Consider the multistep reaction. What is the best rate law for the overall reaction? 2A K₁ + B → B + C 11 5 C + D (slow) 2E (fast)

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### Reaction Rate Equations

This section provides different rate equations for chemical reactions, each representing various dependencies on the concentration of reactants.

**A)** Rate = \( k_1[A][B][C] \)
- This equation suggests a rate that is dependent on the concentrations of reactants A, B, and C, with each appearing linearly in the rate expression.

**B)** Rate = \( k_2[C] \)
- Here, the rate is only dependent on the concentration of reactant C, indicating a simpler reaction mechanism involving C.

**C)** Rate = \( k_1[A]^2[B] \)
- This equation indicates that the reaction rate depends on the concentration of A squared and B, implying a second-order dependence on A.

**D)** Rate = \( \frac{k_1[A][B]}{k_2[C]} \)
- The rate is given by a ratio, suggesting a dependence on the concentrations of A and B divided by C. This could reflect a situation where C negatively impacts the rate.

**E)** Rate = \( k[A]^2[B]^2 \)
- This indicates a reaction where the rate depends on the square of the concentrations of both A and B, suggesting a more complex interaction.

Explore the rate laws to understand the order of reactions and how each reactant influences the reaction pace. Engage with additional resources for a deeper dive into reaction kinetics by tapping below.
Transcribed Image Text:### Reaction Rate Equations This section provides different rate equations for chemical reactions, each representing various dependencies on the concentration of reactants. **A)** Rate = \( k_1[A][B][C] \) - This equation suggests a rate that is dependent on the concentrations of reactants A, B, and C, with each appearing linearly in the rate expression. **B)** Rate = \( k_2[C] \) - Here, the rate is only dependent on the concentration of reactant C, indicating a simpler reaction mechanism involving C. **C)** Rate = \( k_1[A]^2[B] \) - This equation indicates that the reaction rate depends on the concentration of A squared and B, implying a second-order dependence on A. **D)** Rate = \( \frac{k_1[A][B]}{k_2[C]} \) - The rate is given by a ratio, suggesting a dependence on the concentrations of A and B divided by C. This could reflect a situation where C negatively impacts the rate. **E)** Rate = \( k[A]^2[B]^2 \) - This indicates a reaction where the rate depends on the square of the concentrations of both A and B, suggesting a more complex interaction. Explore the rate laws to understand the order of reactions and how each reactant influences the reaction pace. Engage with additional resources for a deeper dive into reaction kinetics by tapping below.
**Multistep Reaction Analysis and Rate Law Determination**

**Problem Statement:**
Consider the multistep reaction. What is the best rate law for the overall reaction?

**Reaction Steps:**

1. **First Step (Slow):**
   \[
   2A + B \xrightarrow{k_1} C + D 
   \]
   - This step is characterized as slow.

2. **Second Step (Fast Reversible):**
   \[
   B + C \xleftrightarrow{k_2} 2E
   \]
   - This step is fast and reversible.

**Explanation:**
In this multistep reaction, the slow step is the rate-determining step. The rate law for the overall reaction is typically determined by this rate-determining step. The reaction proceeds via an intermediate, C, which is formed and consumed in subsequent steps.

1. **Rate of the Slow Step:**
   - The rate can be expressed as:
     \[
     \text{Rate} = k_1 [A]^2 [B]
     \]
   Here, \( k_1 \) is the rate constant for the slow step, and \( [A] \) and \( [B] \) represent the concentrations of A and B, respectively.

2. **Fast Step Equilibrium:**
   - The fast equilibrium implies that concentrations can be expressed in terms of each other using the equilibrium constant if needed.

Efforts to derive the overall reaction rate must focus on substituting for any intermediates based on the fast equilibrium. However, the dominant concentration terms in the initial slow step predominantly dictate the overall rate law.

This multistep mechanism suggests a reaction heavily dependent on the concentrations of A and B relevant to the first, slow step.
Transcribed Image Text:**Multistep Reaction Analysis and Rate Law Determination** **Problem Statement:** Consider the multistep reaction. What is the best rate law for the overall reaction? **Reaction Steps:** 1. **First Step (Slow):** \[ 2A + B \xrightarrow{k_1} C + D \] - This step is characterized as slow. 2. **Second Step (Fast Reversible):** \[ B + C \xleftrightarrow{k_2} 2E \] - This step is fast and reversible. **Explanation:** In this multistep reaction, the slow step is the rate-determining step. The rate law for the overall reaction is typically determined by this rate-determining step. The reaction proceeds via an intermediate, C, which is formed and consumed in subsequent steps. 1. **Rate of the Slow Step:** - The rate can be expressed as: \[ \text{Rate} = k_1 [A]^2 [B] \] Here, \( k_1 \) is the rate constant for the slow step, and \( [A] \) and \( [B] \) represent the concentrations of A and B, respectively. 2. **Fast Step Equilibrium:** - The fast equilibrium implies that concentrations can be expressed in terms of each other using the equilibrium constant if needed. Efforts to derive the overall reaction rate must focus on substituting for any intermediates based on the fast equilibrium. However, the dominant concentration terms in the initial slow step predominantly dictate the overall rate law. This multistep mechanism suggests a reaction heavily dependent on the concentrations of A and B relevant to the first, slow step.
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