Mean Free Path & Real Gases

The mean free path of molecules in an ideal gas $A$ is half that of another ideal gas $B$. The diameter of the spherical molecules of gas $A$ is twice the diameter of the molecules of $B$. If number densities of the gases $A$ and $B$ are $n_A$ and $n_B$, respectively, the correct option is:

The mean free path of a molecule of diameter $5 \times 10^{-10}$ m at the temperature $41^\circ$ C and pressure $1.38 \times 10^{5}$ Pa, is given as ________ m. (Given $k_B = 1.38 \times 10^{-23}$ J/K).

Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures and number densities are same. The molecular size of $A$ is half of that of $B$ and mass of molecule $A$ is four times that of $B$. If the collision frequency in gas $B$ is $32 \times 10^{18}\text{/s}$ then collision frequency in gas $A$ is ______ /s.

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7}\text{ m}$ and $600\text{ m/s}$, respectively. Find the frequency of its collisions.

Given below are two statements:

Statement (I): The mean free path of gas molecules is inversely proportional to square of molecular diameter.

Statement (II): Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.

In the light of the above statements, choose the correct answer from the options given below:

If $n$ is the number density and $d$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by:

A real gas behaves as an ideal gas at

At S.T.P., the mean free path of gas molecule is 1500 d, where ' $d$ ' is diameter of molecule. What will be the mean free path at 373 K at constant volume?

If the collision frequency of hydrogen molecules in a closed chamber at $27^\circ\text{C}$ is $Z$, then the collision frequency of the same system at $127^\circ\text{C}$ is:

According to kinetic theory of gases, which one of the following statements is wrong?

The mean free path of molecules of a certain gas at STP is $1500\text{ d}$, where $d$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $373\text{ K}$ is approximately:

The number of air molecules per cm$^{3}$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is:

According to kinetic theory of gases,

A. The motion of the gas molecules freezes at 0$^\circ$C.

B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.

D. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2} k_B T$ (for monoatomic gases). Choose the most appropriate answer from the options given below:

Calculate the value of mean free path ($\lambda$) for oxygen molecules at temperature 27$^\circ$ C and pressure 1.01 $\times$ 105 Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 $\times$ 10$-$23 JK${}^{-1}$)

A system consists of two types of gas molecules A and B having same number density 2 $\times$ 1025/m3. The diameter of A and B are 10 $\mathring{\text{A}}$ and 5 $\mathring{\text{A}}$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ____________ $\times$ 10$-$2

The mean free path $\ell$ for a gas molecule depends upon diameter, $d$ of the molecule as

The mean free path for a gas, with molecular diameter d and number density n can be expressed as:

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as:

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true?

(A) the mean free path of the molecules decreases.

(B) the mean collision time between the molecules decreases.

(C) the mean free path remains unchanged.

(D) the mean collision time remains unchanged.

The plot that depicts the behavior of the mean free time t (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to:

A 25 × 10–3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300K). The molecular diameter of O2, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule?

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 $\times$ 10–8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

The mean free path of molecules of a gas, (radius r) is inversely proportional to

The value of critical temperature in terms of van der Waals' constant $a$ and $b$ is given by

At constant volume temperature is increased then