Advertisements
Advertisements
Question
Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1 A and 2 A. The gases may be considered under identical conditions of temperature, pressure and volume.
Solution
Mean free path of a molecule is given by `l = 1/(sqrt(2)d^2n)`
Where n = number of molecules/volume
d = diameter of the molecule
Now, we can write `l ∝ 1/d^2`
Given, `d_1 = 1Å, d_2 = 2Å`
As `l_1 ∝ 1/d_1^2` and `l_2 ∝ 1/d_2^2`
⇒ So, `l_1/l_2 = (d_2/d_1)^2 = (2/1)^2 = 4/1`
Hence, `l_1 : l_2` = 4 : 1
APPEARS IN
RELATED QUESTIONS
Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17 °C. Take the radius of a nitrogen molecule to be roughly 1.0 Å. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of N2 = 28.0 u).
Choose the correct option.
The mean free path λ of molecules is given by where n is the number of molecules per unit volume and d is the diameter of the molecules.
If the temperature and pressure of a gas is doubled the mean free path of the gas molecules ____________.
Define mean free path and write down its expression.
List the factors affecting the mean free path.
What is the reason for the Brownian motion?
Derive the expression for the mean free path of the gas.
Consider an ideal gas at pressure P, volume V and temperature T. The mean free path for molecules of the gas is L. If the radius of gas molecules, as well as pressure, volume and temperature of the gas are doubled, then the mean free path will be:
Mean free path of molecules of a gas is inversely proportional to ______.
Ten small planes are flying at a speed of 150 km/h in total darkness in an air space that is 20 × 20 × 1.5 km3 in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a saftey region around the plane can be approximated by a sphere of radius 10 m.
