MISSED THIS? Watch KCV: The Rate Law for a Chemical Reaction, IWE: Determining the Order and Rate Constant of a Reaction ; Read Section 15.3. You can click on the Review link to access the section in your e Text. Consider the data showing the initial rate of a reaction ( A → products) at several different concentrations of A. [A] (M)Initial rate (M/s) 0.100 2.02 × 10-2 0.200 4.04 x 10-2 0.300 6.06 × 10-2 ▼ Submit k[A] k[A] ✓ Correct As was determined in Part A, the reaction is a first-order reaction, so n = 1 Part C Previous Answers k = rate = k[A]¹ where k is the rate constant. Estimate the value of the rate constant k. Express your answer in inverse seconds to three significant figures. 195) ΑΣΦ ? 8-1

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## Understanding Reaction Rates

### Introduction

In the study of chemical kinetics, understanding the rate of reactions is crucial. The rate of a reaction can be determined by examining the change in concentration of reactants over time. Here, we will explore how the initial rate of a reaction depends on the concentration of reactant \( A \).

### Reaction Data

Consider the following data showing the initial rate of the reaction \( A \rightarrow \text{products} \) for varying concentrations of \( A \).

| \([A] \, (\text{M})\) | Initial rate \((\text{M/s})\) |
|-----------------|---------------------|
| 0.100           | \( 2.02 \times 10^{-2} \)      |
| 0.200           | \( 4.04 \times 10^{-2} \)      |
| 0.300           | \( 6.06 \times 10^{-2} \)      |

### Determining Reaction Order

The initial rates suggest a linear relationship between the concentration of \( A \) and the rate, indicating a first-order reaction. Mathematically, this can be expressed as:

\[ \text{rate} = k[A]^1 \]

where \( k \) is the rate constant.

### Part C: Calculating the Rate Constant \( k \)

To calculate the value of the rate constant \( k \) for a first-order reaction, use the initial rate data and the relationship:

\[ k = \frac{\text{rate}}{[A]} \]

Ensure that your answer is expressed in inverse seconds (s\(^{-1}\)) and rounded to three significant figures.

### Conclusion

Understanding the relationship between reactant concentration and reaction rate is essential for determining the order of a reaction and its rate constant, both of which are foundational concepts in chemical kinetics.
Transcribed Image Text:## Understanding Reaction Rates ### Introduction In the study of chemical kinetics, understanding the rate of reactions is crucial. The rate of a reaction can be determined by examining the change in concentration of reactants over time. Here, we will explore how the initial rate of a reaction depends on the concentration of reactant \( A \). ### Reaction Data Consider the following data showing the initial rate of the reaction \( A \rightarrow \text{products} \) for varying concentrations of \( A \). | \([A] \, (\text{M})\) | Initial rate \((\text{M/s})\) | |-----------------|---------------------| | 0.100 | \( 2.02 \times 10^{-2} \) | | 0.200 | \( 4.04 \times 10^{-2} \) | | 0.300 | \( 6.06 \times 10^{-2} \) | ### Determining Reaction Order The initial rates suggest a linear relationship between the concentration of \( A \) and the rate, indicating a first-order reaction. Mathematically, this can be expressed as: \[ \text{rate} = k[A]^1 \] where \( k \) is the rate constant. ### Part C: Calculating the Rate Constant \( k \) To calculate the value of the rate constant \( k \) for a first-order reaction, use the initial rate data and the relationship: \[ k = \frac{\text{rate}}{[A]} \] Ensure that your answer is expressed in inverse seconds (s\(^{-1}\)) and rounded to three significant figures. ### Conclusion Understanding the relationship between reactant concentration and reaction rate is essential for determining the order of a reaction and its rate constant, both of which are foundational concepts in chemical kinetics.
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