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### Topic: Finding van der Waals constants a and b using critical temperature and pressure?  (Read 10444 times)

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#### yg7s7

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##### Finding van der Waals constants a and b using critical temperature and pressure?
« on: September 27, 2009, 06:46:25 PM »
Say naphthalene's critical temperature and pressure are 474.8 K and 40.6 atm , respectively, then how would you calculate the van der Waals constants a and b (where (P+a*n^2/V^2)(V-nb) = nRT)?

#### MrTeo

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##### Re: Finding van der Waals constants a and b using critical temperature and press
« Reply #1 on: September 28, 2009, 12:40:48 AM »
How would you do that?

Hint#1: there are some formulas that link a and b to the critical values. You can get them starting from the definition of critical point and using van der Waals equation. Think at the isotherms of a real gas.

Hint#2:

$$\left\{ \begin{array}{l} \left({\frac{{\partial p}}{{\partial V}}} \right)_T=0\\ \left({\frac{{\partial ^2 p}}{{\partial V^2 }}} \right)_T=0\\ \end{array} \right. /$$

I don't know if there's an easier way to find them out but I'll think at it
The way of the superior man may be compared to what takes place in traveling, when to go to a distance we must first traverse the space that is near, and in ascending a height, when we must begin from the lower ground. (Confucius)

#### yg7s7

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##### Re: Finding van der Waals constants a and b using critical temperature and pressure?
« Reply #2 on: September 29, 2009, 12:35:42 AM »

How would you know that the first and second derivatives of P in terms of V are zero?

#### MrTeo

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##### Re: Finding van der Waals constants a and b using critical temperature and press
« Reply #3 on: September 29, 2009, 12:51:38 AM »
There's an inflection point in the critical isotherm

The way of the superior man may be compared to what takes place in traveling, when to go to a distance we must first traverse the space that is near, and in ascending a height, when we must begin from the lower ground. (Confucius)