Calculate the number of moles in a real gas

In summary, to calculate the amount of moles of gas in a cylinder with a certain volume and pressure, one can use the ideal gas law or the Van der Waals equation. In this specific case, the gas in the cylinder is a mixture of air, oxygen, helium, and argon, with a volume of 24 liters and a pressure of 200 bar. The a and b values for the gas mixture can be calculated and used in the Van der Waals equation to obtain a value near 174 mol.
  • #1
larsb
3
0

Homework Statement


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 L2bar mol-2
b = 0,0388 L mol-1

Homework Equations


PV = nRT ( ideal gas law)

P = nRT (V-nb)-1 - n2a V-2

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 accommodate 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 - 0,00152n2

So please enlighten me, how can I proceed to calculate the value for n?
 
Physics news on Phys.org
  • #2
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
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
Char. Limit said:
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?

Thanks, I know that it doesn't match the actual pressure and the ideal pressure do not have to match...
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
ehild said:
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

Ok, that indeed helps me a lot! I do not have to be completely spot on, however the closer the better.
 

1. How do you calculate the number of moles in a real gas?

To calculate the number of moles in a real gas, you need to know the pressure, volume, and temperature of the gas. The formula for calculating moles is n = (PV)/(RT), where n is the number of moles, P is the pressure, V is the volume, R is the gas constant, and T is the temperature.

2. What is the gas constant in the formula for calculating moles?

The gas constant, denoted by R, is a proportionality constant that relates the energy of a gas to its temperature. The value of the gas constant depends on the units used for pressure, volume, and temperature. In SI units, the value of R is 8.314 J/(mol·K).

3. Can the ideal gas law be used to calculate the number of moles in a real gas?

The ideal gas law, PV = nRT, can be used to calculate the number of moles in a real gas, but it is only accurate under certain conditions. Real gases deviate from ideal behavior at high pressures and low temperatures. In these cases, the ideal gas law may not give an accurate value for the number of moles.

4. How does the number of moles affect the behavior of a real gas?

The number of moles affects the behavior of a real gas in several ways. First, increasing the number of moles in a fixed volume will increase the pressure of the gas. Second, increasing the number of moles while keeping the volume constant will increase the temperature of the gas. Lastly, increasing the number of moles while keeping the temperature constant will decrease the volume of the gas.

5. What is the significance of calculating the number of moles in a real gas?

Calculating the number of moles in a real gas is important in understanding the behavior and properties of gases. It allows us to determine the amount of gas present in a given volume, as well as the pressure, temperature, and volume relationships of the gas. This information is crucial in many scientific and industrial applications, such as in the production of chemicals and fuels.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
955
  • Introductory Physics Homework Help
Replies
4
Views
856
  • Introductory Physics Homework Help
Replies
2
Views
2K
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
762
  • Introductory Physics Homework Help
Replies
19
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
765
Replies
69
Views
4K
  • Introductory Physics Homework Help
Replies
6
Views
4K
  • Materials and Chemical Engineering
Replies
1
Views
342
Back
Top