A reactant decomposes with a half-life of 103 s when its initial concentration is 0.270 M. When the initial concentration is 0.605 M, this same reactant decomposes with the same half-life of 103 s. What is the order of the reaction? O 2 01 What is the value and unit of the rate constant for this reaction?

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### Reaction Kinetics Problem

A reactant decomposes with a half-life of 103 s when its initial concentration is 0.270 M. When the initial concentration is 0.605 M, this same reactant decomposes with the same half-life of 103 s.

**Questions:**

1. **What is the order of the reaction?**
   - [ ] 0
   - [ ] 2
   - [ ] 1

2. **What is the value and unit of the rate constant for this reaction?**
   
   \( k = \) [________] Units: [________] 

### Explanation

To solve the problem:

- **Determine the order of the reaction:** A reaction whose half-life is independent of initial concentration is a first-order reaction.
  
- **Calculate the rate constant \( k \):** For a first-order reaction, the rate constant \( k \) can be calculated using the relation:

  \[
  t_{1/2} = \frac{0.693}{k}
  \]

  Given that the half-life \( t_{1/2} \) is 103 s, solve for \( k \):

  \[
  k = \frac{0.693}{103 \text{ s}}
  \] 

Fill in the value and unit for \( k \) in the provided space.
Transcribed Image Text:### Reaction Kinetics Problem A reactant decomposes with a half-life of 103 s when its initial concentration is 0.270 M. When the initial concentration is 0.605 M, this same reactant decomposes with the same half-life of 103 s. **Questions:** 1. **What is the order of the reaction?** - [ ] 0 - [ ] 2 - [ ] 1 2. **What is the value and unit of the rate constant for this reaction?** \( k = \) [________] Units: [________] ### Explanation To solve the problem: - **Determine the order of the reaction:** A reaction whose half-life is independent of initial concentration is a first-order reaction. - **Calculate the rate constant \( k \):** For a first-order reaction, the rate constant \( k \) can be calculated using the relation: \[ t_{1/2} = \frac{0.693}{k} \] Given that the half-life \( t_{1/2} \) is 103 s, solve for \( k \): \[ k = \frac{0.693}{103 \text{ s}} \] Fill in the value and unit for \( k \) in the provided space.
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