https://file.aiquickdraw.com/mathbot/file/17278503558946e6l5lhb.jpg

The image shows a chemical reaction with the following details:

The reaction is:

\[
A + 3B \rightarrow D + F
\]

It was studied carefully, and the mechanism of the reaction was provided. The task is to determine the rate law for the reaction based on the mechanism, which is as follows:

- Step 1: \( A + B \rightleftharpoons C \) (fast equilibrium)
- Step 2: \( C + B \rightarrow D + E \) (slow step)
- Step 3: \( E + B \rightarrow F \) (very fast step)

Since the rate law depends on the slowest step (the rate-determining step), we focus on Step 2: \( C + B \rightarrow D + E \).

### Explanation of the Rate Law

1. The rate of the reaction is determined by the slowest step, which involves \( C \) and \( B \).
   
2. However, \( C \) is an intermediate, and it is produced in Step 1, which is in fast equilibrium with \( A \) and \( B \). Therefore, we need to express the concentration of \( C \) in terms of \( A \) and \( B \).

3. From Step 1: \( A + B \rightleftharpoons C \), using the equilibrium approximation:
   
   \[
   [C] = k[A][B]
   \]

4. Substituting this into the rate-determining step (Step 2):
   
   \[
   \text{Rate} = k'[C][B] = k'[k[A][B]][B] = k[A][B]^2
   \]

So, the correct rate law is:

\[
\boxed{\text{Rate} = k[A][B]^2}
\]

This corresponds to the third option.

Would you like further clarification or details?

### Relative questions:
1. Why is the slowest step used to determine the rate law?
2. What role does the fast equilibrium step play in determining the rate law?
3. How do you express an intermediate concentration in terms of reactants?
4. What is the significance of the reaction mechanism in deriving the rate law?
5. How does the order of a reaction relate to the stoichiometry of the mechanism?

**Tip:** The slowest step in a reaction mechanism is crucial because it acts as a bottleneck, controlling the overall reaction rate.

The reaction: A + 3 B → D + F was studied carefully, and the mechanism below was determined. What is the rate law for the reaction?

Determine the rate law for the reaction A + 3B → D + F based on its mechanism. Focus on the rate-determining step and fast equilibrium. Suitable for advanced chemistry students.

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