Calculating the Mean Free Path of Argon Atom

[hhhmortal]

Homework Statement

Hi, I am not sure about the following question:

(Q) Argon (atomic weight 40) exists as a monatomic gas at room temperature and pressure. The density of liquid argon is 1784kg/m^3.

(a) Calculate the atomic density (atoms/m^3) in liquid argon *Done*

(b) Hence assumming the packing fraction in liquid argon is 0.7, determine the radius of an argon atom. *Done*

(c) calculate the atomic density in gaseous argon at a pressure of 1atm and a temperature of 300K *Done*

(d) hence calculate the mean free path of an argon atom at a pressure of 1 atm and a temperature of 300K?

Homework Equations

It is part (d) which I'm having trouble with

The mean free path formula is 1/[(4pi)nσ²]

The Attempt at a Solution

For part (d) which 'n' should I use the one for gas argon or for liquid argon, the question given doesn't seem to state which mean free path to calculate?

 

[Cyosis]

The 'hence' suggests they want you to calculate it for gaseous argon.

 

[hhhmortal]

The 'hence' suggests they want you to calculate it for gaseous argon.

Oh Hi! right! I actually forgot the next question which was:

(e) Calculate the root mean square of an argon atom at a temperature of 300K.

Again do you calculate it for gaseous or liquid argon? and why would they put both types of argon in the same question, its confusing..and they don't really ask any questions about comparing both types at the end.

I also found another question very similar to the above but how do I tackle this one?

(Q2.) The viscosity of argon gas (atomic weight 40) at a temperature of 273K and a pressure of 1atm is equal to 2.1 x 10^5 Pa s. The density of liquid argon is 1784kg/m^3 . Use these two pieces of data to determine the mean speed of an argon atom at 273k, its effective radius and Avogadro's number.

 

[Cyosis]

What is the boiling point of argon?

 

[hhhmortal]

What is the boiling point of argon?

87.3K approx, how does this help me?

 

[Cyosis]

Seeing as the temperature of argon in question e) is 300K it would stand to reason that they are interested in gaseous argon.