The partition coefficient (Kp) for caffeine in dichloromethane is 5.2 You have an aqueous solution of caffeine (80 mg) in 30 mL of water. Calculate the amount (in mg) of caffeine that can be extracted with 1 portion of 30 mL of dichloromethane (i.e. how much caffeine will be in dichloromethane). Write your answer in the form (xx.x mg)
The partition coefficient (Kp) for caffeine in dichloromethane is 5.2 You have an aqueous solution of caffeine (80 mg) in 30 mL of water. Calculate the amount (in mg) of caffeine that can be extracted with 1 portion of 30 mL of dichloromethane (i.e. how much caffeine will be in dichloromethane). Write your answer in the form (xx.x mg)
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
![### Partition Coefficient Calculation: Caffeine Extraction
**Problem Statement:**
The partition coefficient (K\(_p\)) for caffeine in dichloromethane is 5.2.
You have an aqueous solution of caffeine (80 mg) in 30 mL of water. Calculate the amount (in mg) of caffeine that can be extracted with 1 portion of 30 mL of dichloromethane (i.e., how much caffeine will be in dichloromethane). Write your answer in the form (xx.x mg).
**Solution Explanation:**
To solve this problem, we can use the partition coefficient \( K_p \), which is the ratio of the concentration of solute in the organic phase (dichloromethane) to the concentration of solute in the aqueous phase (water).
The partition coefficient formula is given by:
\[ K_p = \frac{[Caffeine]_{organic}}{[Caffeine]_{aqueous}} \]
Given data:
- \( K_p \) for caffeine in dichloromethane: 5.2
- Initial caffeine amount \( C_{total} \): 80 mg
- Volume of water \( V_{water} \): 30 mL
- Volume of dichloromethane \( V_{DCM} \): 30 mL
Let \( x \) be the amount of caffeine in dichloromethane after extraction.
According to the partition coefficient:
\[ K_p = \frac{\frac{x}{V_{DCM}}}{\frac{C_{total} - x}{V_{water}}} \]
Substituting the known values:
\[ 5.2 = \frac{\frac{x}{30}}{\frac{80 - x}{30}} \]
Solving for \( x \):
\[ 5.2 = \frac{x}{80 - x} \]
\[ 5.2 (80 - x) = x \]
\[ 416 - 5.2x = x \]
\[ 416 = 6.2x \]
\[ x = \frac{416}{6.2} \]
\[ x \approx 67.1 \text{ mg} \]
Thus, the amount of caffeine that can be extracted with 30 mL of dichloromethane is approximately \( \mathbf{67.1 \text{ mg}} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4167b07b-ab2c-42e3-ab89-9f12261de975%2Fac06f664-45a6-4cee-a39f-e160887daf38%2F9dprwc_processed.png&w=3840&q=75)
Transcribed Image Text:### Partition Coefficient Calculation: Caffeine Extraction
**Problem Statement:**
The partition coefficient (K\(_p\)) for caffeine in dichloromethane is 5.2.
You have an aqueous solution of caffeine (80 mg) in 30 mL of water. Calculate the amount (in mg) of caffeine that can be extracted with 1 portion of 30 mL of dichloromethane (i.e., how much caffeine will be in dichloromethane). Write your answer in the form (xx.x mg).
**Solution Explanation:**
To solve this problem, we can use the partition coefficient \( K_p \), which is the ratio of the concentration of solute in the organic phase (dichloromethane) to the concentration of solute in the aqueous phase (water).
The partition coefficient formula is given by:
\[ K_p = \frac{[Caffeine]_{organic}}{[Caffeine]_{aqueous}} \]
Given data:
- \( K_p \) for caffeine in dichloromethane: 5.2
- Initial caffeine amount \( C_{total} \): 80 mg
- Volume of water \( V_{water} \): 30 mL
- Volume of dichloromethane \( V_{DCM} \): 30 mL
Let \( x \) be the amount of caffeine in dichloromethane after extraction.
According to the partition coefficient:
\[ K_p = \frac{\frac{x}{V_{DCM}}}{\frac{C_{total} - x}{V_{water}}} \]
Substituting the known values:
\[ 5.2 = \frac{\frac{x}{30}}{\frac{80 - x}{30}} \]
Solving for \( x \):
\[ 5.2 = \frac{x}{80 - x} \]
\[ 5.2 (80 - x) = x \]
\[ 416 - 5.2x = x \]
\[ 416 = 6.2x \]
\[ x = \frac{416}{6.2} \]
\[ x \approx 67.1 \text{ mg} \]
Thus, the amount of caffeine that can be extracted with 30 mL of dichloromethane is approximately \( \mathbf{67.1 \text{ mg}} \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The