Mean Free Path, Collision Frequency

Q. The curve shows Maxwell’s distribution of velocities with increase of temperature.

Statement 1: Most probable velocity increases
Statement 2: Fraction of molecules possessing most probable velocity decreases with increasing T

1. Statement 1 correct, Statement 2 incorrect
2. Statement 1 and Statement 2 both are correct
3. Statement 1 and Statement 2 are incorrect
4. Statement 1 incorrect, Statement 2 correct
   

Q. 54. 2A+B====Product (elementary reaction) If its pressure increases 3 times its initial pressure then its velocity will become how many of its previous velocity A)9 times B)27 times C)1/9 times D)1/27 times

Q. If $X$ is the total number of collision which a gas molecule registers with other molecules per unit time under particular conditions, then the collision frequency of the gas containing $N$ molecules per unit volume is:

1. $X/N$
2. $NX$
3. $2NX$
4. $NX/2$

Q. Define mean free path.

Q. Assertion :Mean free path of a gas molecules varies inversely as density of the gas. Reason: Mean free path varies inversely as pressure of the gas.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Which relation is not true about the mean free path of a gas?

1. It is directly proportional to the temperature at a given density of the gas
2. It is inversely proportional to the pressure at a given temperature for a fixed amount of a gas
3. It is directly proportional to the volume of a fixed amount of a gas
4. It is constant for an ideal gas if the number of gas molecules per litre of volume is fixed

Q.

The mean free path is ________.

Q. Assertion :Mean free path of a gas molecules varies inversely as density of the gas Reason: Mean free path varies inversely as pressure of the gas

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect and Reason is correct

Q. The mean free path of a molecule of He gas is a its mean free path along any arbitary coordinate axis will be.

Q. A gas has an average speed of $10m/s$ and a collision frequency of $10$ $s^{-1}$. What is its mean free path?

1. $2m$
2. $0.1m$
3. $3m$
4. $1m$

Q. Under the same conditions of temperature and pressure, the ratio of times of diffusion of two gases $A$ and $B$ is $4:1$. So the ratio of the molecular weights of the gases $A$ and $B$ is:

1. $16:1$
2. $4:1$
3. $1:4$
4. $1:16$

Q. Assertion : HCl diffuses faster than ammonia.
Reason : Rate of diffusion of a gas is inversely proportional to the square root of its density.

1. Both assertion and reason are correct and reason is the correct explanation of the assertion.
2. Both assertion and reason are correct, but reason is not the correct explanation of the assertion.
3. Assertion is correct, but reason is incorrect.
4. Both assertion and reason are incorrect.
5. Assertion is incorrect, but reason is correct.

Q. Estimate the number of collision per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) $=1.38\times {10}^{-5}cm$.

Q. Which of the following gases will have the lowest rate of diffusion?

1. $O_2$
2. $H_2$
3. $N_2$
4. $F_2$

Q. Which relation is not true about the mean free path of a gas?

1. It is constant for an ideal gas if the number of gas molecules per litre of volume is fixed
2. It is inversely proportional to the pressure at a given temperature for a fixed amount of a gas
3. It is directly proportional to the volume of a fixed amount of a gas
4. It is directly proportional to the temperature at a given density of the gas

Q. The rate of diffusion of $S{O}_2,C{O}_2,PC{l}_3$ and $S{O}_3$ are in the following order

1. $PC{l}_3>S{O}_3>S{O}_2>C{O}_2$
2. $C{O}_2>S{O}_2>PC{l}_3>S{O}_3$
3. $S{O}_2>S{O}_3>PC{l}_3>C{O}_2$
4. $C{O}_2>S{O}_2>S{O}_3>PC{l}_3$

Q. All gases at the same $P$ and $T$ diffuses at the same rate.

1. True
2. False

Q. The mean free path and rms velocity of a nitrogen molecule at a temperature 17C are $1.2\times {10}^{-7}$ m and $5\times {10}^2$ m/s respectively.The time between two successive collisions

1. $2.4\times {10}^{-10}$ S
2. $1.2\times {10}^{-10}$ S
3. $3.4\times {10}^{-13}$ S
4. $3.4\times {10}^{-10}$ S

Q. Calculate the means free path of nitrogen molecule at ${27}^o$C when pressure is $1.0$ atm. Given, diameter of nitrogen molecule $=1.5\stackrel{o}{A}$, $k_B=1.38\times {10}^{-23}$J $K^{-1}$. If the average speed of nitrogen molecule is $675$ $m{s}^{-1}$. The time taken by the molecule between two successive collisions is?

1. $0.6$ns
2. $0.4$ns
3. $0.3$ns
4. $0.8$ns

Q. In physics, the mean free path is the average distance traveled by a moving particle (such as an atom , a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties. In which of the following mean free path is used ?

1. to estimate the resistivity of a material
2. All of the above
3. to design a chemical apparatus
4. It can be used in optics and in acoustics

Q.

Mean free path does not depend on

1. $\rho$
2. T
3. b
4. d

Q. $N{H}_3$ & $S{O}_2$ gases are being prepared in two corners of a laboratory. The gas that will be detected first in the middle of the laboratory is

1. $N{H}_3$
2. $S{O}_2$
3. both at the same time
4. can't determine

Q. If the pressure of a gas is increased then its mean free path becomes :

1. zero
2. less
3. more
4. $\infty$

Q. The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases $x$ times. The value of $x$ is:___

Q. The relative rate of diffusion of gas (Molecular weight = 128) as compared to oxygen is:

1. $1/2$
2. $\frac{1}{2\times \sqrt{2}}$
3. $2$ times
4. $2\times \sqrt{2}$ times

Q. If $\overline{v},v_{rms}$ and $v_p$ represent the mean speed, root mean square and most probable speed of the molecules in an ideal monoatomic gas at temperature $T$ and if $m$ is mass of the molecule, then

1. $v_p<\overline{v}<v_{rms}$
2. No molecule can have a speed less than $v_p/\sqrt{2}$
3. None of the above
4. No molecule can have a speed greater than $\sqrt{2v_{rms}}$

Q. Show that the mean free path for the molecules of an ideal gas at temperature $T$ and pressure $P$ is $\lambda =\frac{k_{B}T}{\sqrt{2}\pi d^{2}P}$ where $d$ is the molecular diameter .

Q. A gas has a density of $10$ particles$/m^3$ and a molecular diameter of $0.1$m. What is its mean free path?

1. $2.25m$
2. $1m$
   
3. $3m$
   
4. $0.25m$
   

Q. A container is divided into two equal parts I and II by a partition with a small hole of diameter d. The two partitions are filled with same ideal gas, but held at temperatures $T_I=150$K and $T_{II}=300$K by connecting to heat reservoirs. Let ${\lambda }_I$ and ${\lambda }_{II}$ be the mean free paths of the gas particles in the two parts such that $d>>{\lambda }_I$ and $d>>{\lambda }_{II}$. Then ${\lambda }_I/{\lambda }_{II}$ is close to.

1. $0.25$
2. $0.5$
3. $0.7$
4. $1.0$

Q. Which of the gases diffused faster among $N_2,O_2,C{H}_4$. Why?