Ideal Gas Law and pressure in a holder

In summary, the conversation is about determining the pressure inside a 50.0 L container holding 105.0 kg of argon gas at 20°C using the ideal gas law. The calculated pressure is 25258 atm, which seems reasonable. After some discussion, it is determined that the molar mass of argon should be 39.95 g/mol, resulting in a pressure of 1265.1 atm or 1.27 x 10^3 atm.
  • #1
JSGandora
95
0

Homework Statement


What is the pressure inside a $50.0$ L container holding $105.0$ kg of argon gas at $20^\circ$ C?

Homework Equations


Ideal Gas Law: PV=nRT

The Attempt at a Solution


From the ideal gas law, I get
[itex]
P=\frac{nRT}{V}=\frac{\frac{105.0\times 10^3g}{36g/mol}\times 0.08214\frac{L\cdot atm}{mol\cdot K}\times 293^\circ K}{50.0 L}=25258atm
[/itex]
which seems much too large. Am I doing something wrong?
 
Last edited:
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  • #2
Nope! Your answer is quite reasonable, and it seems like nothing looks wrong in your setup of P= nRT/V and all the units match, your value for R is correct and you've converted C to K. Unless you made a calculating mistake, everything looks correct to me.
 
  • #3
Oh wow, thanks! It's hard to believe the massive pressure inside, which was why I was skeptical. Thanks again.
 
  • #4
On second glance, your molar mass for Argon seems to be off, also, you've made a calculation error. Try again and tell me what you got. (I've worked it out this time).
 
  • #5
Oh, should it be [itex]39.95\times 2[/itex] since it's diatomic?
 
  • #6
Nono, on the work you've showed in your original post, it looks like you've put 36 g/mol.
 
  • #7
But the molecular mass of Argon is 39.95 isn't it? I'm just substituting the 36 for 39.95x2.
 
  • #8
By looking at the problem you've presented it should look like this:

P = [(105000/39.95)(0.08214)(293)]/(50)
P = 1265.1 atm
P = 1.27 x 10^3 atm

I've left out the units for simplicity, but you should write them in yourself.
 
  • #9
Oh, yeah. For some reason I thought argon was diatomic...
 

1. What is the Ideal Gas Law?

The Ideal Gas Law is a formula that describes the relationship between the pressure, volume, temperature, and number of moles of a gas. It is written as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

2. How does the Ideal Gas Law relate to pressure in a holder?

The Ideal Gas Law can be used to calculate the pressure of a gas in a holder. As the volume of the holder decreases, the pressure of the gas inside increases, and vice versa. This is because the number of gas molecules remains constant, but the space they occupy changes.

3. What is the significance of pressure in a holder?

Pressure in a holder is important because it determines the amount of force exerted by the gas molecules on the walls of the holder. This force can be harnessed for various purposes, such as in gas-powered engines or for storing compressed gases.

4. How does temperature affect pressure in a holder?

According to the Ideal Gas Law, temperature and pressure are directly proportional. This means that as the temperature of a gas in a holder increases, its pressure also increases. This is because the increase in temperature causes the gas molecules to move faster and collide with the walls of the holder more frequently, leading to a higher pressure.

5. Can the Ideal Gas Law be applied to all gases?

The Ideal Gas Law is an approximation that is most accurate for low pressures and high temperatures. At extreme conditions, such as very high pressures or very low temperatures, the behavior of gases may deviate from what is predicted by the Ideal Gas Law. In such cases, other equations, such as the Van der Waals equation, may be used to describe the behavior of gases more accurately.

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