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Raoult's Law and Antoine Equation Made Easy: Fun PDFs and Notes
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Antoine Equation and Raoult's Law Calculations
This page focuses on the Antoine equation for calculating vapor pressures and provides a detailed example of Raoult's law calculations for a binary mixture.
The Antoine equation is used to calculate vapor pressures of pure species:
ln Pᵢˢᵃᵗ = Aᵢ - Bᵢ /
Where Aᵢ, Bᵢ, and Cᵢ are Antoine constants specific to each species, and T is the temperature.
Example: The page presents a detailed example of Raoult's law calculations for a mixture of acetonitrile (1) and nitromethane (2) at 75°C.
Given:
- Temperature: 75°C
- Antoine constants for both species
The example demonstrates how to:
- Calculate pure component vapor pressures using the Antoine equation
- Determine vapor-phase compositions (yᵢ) and total pressure (P) for different liquid-phase compositions (xᵢ)
For instance, at x₁ = 0.2:
- P₁ˢᵃᵗ = 83.21 kPa
- P₂ˢᵃᵗ = 41.98 kPa
- P = x₁P₁ˢᵃᵗ + x₂P₂ˢᵃᵗ = 50.226 kPa
- y₁ = x₁P₁ˢᵃᵗ / P = 0.331
Highlight: This example illustrates the practical application of Raoult's law for vapor pressure calculations and demonstrates how composition affects the total pressure and vapor-phase composition in a binary mixture.
The page includes a table showing calculated values for different liquid-phase compositions, providing a comprehensive view of how the mixture behaves across its entire composition range.
Dew Point Calculations Using Raoult's Law
This page focuses on dew point calculations using Raoult's law, presenting a detailed example for a binary mixture of acetonitrile and nitromethane.
Example: The problem involves determining the liquid-phase compositions (x₁ and x₂) and total pressure (P) for a mixture of acetonitrile (1) and nitromethane (2) at 75°C, given a vapor-phase composition of y₁ = 0.600.
The solution approach involves the following steps:
- Use Raoult's law equation: y₁P = x₁P₁ˢᵃᵗ
- Rearrange to solve for x₁: x₁ = y₁P / P₁ˢᵃᵗ
- Use the fact that for a binary system, x₁ + x₂ = 1
- Substitute known values and solve for P
Given:
- y₁ = 0.600
- T = 75°C
- P₁ˢᵃᵗ = 83.21 kPa (acetonitrile)
- P₂ˢᵃᵗ = 41.98 kPa (nitromethane)
Calculations yield:
- P = 59.741 kPa
- x₁ = 0.431
- x₂ = 0.569
Highlight: This example demonstrates the application of Raoult's law for dew point calculations, which are crucial in understanding phase behavior and designing separation processes.
The page emphasizes the importance of using the correct form of Raoult's law equation for dew point calculations, where the vapor-phase composition is known, and the liquid-phase composition and total pressure are to be determined.
Vocabulary: Dew point - The temperature at which vapor begins to condense into liquid at a given pressure.
This example provides valuable insight into how Raoult's law can be applied to solve practical problems in chemical engineering and thermodynamics, particularly in the analysis of vapor-liquid equilibria.
Raoult's Law: Assumptions, Applications, and Calculations
This page introduces Raoult's law, its assumptions, applications, and limitations. It also provides the mathematical formulation of the law and outlines various calculations that can be performed using it.
Definition: Raoult's law states that the partial vapor pressure of each component in an ideal mixture is dependent on the liquid-phase mole fraction of the component multiplied by its pure component vapor pressure at a certain temperature.
The law is expressed mathematically as:
yᵢP = xᵢPᵢˢᵃᵗ
Where:
- yᵢ is the vapor-phase mole fraction
- xᵢ is the liquid-phase mole fraction
- P is the total pressure
- Pᵢˢᵃᵗ is the vapor pressure of pure species i
Highlight: Raoult's law is applicable only to species below their critical temperature and at low to moderate pressures.
The page also outlines various calculations that can be performed using Raoult's law, including:
- Bubble Point Pressure (Bubl P): Calculate {yᵢ} and P given {xᵢ} and T
- Dew Point Pressure (Dew P): Calculate {xᵢ} given {yᵢ} and P
- Bubble Point Temperature (Bubl T): Calculate {yᵢ} and T given {xᵢ} and P
- Dew Point Temperature (Dew T): Calculate {xᵢ} and T given {yᵢ} and P
For a binary system, the total pressure can be calculated using:
P = x₁P₁ˢᵃᵗ + x₂P₂ˢᵃᵗ
Example: This equation can be rearranged to express pressure in terms of x₁: P = x₁ + P₂ˢᵃᵗ
This formulation is particularly useful for Raoult's law vapor pressure calculations in binary mixtures.
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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
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Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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Android user
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iOS user
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iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Raoult's Law and Antoine Equation Made Easy: Fun PDFs and Notes
This binary mixture of acetonitrile and nitromethane demonstrates the application of Rault's Law in binary systems and uses the Antoine Equation for vapor pressure calculation. The example illustrates how to determine vapor-liquid equilibrium compositions and pressures at different conditions.... Show more
Antoine Equation and Raoult's Law Calculations
This page focuses on the Antoine equation for calculating vapor pressures and provides a detailed example of Raoult's law calculations for a binary mixture.
The Antoine equation is used to calculate vapor pressures of pure species:
ln Pᵢˢᵃᵗ = Aᵢ - Bᵢ /
Where Aᵢ, Bᵢ, and Cᵢ are Antoine constants specific to each species, and T is the temperature.
Example: The page presents a detailed example of Raoult's law calculations for a mixture of acetonitrile (1) and nitromethane (2) at 75°C.
Given:
- Temperature: 75°C
- Antoine constants for both species
The example demonstrates how to:
- Calculate pure component vapor pressures using the Antoine equation
- Determine vapor-phase compositions (yᵢ) and total pressure (P) for different liquid-phase compositions (xᵢ)
For instance, at x₁ = 0.2:
- P₁ˢᵃᵗ = 83.21 kPa
- P₂ˢᵃᵗ = 41.98 kPa
- P = x₁P₁ˢᵃᵗ + x₂P₂ˢᵃᵗ = 50.226 kPa
- y₁ = x₁P₁ˢᵃᵗ / P = 0.331
Highlight: This example illustrates the practical application of Raoult's law for vapor pressure calculations and demonstrates how composition affects the total pressure and vapor-phase composition in a binary mixture.
The page includes a table showing calculated values for different liquid-phase compositions, providing a comprehensive view of how the mixture behaves across its entire composition range.
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Dew Point Calculations Using Raoult's Law
This page focuses on dew point calculations using Raoult's law, presenting a detailed example for a binary mixture of acetonitrile and nitromethane.
Example: The problem involves determining the liquid-phase compositions (x₁ and x₂) and total pressure (P) for a mixture of acetonitrile (1) and nitromethane (2) at 75°C, given a vapor-phase composition of y₁ = 0.600.
The solution approach involves the following steps:
- Use Raoult's law equation: y₁P = x₁P₁ˢᵃᵗ
- Rearrange to solve for x₁: x₁ = y₁P / P₁ˢᵃᵗ
- Use the fact that for a binary system, x₁ + x₂ = 1
- Substitute known values and solve for P
Given:
- y₁ = 0.600
- T = 75°C
- P₁ˢᵃᵗ = 83.21 kPa (acetonitrile)
- P₂ˢᵃᵗ = 41.98 kPa (nitromethane)
Calculations yield:
- P = 59.741 kPa
- x₁ = 0.431
- x₂ = 0.569
Highlight: This example demonstrates the application of Raoult's law for dew point calculations, which are crucial in understanding phase behavior and designing separation processes.
The page emphasizes the importance of using the correct form of Raoult's law equation for dew point calculations, where the vapor-phase composition is known, and the liquid-phase composition and total pressure are to be determined.
Vocabulary: Dew point - The temperature at which vapor begins to condense into liquid at a given pressure.
This example provides valuable insight into how Raoult's law can be applied to solve practical problems in chemical engineering and thermodynamics, particularly in the analysis of vapor-liquid equilibria.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Raoult's Law: Assumptions, Applications, and Calculations
This page introduces Raoult's law, its assumptions, applications, and limitations. It also provides the mathematical formulation of the law and outlines various calculations that can be performed using it.
Definition: Raoult's law states that the partial vapor pressure of each component in an ideal mixture is dependent on the liquid-phase mole fraction of the component multiplied by its pure component vapor pressure at a certain temperature.
The law is expressed mathematically as:
yᵢP = xᵢPᵢˢᵃᵗ
Where:
- yᵢ is the vapor-phase mole fraction
- xᵢ is the liquid-phase mole fraction
- P is the total pressure
- Pᵢˢᵃᵗ is the vapor pressure of pure species i
Highlight: Raoult's law is applicable only to species below their critical temperature and at low to moderate pressures.
The page also outlines various calculations that can be performed using Raoult's law, including:
- Bubble Point Pressure (Bubl P): Calculate {yᵢ} and P given {xᵢ} and T
- Dew Point Pressure (Dew P): Calculate {xᵢ} given {yᵢ} and P
- Bubble Point Temperature (Bubl T): Calculate {yᵢ} and T given {xᵢ} and P
- Dew Point Temperature (Dew T): Calculate {xᵢ} and T given {yᵢ} and P
For a binary system, the total pressure can be calculated using:
P = x₁P₁ˢᵃᵗ + x₂P₂ˢᵃᵗ
Example: This equation can be rearranged to express pressure in terms of x₁: P = x₁ + P₂ˢᵃᵗ
This formulation is particularly useful for Raoult's law vapor pressure calculations in binary mixtures.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user