What is the half-life for a particular reaction if the rate law is rate = (1131 M-1*min 1)[A]² 2 %3D and the initial concentration of A is 0.250 M?
What is the half-life for a particular reaction if the rate law is rate = (1131 M-1*min 1)[A]² 2 %3D and the initial concentration of A is 0.250 M?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Question:**
What is the half-life for a particular reaction if the rate law is \( \text{rate} = (1131 \, \text{M}^{-1} \cdot \text{min}^{-1})[A]^2 \) and the initial concentration of A is 0.250 M?
**Explanation:**
The given rate law shows a second-order reaction, where the rate depends on the square of the concentration of reactant A. For second-order reactions, the half-life is given by the formula:
\[ t_{1/2} = \frac{1}{k[A]_0} \]
where:
- \( t_{1/2} \) is the half-life,
- \( k \) is the rate constant (\( 1131 \, \text{M}^{-1} \cdot \text{min}^{-1} \)),
- \( [A]_0 \) is the initial concentration of A (0.250 M).
By substituting the values into the formula, you can calculate the half-life.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7e025f6-315e-487c-94cf-1666eb5804e7%2Ff0961d24-1f86-47fd-acc4-5978d9f74886%2Fadkm82_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the half-life for a particular reaction if the rate law is \( \text{rate} = (1131 \, \text{M}^{-1} \cdot \text{min}^{-1})[A]^2 \) and the initial concentration of A is 0.250 M?
**Explanation:**
The given rate law shows a second-order reaction, where the rate depends on the square of the concentration of reactant A. For second-order reactions, the half-life is given by the formula:
\[ t_{1/2} = \frac{1}{k[A]_0} \]
where:
- \( t_{1/2} \) is the half-life,
- \( k \) is the rate constant (\( 1131 \, \text{M}^{-1} \cdot \text{min}^{-1} \)),
- \( [A]_0 \) is the initial concentration of A (0.250 M).
By substituting the values into the formula, you can calculate the half-life.
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