## Van der Waals Equation - solve for n

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YukiCormyr
Newbie
Posts: 1
Joined: Wed Feb 26, 2020 11:25 am

### Van der Waals Equation - solve for n

I'm currently having trouble solving for n in the VdW gas equation for a calculator in excel for a variation of gases. I know there is a calculator on the site and I've tried my hand at doing the algebra, but I keep seeming to be just a touch off.

Is there anyone out there that has solved for n in this equation? If so, what is it???

Thanks!
ChenBeier
Distinguished Member
Posts: 493
Joined: Wed Sep 27, 2017 7:25 am
Location: Berlin, Germany
p = nRT/(V - nb) -n^2 *a/V^2

p ( V - nb) = nRT - n^2*a*(V-nb)/V^2

pV^3 -pnbV^2 = nRTV^2 -n^2aV - n^3ab
n^3ab + n^2aV - nRTV^2- pnbV^2 + pV^3 = 0
n^3ab + n^2aV - n( RTV^2+pbV^2) + pV^3 = 0
n^3 + n^2*V/b - n( RTV^2+pV^2)/ab +pV^3/ab =0

This cubic equation is a type of

ax^3 + bx^2 + cx+ d = 0

This kind of questions have to be solved with tools of mathematics like curve discussion and differential equation, etc.