \) is much smaller than \( k_I \), the product forms slowly (graph c). 2. **Intermediate Concentrations**: The peak of the intermediate [I] is highest when the rate constants \( k_A
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