(adsbygoogle = window.adsbygoogle || []).push({}); 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 (V-nb)^{-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?

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# Calculate the number of moles in a real gas

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