t = 1/₂-k₁ In K₂ CB= Св= кi сао no e-kit_ e-kat K₂-K₁ How would you Shomify it to this? кукуки K₁ CAO [ (K₁₂) сао ка-к 1 1 57/23 +4 ] ki (K1) * 3142₂2-4₁ K₂
t = 1/₂-k₁ In K₂ CB= Св= кi сао no e-kit_ e-kat K₂-K₁ How would you Shomify it to this? кукуки K₁ CAO [ (K₁₂) сао ка-к 1 1 57/23 +4 ] ki (K1) * 3142₂2-4₁ K₂
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
show how to simplyfy this expression with steps so I can undsertand
![The image contains mathematical expressions related to chemical kinetics or reaction rates. Below is the transcription and explanation:
**Initial Equation:**
\[ C_B = k_1 C_{A0} \left[ \frac{e^{-k_1 t} - e^{-k_2 t}}{k_2 - k_1} \right] \]
**Intermediate Step:**
\[ t = \frac{1}{k_2 - k_1} \ln \frac{k_2}{k_1} \]
There is an arrow pointing downward with the text:
"How would you simplify it to this?"
**Simplified Equation:**
\[ C_B = \frac{k_1 C_{A0}}{k_2 - k_1} \left[ \left( \frac{k_1}{k_2} \right)^{k_1 / (k_2-k_1)} - \left( \frac{k_1}{k_2} \right)^{k_2 / (k_2-k_1)} \right] \]
**Explanation:**
- The equations describe the concentration \( C_B \) as a function of time \( t \).
- These are typical forms used in chemical reaction kinetics to describe concentrations over time, often seen with reactions involving two different rate constants \( k_1 \) and \( k_2 \).
- The equations demonstrate how the concentration of substance B changes with time, based on the exponential terms involving \( k_1 \) and \( k_2 \).
**Note:** No graphs or diagrams are present in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F403d5df5-c9a3-47af-a06d-d9770154fd48%2Ffb08eec2-1e08-4444-9a1f-e0575d625edd%2Fp3vqxac_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains mathematical expressions related to chemical kinetics or reaction rates. Below is the transcription and explanation:
**Initial Equation:**
\[ C_B = k_1 C_{A0} \left[ \frac{e^{-k_1 t} - e^{-k_2 t}}{k_2 - k_1} \right] \]
**Intermediate Step:**
\[ t = \frac{1}{k_2 - k_1} \ln \frac{k_2}{k_1} \]
There is an arrow pointing downward with the text:
"How would you simplify it to this?"
**Simplified Equation:**
\[ C_B = \frac{k_1 C_{A0}}{k_2 - k_1} \left[ \left( \frac{k_1}{k_2} \right)^{k_1 / (k_2-k_1)} - \left( \frac{k_1}{k_2} \right)^{k_2 / (k_2-k_1)} \right] \]
**Explanation:**
- The equations describe the concentration \( C_B \) as a function of time \( t \).
- These are typical forms used in chemical reaction kinetics to describe concentrations over time, often seen with reactions involving two different rate constants \( k_1 \) and \( k_2 \).
- The equations demonstrate how the concentration of substance B changes with time, based on the exponential terms involving \( k_1 \) and \( k_2 \).
**Note:** No graphs or diagrams are present in the image.
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