# Calculating the Mean Free Path of Argon Atom

• hhhmortal
In summary: However, in Q1 it is stated that the density of liquid argon is 1784kg/m^3, so it's not clear what they are looking for in Q1.In summary, Argon exists as a monatomic gas at room temperature and pressure. The density of liquid argon is 1784kg/m^3. The viscosity of argon gas at a temperature of 273K and a pressure of 1atm is equal to 2.1 x 10^5 Pa s. The mean speed of an argon atom at 273k, its effective radius and Avogadro's number is 87.3K approx.
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?

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

Cyosis said:
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.

What is the boiling point of argon?

Cyosis said:
What is the boiling point of argon?

87.3K approx, how does this help me?

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

## 1. What is the mean free path of an argon atom?

The mean free path of an argon atom is the average distance an individual argon atom travels in a gas before colliding with another atom or molecule. It is typically measured in nanometers (nm) or centimeters (cm).

## 2. How is the mean free path of an argon atom calculated?

The mean free path of an argon atom can be calculated by dividing the average speed of the atoms by the collision frequency. This can be further simplified by using the kinetic theory of gases, which takes into account the temperature, pressure, and density of the gas.

## 3. What factors affect the mean free path of an argon atom?

The mean free path of an argon atom is affected by the temperature, pressure, and density of the gas. It also depends on the size and shape of the container in which the gas is contained, as well as the concentration and size of other molecules or atoms in the gas.

## 4. Why is it important to calculate the mean free path of an argon atom?

Calculating the mean free path of an argon atom is important in understanding the behavior of gases, particularly in high pressure or low temperature environments. It is also useful in studying the properties of materials, such as thermal conductivity and electrical conductivity.

## 5. Can the mean free path of an argon atom be measured experimentally?

Yes, the mean free path of an argon atom can be measured experimentally using various techniques such as laser scattering, gas diffusion, and electrical conductivity measurements. These methods involve measuring the distance traveled by the atoms and the frequency of collisions in a controlled environment.

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