Show work please **Multiple Choice Question**Please select the correct duration:- ○ 20 min- ○ 101 min- ○ 21 min- ○ 42 min- ○ 84 min**Navigation Options:**- Previous: Click "Prev" to go back to the previous question.- Next: Click "Next" to proceed to the next question._Currently on question 3 of 18._ **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 \( t_{1/2} \).

Here 25 % of reaction completes in 42 minute, then N=N0e-λt34N0=N0e-λ42e-λ42=0.75-λ42=-0.287λ=0.0068

Answered: A certain first-order reaction A - B is…

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

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Show work please

**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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