Professor Dirac once said, "I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it." You have just helped me achieve this higher state of learning without spoonfeeding! Thank you from the bottom of my heart.
(for *mobile* users) 00:15 Introduction 00:34 Differential equation 00:51 Separation of variables 01:12 Integrate each side 01:41 Apply Fundamental Theorem 02:08 Alternate form of solution useful for graphing 03:08 Let [A] = A₀ 03:26 Let t = t ₁/₂ 03:53 Cancel Ao's 04:09 Use property of logs 04:25 Divide each side by -k Don't forget to like, comment, share, and subscribe!
Haha this is nice we just got done learning all the rules for deriving in AP calculus and I remembered that we had looked over derived and integrated rate laws in kinetics for AP Chem last year but it never really crossed my mind until then. This video has helped me grasp the concept of integrating, as you take the anti derivative and work in reverse which is pretty fascinating to me, of course I need to iron out the nuances to get a full picture of the various applied forms of calculus.
This is first order. Note that, while one can define "half-life" for any system, it is only in a first order reaction that the half-life is independent of the initial value of reactant. Also note that for a zeroth order reaction, d[A] = k[A]⁰ = k.
my calculus is so rough and this brought everything back for me. Thank you
Professor Dirac once said, "I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it." You have just helped me achieve this higher state of learning without spoonfeeding! Thank you from the bottom of my heart.
You are very kind!
(for *mobile* users)
00:15 Introduction
00:34 Differential equation
00:51 Separation of variables
01:12 Integrate each side
01:41 Apply Fundamental Theorem
02:08 Alternate form of solution useful for graphing
03:08 Let [A] = A₀
03:26 Let t = t ₁/₂
03:53 Cancel Ao's
04:09 Use property of logs
04:25 Divide each side by -k
Don't forget to like, comment, share, and subscribe!
Haha this is nice we just got done learning all the rules for deriving in AP calculus and I remembered that we had looked over derived and integrated rate laws in kinetics for AP Chem last year but it never really crossed my mind until then. This video has helped me grasp the concept of integrating, as you take the anti derivative and work in reverse which is pretty fascinating to me, of course I need to iron out the nuances to get a full picture of the various applied forms of calculus.
much helpful, thankyou sir :))
Most welcome!
Great video, thank you!
Thank you very much 😊
Isn't this zero order
This is first order. Note that, while one can define "half-life" for any system, it is only in a first order reaction that the half-life is independent of the initial value of reactant. Also note that for a zeroth order reaction, d[A] = k[A]⁰ = k.