A certain first-order reaction A - B is 25% complete in 42 min at 25°C. What is the half-life of the reaction? Multiple Choice 20 min 101 min 21 min 42min 84 min
A certain first-order reaction A - B is 25% complete in 42 min at 25°C. What is the half-life of the reaction? Multiple Choice 20 min 101 min 21 min 42min 84 min
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:**Multiple Choice Question**
Please select the correct duration:
- ○ 20 min
- ○ 101 min
- ○ 21 min
- ○ 42 min
- ○ 84 min
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![**Question:**
A certain first-order reaction A → B is 25% complete in 42 min at 25°C. What is the half-life of the reaction?
**Multiple Choice:**
- ○ 20 min
- ○ 101 min
- ○ 21 min
- ○ 42 min
- ○ 84 min
---
**Explanation:**
To find the half-life of a first-order reaction, we need to use the first-order kinetics formula:
\[ t_{1/2} = \frac{0.693}{k} \]
First, we determine the rate constant \( k \) using the formula:
\[ k = \frac{-\ln(1 - \text{fraction completed})}{t} \]
Given that the reaction is 25% complete, the fraction completed is 0.25.
\[ k = \frac{-\ln(1 - 0.25)}{42} = \frac{-\ln(0.75)}{42} \]
After calculating \( k \), substitute it back into the half-life formula to find \( t_{1/2} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0df2326-c735-4e1b-ae2a-9c0c3c1c71e6%2Fe2a08b7e-5899-4db7-bc53-30ba8ba6f50a%2Feackkj4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
A certain first-order reaction A → B is 25% complete in 42 min at 25°C. What is the half-life of the reaction?
**Multiple Choice:**
- ○ 20 min
- ○ 101 min
- ○ 21 min
- ○ 42 min
- ○ 84 min
---
**Explanation:**
To find the half-life of a first-order reaction, we need to use the first-order kinetics formula:
\[ t_{1/2} = \frac{0.693}{k} \]
First, we determine the rate constant \( k \) using the formula:
\[ k = \frac{-\ln(1 - \text{fraction completed})}{t} \]
Given that the reaction is 25% complete, the fraction completed is 0.25.
\[ k = \frac{-\ln(1 - 0.25)}{42} = \frac{-\ln(0.75)}{42} \]
After calculating \( k \), substitute it back into the half-life formula to find \( t_{1/2} \).
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