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It appears that you uploaded an assignment for **CHEM 151** that includes a task involving deriving the rate for a 3rd order reaction, but the text of the problem isn't fully visible. Based on the information provided, here’s a general guide on how to derive the rate law for a third-order reaction.

### Steps to derive the rate law for a third-order reaction:

1. **Understand the Reaction Mechanism**:
   Assume the reaction is of the form:
   \[
   A + 2B \rightarrow Products
   \]
   or 
   \[
   A + B + C \rightarrow Products
   \]
   In either case, the reaction is third-order, meaning the sum of the exponents in the rate law will add up to 3.

2. **Write the Rate Law**:
   The general rate law for a third-order reaction is:
   \[
   Rate = k[A]^m[B]^n
   \]
   where \(m + n = 3\), depending on how the concentration of reactants affects the rate.

3. **Derive Rate from Mechanism**:
   If the reaction occurs in multiple steps, identify each step's rate law. For example, for a reaction:
   \[
   A \xrightarrow{k_1} Intermediate \xrightarrow{k_2} Products
   \]
   or with reversible steps like:
   \[
   A \xleftrightarrow{k_1, k_{-1}} Intermediate \xrightarrow{k_2} Products
   \]
   You might need to apply the **steady-state approximation** or **pre-equilibrium approximation** to solve for intermediates and substitute them back into the overall rate law.

4. **Use Constants and Eliminate Intermediates**:
   Substitute the intermediate concentrations into the overall rate law, using approximations if necessary, to arrive at the final expression for the rate.

Would you like a more specific solution or help with another problem from your assignment?

Here are five possible follow-up questions:
1. How do you apply the steady-state approximation to solve for intermediates?
2. What is the significance of each rate constant in the reaction mechanism?
3. How do you experimentally determine the rate law for a reaction?
4. What is the difference between a second-order and third-order reaction in terms of kinetics?
5. How do you derive the integrated rate law for a third-order reaction?

### Tip: When dealing with reaction mechanisms, always consider the slowest step (rate-determining step) as the one controlling the overall reaction rate.

Derive the given rate for the 3rd order of the reaction.

This page provides a step-by-step guide to deriving the rate law for a third-order reaction in chemistry, including key concepts such as reaction kinetics, steady-state approximation, and rate-determining steps. Suitable for college-level students in CHEM 151.

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