### Reaction Mechanism Analysis#### Problem 10.2:Suppose that a reaction \( A + 2B = 2Y + 2Z \) is believed to occur according to the mechanism:\[ A \xrightarrow{k_1} 2X \quad (\text{very rapid equilibrium}) \]\[ X + B \xrightarrow{k_2} Y + Z \quad (\text{slow}) \]**Task: Obtain an expression for the rate of formation of the product Y.**### Detailed Diagram Description- The diagram presents a two-step reaction mechanism.- The first step shows a reactant \( A \) converting into \( 2X \) with a rate constant \( k_1 \). This step is characterized by very rapid equilibrium.- The second step involves the intermediate \( X \) reacting with \( B \) to form products \( Y \) and \( Z \) with a rate constant \( k_2 \). This step is considered slow, indicating it is the rate-determining step of the overall reaction.### Rate of Formation of Product YTo find the expression for the rate of formation of \( Y \), we need to consider the slow step in the mechanism:\[ X + B \rightarrow Y + Z \]Since this is the rate-determining step, the rate of formation of \( Y \) depends on the concentration of \( X \) and \( B \):\[ \text{Rate}_{Y} = k_2 [X][B] \]However, since \( [X] \) is produced in the first step and is in rapid equilibrium with \( A \):\[ A \xrightarrow{k_1} 2X \]We can assume the concentration of \( X \) reaches a steady state quickly. Therefore, we can express \( [X] \) in terms of \( [A] \), and substitute this into the rate equation for \( Y \).Finalizing the equations and solving to derive the exact expression for \( [Y] \) requires additional steps in kinetics and equilibrium assumptions, often involving \( k_1 \) being much larger compared to \( k_2 \). The detailed kinetic derivation is left as an exercise.

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= 10.2. Suppose that a reaction A + 2B = 2Y + 2Z is believed to occur according to the mechanism A → 2X (very rapid equilibrium) k₂ X + B Y + Z (slow) Obtain an expression for the rate of formation of the product Y.

= 10.2. Suppose that a reaction A + 2B = 2Y + 2Z is believed to occur according to the mechanism A → 2X (very rapid equilibrium) k₂ X + B Y + Z (slow) Obtain an expression for the rate of formation of the product Y.

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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