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The linear regression results indicate the following:

- The \( R^2 \) value for the first-order reaction (\( \ln[\text{H}_2\text{O}_2] \) vs. \( t \)) is approximately \( 0.999999 \), which is very close to 1, indicating a strong linear relationship.
- The \( R^2 \) value for the second-order reaction (\( \frac{1}{[\text{H}_2\text{O}_2]} \) vs. \( t \)) is approximately \( 0.987491 \), which is also high but not as close to 1 as the first-order plot.

Given the much higher \( R^2 \) value for the first-order reaction plot, it is reasonable to conclude that the decomposition of \( \text{H}_2\text{O}_2 \) is a first-order reaction.

### Determining the Rate Constant
For a first-order reaction, the slope of the \( \ln[\text{H}_2\text{O}_2] \) vs. \( t \) plot gives us \(-k\).

The slope of the first-order reaction plot is \(-0.000830 \, \text{s}^{-1}\).

Therefore, the rate constant \( k \) is:

\[ k = 0.000830 \, \text{s}^{-1} \]

Would you like more details or have any questions?

Here are some related questions you might find useful:

1. How do you determine the order of a reaction using experimental data?
2. What is the significance of the rate constant in a chemical reaction?
3. How does the reaction order affect the concentration of reactants over time?
4. Why is it important to know the reaction order in kinetics?
5. Can you explain the integrated rate laws for zero, first, and second-order reactions?

**Tip:** Always check the units of the rate constant; they vary depending on the reaction order and provide insights into the kinetics of the reaction.

Understand how to determine the rate constant in chemical kinetics through a detailed explanation. Learn about first-order reactions, rate law equations, and integrated rate laws with practical examples. Suitable for advanced undergraduate students studying chemistry or chemical engineering.

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