It's a gas: critical behavior in the van der Waals gas derivation

00:07 Graph of pressure (p) as function of molar volume (Vₘ) for ideal and real gases
02:01 Values at critical point
03:00 Van der Waals equation
03:45 Evaluation of dp/dVₘ
05:00 Evaluation of d²p/dV²ₘ
06:45 Solve first derivative in terms of RT
08:00 Solve second derivative in terms of RT
09:05 Set both RT expressions equal to each other
10:00 Solve for Vₘ
11:30 Set first derivative equal to 0
12:20 Substitute value of Vₘ into first derivative equation
14:20 Solve for Tc
15:50 Substitute value of Vₘ and Tc into van der Waals equation
16:45 Solve for p at critical point
17:52 A factor of "R" is mistakenly written in the denominator, when it should have cancelled out. I apologize for this typo here.
Derivation of the critical constants - the critical molar volume V, the critical temperature T, and the critical pressure p - for a gas obeying the van der Waals equation of state.
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[@lseinjr1]

(For mobile users) 00:07 Graph of pressure (p) as function of molar volume (Vₘ) for ideal and real gases 02:01 Values at critical point 03:00 Van der Waals equation 03:45 Evaluation of dp/dVₘ 05:00 Evaluation of d²p/dV²ₘ 06:45 Solve first derivative in terms of RT 08:00 Solve second derivative in terms of RT 09:05 Set both RT expressions equal to each other 10:00 Solve for Vₘ 11:30 Set first derivative equal to 0 12:20 Substitute value of Vₘ into first derivative equation 14:20 Solve for Tc 15:50 Substitute value of Vₘ and Tc into van der Waals equation 16:45 Solve for p at critical point

[@ibrahimr4690]

Sir for critical pressure you forget put gas constant R in denominator

[@lseinjr1]

@@ibrahimr4690 That is a typographical mistake on my part. The "R" shown at 17:52 in the denominator should not be there; it cancels with the other "R" in the numerator. The final form of pc is correct.

[@ibrahimr4690]

Thank you

[@cristellemirador910]

THANK YOU FOR HELPING ME UNDERSTAND THERMODYNAMICS

[@beepboopbs98]

This topic was explained so clearly and was extremely helpful, thanks a lot!

[@prashanthkumar0]

Thanks a lot sir . This channel is gold mine to me . These things in school they say to just memorize the formula for critical points without any logic .... now it makes complete sense ... Thank you so so much ... now i decide that i will study whole chemistry here ...

[@duckplushie8421]

You have saved my Physical Chemistry class thank you so much

[@millardbalatucan3019]

Thank you so much!!!!! I’m on my Physical Chemistry 2 now, but I just understand this derivations now with the help of your video!!! I can’t be thankful enough

[@lseinjr1]

Wonderful!

[@nurnasriyah7974]

excellent, thanks a lot sir

[@panda_gaming_official]

Very helpful thanks

[@LuisFernando-dh5vp]

Thanks for the video

[@pardiskhodakarami8525]

thank you for teaching us thermodynamic. please upload more lessons.

[@lseinjr1]

I will try my best

[@hafidatayebbey3719]

THANK U THANK U THANK U

[@lseinjr1]

You're welcome!!

[@user-op4kx8nf8g]

The ture instructor.

[@riceplacebo3137]

Thank you very much, this helps me alot

[@lseinjr1]

Glad it helped!

[@felipeanacleto11]

Thank you!!

[@meermohammad1672]

What about moles ? n²

[@lseinjr1]

Vₘ is the molar volume (Vₘ = V / n), where V is the volume and n is the number of moles of gas. So n is included in the Vₘ term.

[@brianwiley6349]

At 17:50 its just 27b in the denominator not 27bR

[@lseinjr1]

Yes, this was already noted in the time stamps in the video description.