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Calculate the number of moles in a real gas 
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#1
Jan1910, 03:19 PM

P: 3

1. The problem statement, all variables and given/known data
I would like to know how to calculate how much moles of gas I have in the following in a cylinder with a certain volume and pressure. The gas in the cylinder is a mixture of air, with added oxygen and helium, the mixture is 18% Oxygen, 36,6% Nitrogen, 45% Helium and 0,4% Argon. The cylinder is 24 liters big, the pressure in the cylinder is 200bar. I can calculate the a and b values for the gas mixture. P = 200 bar V = 24 L T = 293,15 K R = 0,083145 L bar K^{1} mol ^{1} a = 0,8746 L^{2}bar mol^{2} b = 0,0388 L mol^{1} 2. Relevant equations PV = nRT ( ideal gas law) P = nRT (Vnb)^{1}  n^{2}a V^{2} 3. The attempt at a solution According to the ideal gas law this should be 196,93 moles, but that is not right, since if I use the Vanderwaals equation I end up at a pressure of 234,6 bar to accomodate 196,93 moles of this gasmixture. Using the Vanderwaals equation I can't calculate the exact number of moles, this is where is end up: 200 = 24,37n (24  0,0388n)^{1}  0,00152n^{2} So please enlighten me, how can I proceed to calculate the value for n? 


#2
Jan1910, 03:36 PM

PF Gold
P: 1,941

First, remember that the Van Der Waals pressure doesn't have to match the ideal pressure: in fact, it won't, unless a is 0. With an a as large as yours, the pressure can actually have quite a bit of variation between ideal and Van Der Waals.
For that last equation, have you considered quadratics? 


#3
Jan2010, 02:21 AM

HW Helper
Thanks
P: 10,375

You can apply some iteration procedure. Rewrite the Van der Waals equation in the form
[tex]n=\frac{PV}{RT}(1+\frac{n^2a}{PV^2})(1\frac{nb}{V}) [/tex] Plug in the data, start with n you got for the ideal gas, substitute for n at the right side, and you get a new n. Continue the procedure with the new n... You get a value near 174 mol, if I am not mistaken. ehild 


#4
Jan2010, 04:40 AM

P: 3

Calculate the number of moles in a real gas
I know for sure that the pressure in the cylinder is 200 bar, or actually 201 bar, because I am reading the pressure from a gauge. What do you mean by "considering quadratics"? 


#5
Jan2010, 05:10 AM

P: 3




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