Thank you once again for your fantastic lectures! I have a question regarding the energy term: I sometimes see it being regarded as the potential energy of a system and sometimes as the hamiltonian of a system (encompassing the kinetic energy term). Which one is the right one? Or are both valid in different circumstances? This confuses me quite a bit, as for me it only makes sense to regard E_i as the potential energy, since the temperature term in beta already accounts for the kinetic energy of the system.
Superb explanation!! Could we theoretically include conservation of momentum as a third constraint? And if so, would we still be able to derive the Maxwell-Boltzmann distribution from there?
You can indeed use the Boltzmann distribution as a starting point to derive the Maxwell-Boltzmann distribution. You don't need to use conservation of momentum. Instead, the Boltzmann distribution can directly give you the distribution of velocities (th-cam.com/video/hon05fziwAY/w-d-xo.html) and then that can be converted to a distribution of speeds (th-cam.com/video/4KRZTZZLNEM/w-d-xo.html)
I had a doubt . I am currently studying reaction kinetics .There ,I got to know of the Arrhenius equation .It is very closely linked with the Maxwell Boltzman distribution curve .However I am unable to understand the one thing regarding the pre exponential factor .looking at the exponential part we can say that as T approaches infinity the rate of reaction becomes equal to A (the pre exponential factor ) However we know that A itself is dependent on Temperature .It takes into account the collision frequency which itself increases with temperature .So how can we say ,based on this ,that the reaction constant reaches a finite limit ? Can you please explain .
You're definitely right that Arrhenius kinetics are closely related to Boltzmann distribution. We often use the approximation that the Arrhenius prefactor, A, is a constant. But that's not really true, as you point out. A does have some temperature dependence. But A doesn't increase without bound as the temperature increases. It depends not only on the collision frequency, but also on geometric factors and collision cross sections. When the temperature gets too high, the probability of a collision resulting in a productive reaction actually decreases. A full description of how the Arrhenius prefactor depends on temperature can get quite complex.
@@rachealbrimberry8918 Not necessarily. The question is a little unclear. You can measure collision frequency at any temperature you like. There's not really an ideal temperature at which to measure it. The collision frequency does change with temperature, and the Boltzmann distribution can help us understand (in part) how that is true, as is discussed in some later videos on the kinetic theory of gases.
The index represents the state of the system. This could be an energy level, or confirmational state, or anything that distinguishes the particular variation that you want to calculate the probability of.
@@psychemist They are just indices. I could have used any letter. But in this video I used j for a specific state and i inside summations where all possible states are being summed over
That's actually the subject of the previous ~20 videos in the sequence. You've started with the punchline! The short version is that a system will be found most often in the state that has the highest multiplicity -- or the most different ways of existing. It turns out that entropy is a way of measuring the multiplicity. So we maximize the entropy in order to predict what state we will find a system in. For the full explanation, back up to around this video: th-cam.com/video/o9fqw2CSKVo/w-d-xo.html and watch in sequence from there.
I really don't know how would my life be without guys like you on youtube.
What are/were you studying?
Boltzmann? More like "Beautiful work, man!" Your explanation was amazing 👍
@@PunmasterSTP Lol, thanks! I appreciate it
@ I’m glad! Just let me know if you ever want to hear a pun on a particular topic.
@PunmasterSTP Bon skills, man. Now do Schrodinger
@@PhysicalChemistry Schro, schro, schro your boat, gently down the stream. Merrily, merrily, merrily, merrily, life may or may not be a dream.
@@PunmasterSTP nicely done! 💯
How is it possible someone watch these amazing videos and dont like or comment!
Haha, I guess not everyone enjoys PChem as much as you and I do! I definitely enjoy the feedback and interaction, though. Thanks!
There's probably a lot of people cramming right before an exam and trying to run through stuff real fast...
So THAT is the equation in your channel icon! So fascinating!
Yes! And that's the key to everything else, as you'll see if you watch more!
@@PhysicalChemistry That sounds Q-uite intriguing!
Thank you once again for your fantastic lectures! I have a question regarding the energy term: I sometimes see it being regarded as the potential energy of a system and sometimes as the hamiltonian of a system (encompassing the kinetic energy term). Which one is the right one? Or are both valid in different circumstances? This confuses me quite a bit, as for me it only makes sense to regard E_i as the potential energy, since the temperature term in beta already accounts for the kinetic energy of the system.
sorry for bothering, I'm wondering the limitations of boltzmann distribution. Does it apply to interacting system?
What type of interacting system? I suppose it may or may not apply depending on the nature of the interactions.
Superb explanation!! Could we theoretically include conservation of momentum as a third constraint? And if so, would we still be able to derive the Maxwell-Boltzmann distribution from there?
You can indeed use the Boltzmann distribution as a starting point to derive the Maxwell-Boltzmann distribution. You don't need to use conservation of momentum. Instead, the Boltzmann distribution can directly give you the distribution of velocities (th-cam.com/video/hon05fziwAY/w-d-xo.html) and then that can be converted to a distribution of speeds (th-cam.com/video/4KRZTZZLNEM/w-d-xo.html)
I had a doubt .
I am currently studying reaction kinetics .There ,I got to know of the Arrhenius equation .It is very closely linked with the Maxwell Boltzman distribution curve .However I am unable to understand the one thing regarding the pre exponential factor .looking at the exponential part we can say that as T approaches infinity the rate of reaction becomes equal to A (the pre exponential factor ) However we know that A itself is dependent on Temperature .It takes into account the collision frequency which itself increases with temperature .So how can we say ,based on this ,that the reaction constant reaches a finite limit ? Can you please explain .
You're definitely right that Arrhenius kinetics are closely related to Boltzmann distribution.
We often use the approximation that the Arrhenius prefactor, A, is a constant. But that's not really true, as you point out. A does have some temperature dependence.
But A doesn't increase without bound as the temperature increases. It depends not only on the collision frequency, but also on geometric factors and collision cross sections. When the temperature gets too high, the probability of a collision resulting in a productive reaction actually decreases.
A full description of how the Arrhenius prefactor depends on temperature can get quite complex.
@@PhysicalChemistry so were looking for an ideal temperature to measure collision frequency.
@@rachealbrimberry8918 Not necessarily.
The question is a little unclear. You can measure collision frequency at any temperature you like. There's not really an ideal temperature at which to measure it.
The collision frequency does change with temperature, and the Boltzmann distribution can help us understand (in part) how that is true, as is discussed in some later videos on the kinetic theory of gases.
Sir Thanks for Uploading these wonderful lectures, also is there way to communicate with you occasionally, something like a discord channel.
You're welcome; I'm glad you appreciate them. I don't have a discord channel, but my email address is on the TH-cam channel's about page.
Amazing
Thanks
What the 'i' and 'j' indexes represt here
Please help i am a newbie there but almost got it.
Please please anyone reply fast i got the exam coming ahead
The index represents the state of the system. This could be an energy level, or confirmational state, or anything that distinguishes the particular variation that you want to calculate the probability of.
@@PhysicalChemistry what purpose is 'i' and 'j' are they the same ?
@@psychemist They are just indices. I could have used any letter. But in this video I used j for a specific state and i inside summations where all possible states are being summed over
Why would you want to maximize the entropy.
That's actually the subject of the previous ~20 videos in the sequence. You've started with the punchline!
The short version is that a system will be found most often in the state that has the highest multiplicity -- or the most different ways of existing. It turns out that entropy is a way of measuring the multiplicity. So we maximize the entropy in order to predict what state we will find a system in.
For the full explanation, back up to around this video: th-cam.com/video/o9fqw2CSKVo/w-d-xo.html and watch in sequence from there.