What is the Ideal Gas Equation for Calculating Gas Properties?

[max0005]

Homework Statement

Considering a container of 3*10^-2m³ filled with an unknown gas such that the pression is 15MPA (or 1.5*10⁷Pa) and the temperature is 25°C.

Determine the volume occupied by one atom of the gas and determine the average distance between its particles.

Homework Equations

PV = nRT

P = Pressure
V = Volume
n = Number of Moles
R = Constant 8.31
T = Temperature

The Attempt at a Solution

Considering that

$$n=\frac{PV}{RT}$$

$$n=\frac{1.5*10^7*3.2*10^(-2)}{8.31*25}$$

Which returns 2310moles, which is about 1.5*10²⁷ atoms.

However, from here on I'm lost... What should I do? :(

 

[Borek]

I guess you are expected to divide volume by number of atoms/molecules. Assuming each one is in the center of its own cube, calculating distance is just a simple geometry.

But number of moles I got is about 10 times lower.

 

[cupid.callin]

well, the way question is presented, answer should be like this:

volume of 1.5*10^27 atoms = 3*10^-2
so volume of 1 atom = ?

But this will give wrong answer, for this you need to use van der waal eqn

 

[max0005]

Dear Borek,

I understand what you mean, thanks! :)

Just a question, it's probably pathetically stupid but... Doesn't the volume of an atom remain constant?

From your reasoning if I understand correctly the actual volume of the atom would be negligible correct? But why are you speaking of "cube"? Wouldn't it be more correct to speak of sphere? In such case shouldn't I consider the radius?

 

[max0005]

But this will give wrong answer, for this you need to use van der waal eqn

Which is? :)

 

[Borek]

Just a question, it's probably pathetically stupid but... Doesn't the volume of an atom remain constant?

Yes it does. IMHO question is badly worded, it doesn't ask for a volume of an atom but for a volume it is allowed to occupy. Doesn't mean it occupies it all.

From your reasoning if I understand correctly the actual volume of the atom would be negligible correct? But why are you speaking of "cube"? Wouldn't it be more correct to speak of sphere? In such case shouldn't I consider the radius?

Using spheres you can't fill space. How would you account for holes between spheres?

Not that the estimate would be seriously different.

 

[max0005]

So if I understood correctly I should divide the total volume of the box by the number of atoms which I obtain multiplying the number of moles by Avogadro's Number, correct? That should give me the space each atom is allowed to fill.

My guess for a sphere was due to the fact that it is the only 3D shape which would allow a uniform field distribution... I guess you're right in speaking about cubes, but then how do I calculate the distance between one and the other? Just calculating the side of a cube with volume 1/Number of atoms? So the actual distance between one and the other would be [STRIKE]half[/STRIKE]the cubic root of 1/Number of atoms?

(Edit: Took "half" out.)

 

[Borek]

the cubic root of 1/Number of atoms?

Yes. Very reasonable estimate.

 

[cupid.callin]

Which is? :)

Check this: http://en.wikipedia.org/wiki/Van_der_Waals_equation#Equation"

look at the equation given below, here nb is the excluded volume where b is volume of 1 atom!

 

[SammyS]

...

The Attempt at a Solution

Considering that

$$n=\frac{PV}{RT}$$

$$n=\frac{1.5*10^7*3.2*10^(-2)}{8.31*25}$$

Which returns 2310moles, which is about 1.5*10²⁷ atoms.

However, from here on I'm lost... What should I do? :(

Hi max0005.

What is 25°C in Kelvins?

 

[Borek]

Check this: http://en.wikipedia.org/wiki/Van_der_Waals_equation#Equation"

look at the equation given below, here nb is the excluded volume where b is volume of 1 atom!

Show how you are going to use the information given to solve the question using WdV equation, or admit it is completely useless in this case as there is not enough data.

 

[cupid.callin]

I never said that we can use the eqn but i said that Vander Waal's Eqn will be a proper way to find out the size of atom!
And the only way the question can be answered is completely useless!