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Integrated Rate Law, Reaction Mechanisms, and Multistep Energy Diagrams
59
•
Jul 6, 2025
•
The document provides a comprehensive overview of integrated rate laws... Show more
This page covers second-order and zero-order reactions, providing their differential and integrated rate laws. For second-order integrated rate law, the equation is 1/ = kt + 1/₀, which is important to memorize.
Vocabulary: Zero-order reactions have a rate that is independent of concentration, expressed as Rate = k⁰ or simply Rate = k.
The page then transitions to reaction mechanisms, defining them as series of elementary steps by which a chemical reaction occurs. An example of an overall reaction is given, along with its experimentally determined rate law.
Definition: An intermediate is a substance formed and subsequently used up during a reaction mechanism.
Highlight: Elementary steps are reactions within a mechanism whose rate law can be written directly from its molecularity, which is the number of species that must collide to produce the reaction indicated by that step.
This page elaborates on elementary steps and their corresponding rate laws. It provides a table showing various elementary steps and their rate expressions, ranging from unimolecular to termolecular reactions.
The concept of rate-determining steps is introduced, explaining that it is the slowest step in a reaction mechanism and determines the overall rate of the reaction.
Highlight: For a mechanism to be valid, the sum of elementary steps must give the overall balanced equation for the reaction, and the experimental rate law must agree with the rate-determining step.
An example of a valid mechanism is provided for the reaction NO₂ + CO → NO + CO₂, demonstrating how the rate law is determined by the slow, rate-determining step.
Example: The page presents a problem asking to identify the rate-determining step in the reaction 2H₂ + 2NO → N₂ + 2H₂O, given the rate law R = k².
This final page discusses complex rate laws and multi-step energy diagrams. It explains that sometimes rate laws may appear not to match the mechanism, but they actually do.
Example: The H₂ + Br₂ → 2HBr reaction is used to illustrate how a seemingly mismatched rate law can be reconciled with the reaction mechanism.
The page concludes with a detailed explanation of multi-step reaction energy diagrams. These diagrams visually represent:
Highlight: The rate-determining step in a multi-step reaction is characterized by the longest activation energy barrier on the energy diagram.
Vocabulary: Activated complexes are high-energy, unstable arrangements of atoms formed during a reaction, represented as peaks on the energy diagram.
This comprehensive overview provides students with a solid foundation in understanding complex reaction kinetics and mechanisms.
This page introduces the concept of integrated rate laws and focuses on first-order reactions. Integrated rate laws show the relationship between concentration and time for chemical reactions. For first-order reactions, the rate law is Rate = k, where k is the rate constant and is the concentration of reactant A.
The integrated form of the first-order rate law is ln = -kt + ln₀, where ₀ is the initial concentration. This equation produces a linear graph of ln versus time, with a negative slope equal to -k.
Definition: Half-life is the time it takes for half of the original concentration to react.
Example: A problem is presented where the half-life of a reaction is 20.0 minutes. The rate constant is calculated to be 0.347 min⁻¹ using the formula k = 0.693 / t₁/₂.
Highlight: The linear relationship between ln and time is a key characteristic of first-order reactions, distinguishing them from other orders.
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.
You can download the app in the Google Play Store and in the Apple App Store.
You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.
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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 THE SCHOOLGPT. 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 THE SCHOOLGPT. 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 document provides a comprehensive overview of integrated rate laws, reaction mechanisms, and multi-step reactions in chemistry. It covers first-order, second-order, and zero-order reactions, explaining their rate laws and applications. The text also delves into reaction mechanisms, elementary steps,... Show more
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This page covers second-order and zero-order reactions, providing their differential and integrated rate laws. For second-order integrated rate law, the equation is 1/ = kt + 1/₀, which is important to memorize.
Vocabulary: Zero-order reactions have a rate that is independent of concentration, expressed as Rate = k⁰ or simply Rate = k.
The page then transitions to reaction mechanisms, defining them as series of elementary steps by which a chemical reaction occurs. An example of an overall reaction is given, along with its experimentally determined rate law.
Definition: An intermediate is a substance formed and subsequently used up during a reaction mechanism.
Highlight: Elementary steps are reactions within a mechanism whose rate law can be written directly from its molecularity, which is the number of species that must collide to produce the reaction indicated by that step.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page elaborates on elementary steps and their corresponding rate laws. It provides a table showing various elementary steps and their rate expressions, ranging from unimolecular to termolecular reactions.
The concept of rate-determining steps is introduced, explaining that it is the slowest step in a reaction mechanism and determines the overall rate of the reaction.
Highlight: For a mechanism to be valid, the sum of elementary steps must give the overall balanced equation for the reaction, and the experimental rate law must agree with the rate-determining step.
An example of a valid mechanism is provided for the reaction NO₂ + CO → NO + CO₂, demonstrating how the rate law is determined by the slow, rate-determining step.
Example: The page presents a problem asking to identify the rate-determining step in the reaction 2H₂ + 2NO → N₂ + 2H₂O, given the rate law R = k².
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This final page discusses complex rate laws and multi-step energy diagrams. It explains that sometimes rate laws may appear not to match the mechanism, but they actually do.
Example: The H₂ + Br₂ → 2HBr reaction is used to illustrate how a seemingly mismatched rate law can be reconciled with the reaction mechanism.
The page concludes with a detailed explanation of multi-step reaction energy diagrams. These diagrams visually represent:
Highlight: The rate-determining step in a multi-step reaction is characterized by the longest activation energy barrier on the energy diagram.
Vocabulary: Activated complexes are high-energy, unstable arrangements of atoms formed during a reaction, represented as peaks on the energy diagram.
This comprehensive overview provides students with a solid foundation in understanding complex reaction kinetics and mechanisms.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces the concept of integrated rate laws and focuses on first-order reactions. Integrated rate laws show the relationship between concentration and time for chemical reactions. For first-order reactions, the rate law is Rate = k, where k is the rate constant and is the concentration of reactant A.
The integrated form of the first-order rate law is ln = -kt + ln₀, where ₀ is the initial concentration. This equation produces a linear graph of ln versus time, with a negative slope equal to -k.
Definition: Half-life is the time it takes for half of the original concentration to react.
Example: A problem is presented where the half-life of a reaction is 20.0 minutes. The rate constant is calculated to be 0.347 min⁻¹ using the formula k = 0.693 / t₁/₂.
Highlight: The linear relationship between ln and time is a key characteristic of first-order reactions, distinguishing them from other orders.
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.
You can download the app in the Google Play Store and in the Apple App Store.
You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.
App Store
Google Play
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 THE SCHOOLGPT. 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 THE SCHOOLGPT. 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
