If the reaction proceeds at second order kinetics and has half-life of 100.0 seconds. If the reaction is carried out at some temperature, and the initial concentration of NO₂ is 1.225 M, what is the rate constant for the reaction? What will the NO₂ concentration be after 35.4 s? At 175 s? At 865 s?

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A substance decays with second order kinetics. What is the half-life given a rate constant that is 0.37 M⁻¹ s⁻¹ and an initial concentration of 0.75 M? How much of the substance remains after 13.9 seconds? After 55.2 seconds? 

(Note: Any scribbled out section seems to be irrelevant to the core text.)
Transcribed Image Text:A substance decays with second order kinetics. What is the half-life given a rate constant that is 0.37 M⁻¹ s⁻¹ and an initial concentration of 0.75 M? How much of the substance remains after 13.9 seconds? After 55.2 seconds? (Note: Any scribbled out section seems to be irrelevant to the core text.)
**Problem Statement:**

If the reaction proceeds at second-order kinetics and has a half-life of 100.0 seconds, what is the rate constant for the reaction when the initial concentration of NO₂ is 1.225 M? Additionally, what will the NO₂ concentration be after:

- 35.4 seconds?
- 175 seconds?
- 865 seconds? 

**Solution Explanation:**

1. **Rate Constant Calculation:**
   For a second-order reaction, the relationship between half-life (\( t_{1/2} \)) and the rate constant (\( k \)) is given by the equation:
   \[
   t_{1/2} = \frac{1}{k \cdot [A]_0}
   \]
   Where \( [A]_0 \) is the initial concentration.

2. **Concentration Over Time:**
   The concentration at any time \( t \) for a second-order reaction can be determined using:
   \[
   \frac{1}{[A]} = \frac{1}{[A]_0} + k \cdot t
   \]
   Apply this formula to find the concentration at each specified time.
Transcribed Image Text:**Problem Statement:** If the reaction proceeds at second-order kinetics and has a half-life of 100.0 seconds, what is the rate constant for the reaction when the initial concentration of NO₂ is 1.225 M? Additionally, what will the NO₂ concentration be after: - 35.4 seconds? - 175 seconds? - 865 seconds? **Solution Explanation:** 1. **Rate Constant Calculation:** For a second-order reaction, the relationship between half-life (\( t_{1/2} \)) and the rate constant (\( k \)) is given by the equation: \[ t_{1/2} = \frac{1}{k \cdot [A]_0} \] Where \( [A]_0 \) is the initial concentration. 2. **Concentration Over Time:** The concentration at any time \( t \) for a second-order reaction can be determined using: \[ \frac{1}{[A]} = \frac{1}{[A]_0} + k \cdot t \] Apply this formula to find the concentration at each specified time.
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