Kinetic Theory of Gases

Q.

In Vander Waal equation of state, the constant b is a measure of:

1. Intermolecular attractions

2. Intermolecular repulsions

3. Volume occupied by the molecules

4. Intermolecular collisions per unit volume

Q. Calculate the rms speed of $O_2$ at $273\text{K}$ and $1\times {10}^4\text{Pa}$ pressure. The density of $O_2$ under these conditions is $1.50{\text{kg m}}^{-3}$.

1. $2\times {10}^4{\text{m s}}^{-1}$
2. $5\times {10}^2{\text{m s}}^{-1}$
3. $141.42{\text{m s}}^{-1}$
4. $943.6{\text{m s}}^{-1}$

Q. The translational kinetic energy of an ideal gas depends only on its

1. Pressure

2. Force

3. Temperature

4. Molar mass

Q.

At constant volume, for a fixed number of moles of a gas, the pressure of the gas increases with increase in temperature due to

1. Increase in the average molecular speed

2. Increased rate of collision amongst molecules

3. Increase in molecular attraction

4. Decrease in mean free path

Q. Which of the following is incorrect statement for an ideal gas ?

1. When temperature increases at constant pressure, collision frequency increases
2. Mean free path decreases by increasing temperature at constant pressure
3. If all gas molecules are assumed to be rigid sphere of negligible volume, the only possible molecular motion is translation
4. Kinetic energy decreases by increasing pressure at constant temperature

Q.

Helium atom is two times heavier than a hydrogen molecule at 298 K, the average kinetic energy of helium is

1. Two times that of a hydrogen molecule

2. Same as that of a hydrogen molecule

3. Four times that of a hydrogen molecule

4. Half that of a hydrogen molecule

Q. On mixing, which of the following liquid mixture shows contraction in volume?

मिश्रित करने पर, निम्नलिखित में से कौनसा द्रव मिश्रण आयतन में संकुचन दर्शाता है?

1. Acetone + benzene
   
   एसीटोन + बेन्जीन
2. Acetone + carbon disulphide
   
   एसीटोन + कार्बन डाईसल्फाइड
3. Acetone + aniline
   
   एसीटोन + एनिलीन
4. Ethanol + water
   
   एथेनॉल + जल

Q.

As the temperature is raised from ${20}^{\circ }C$ to ${40}^{\circ }C$. The average kinetic energy of neon atoms changes by a factor of which of the following:

1. 313/293

2. 1/2

3. 2/1

4. 

Q. A mixture of gas at NTP for which =1.5 is suddenly compressed to 1/9th of its original volume. The final temperature of mixture is ?

Q. For the given isotherm for one mole of an ideal gas, which follows Boyle's law, what will be the value of temperature.

1. $8.2\text{K}$
2. $122\text{K}$
3. $947\text{K}$
4. $48\text{K}$

Q.

At constant volume, for a fixed number of moles of a gas, the pressure of the gas increases with increase in temperature due to

1. Increase in the average molecular speed

2. Increased rate of collision amongst molecules

3. Increase in molecular attraction

4. Decrease in mean free path

Q. The mean free path of the molecules of a certain gas at $300\text{K}$ is $2.6\times {10}^{-5}\text{m}$. The collision diameter of the molecule is $0.26\times {10}^{-9}\text{m}$. Calculate (a) the pressure of the gas and (b) the number per unit volume of the gas.

1. $5.306\times {10}^2\text{Pa}$ and $2.798\times {10}^{23}{\text{m}}^{-3}$
2. $5.306\times {10}^2\text{Pa}$ and $4.183\times {10}^{23}{\text{m}}^{-3}$
3. $10.6\times {10}^2\text{Pa}$ and $1.281\times {10}^{23}{\text{m}}^{-3}$
4. $5.306\times {10}^2\text{Pa}$ and $1.281\times {10}^{23}{\text{m}}^{-3}$

Q.

The temperature of the gas is raised from 27${}^{\circ }$ C to 927${}^{\circ }$ C, the root mean square velocity is

1. times the earlier value

2. Halved

3. Same as before

4. Doubled

Q. The kinetic energy of $N$ molecules of $O_2$ is $x$ joule at $-{123}^{\circ }\text{C}$. Another sample of $O_2$ at ${27}^{\circ }\text{C}$ has a kinetic energy of $2x$. The latter sample contains ____ molecules of $O_2$:

1. $N$
2. $\frac{N}{2}$
3. $2N$
4. $3N$

Q. Three gases $A,B$ and $C$ are at same temperature if their rms speed are in the ratio $1:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{3}}$ then their molar masses will be in the ratio:

1. $6:3:2$
2. $1:2:3$
3. $1:\sqrt{2}:\sqrt{3}$
4. $\sqrt{3}:\sqrt{2}:1$

Q. Which of the following exhibits the weakest inter-molecular forces?

1. $N{H}_3$
2. $HCl$
3. $He$
4. $H_{2}O$

Q. Three gases $A,B$ and $C$ are at same temperature if their rms speed are in the ratio $1:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{3}}$ then their molar masses will be in the ratio:

1. $6:3:2$
2. $1:2:3$
3. $1:\sqrt{2}:\sqrt{3}$
4. $\sqrt{3}:\sqrt{2}:1$

Q. The mean free path $\left(\lambda \right)$ of a gas sample is given by:

1. $\lambda =\sqrt{2\pi {\sigma }^2{N}^{\ast }}$
2. $\lambda =\frac{1}{\sqrt{2}.\pi {\sigma }^2{N}^{\ast }}$
3. $\lambda =\sqrt{2\pi u{\sigma }^2{N}^{\ast }}$
4. None of these

Q.

The kinetic theory of gases perdicts that total kinetic energy of a gaseous assembly depends on

1. Pressure of the gas

2. Temperature of the gas

3. Volume of the gas

4. Pressure, volume and temperature of the gas

Q. Which of the following gas molecule has the largest mean free path at the same pressure and temperature ?

1. $H_2$
2. $N_2$
3. $O_2$
4. $C{l}_2$

Q. As the temperature is raised from ${20}^o$ C to ${40}^o$ C the average kinetic energy of neon atoms changes by a factor of which of the following

1. 313/293
2. $\sqrt{\left(313/293\right)}$
3. 1/2
4. 2

Q. The kinetic energy of $N$ molecules of $O_2$ is $x$ joule at $-{123}^{\circ }\text{C}$. Another sample of $O_2$ at ${27}^{\circ }\text{C}$ has a kinetic energy of $2x$. The latter sample contains ____ molecules of $O_2$:

1. $N$
2. $\frac{N}{2}$
3. $2N$
4. $3N$

Q. The root mean square velocity of one mole of a monatomic gas having molar mass M is $u_{rms}$. The relation between the average kinetic energy $E$ per mole of the gas and $u_{rms}$ is.

1. $u_{rms}={\left(\frac{2E}{m}\right)}^{\frac{1}{2}}$
2. $u_{rms}={\left(\frac{3E}{2m}\right)}^{\frac{1}{2}}$
3. $u_{rms}={\left(\frac{E}{2m}\right)}^{\frac{1}{2}}$
4. $u_{rms}={\left(\frac{E}{3m}\right)}^{\frac{1}{2}}$

Q.

Which of the assumption of the kinetic - molecular theory best explains Daltons law of partial pressure?

1. Gas molecules move at random with no attractive forces between them.

2. The velocity of gas molecules is proportional to their kelvin temperature.

3. The amount of space occupied by a gas is much greater than the space occupied by the actual gas molecules.

4. Collisions with the walls of the container or with other molecules are elastic.

Q.

The kinetic energy of the emitted electrons is directly proportional to the frequency of incident radiation and is independent of incident radiation.

Q. If the temperature of 1 mole of an ideal gas is increased by ${50}^{\circ }\text{C}$, calculate the change in the kinetic energy of the system.

1. $62.32\text{J}$
2. $6.235\text{J}$
3. $623.5\text{J}$
4. $6235.0\text{J}$

Q. Calculate the kinetic energy (in joule) for $8.00\text{g}$ of methane at ${27}^{\circ }\text{C}$.

Q. A gas at a pressure of 5.0 bar is heated from $0^{\circ }\text{C}$ to ${546}^{\circ }\text{C}$ and simultaneously compressed to one-thirds of its original volume. Hence, the final pressure is:

1. 45.0 bar
2. 15.0 bar
3. 30.0 bar
4. 5/9 bar

Q.

According to the kinetic theory of gases, in an ideal gas between two successive collisions, a gas molecule travels.....

1. In a circular path.

2. In a wavy path.

3. ​In a straight line path.

4. With an accelerated velocity.

Q.

The kinetic energy of ${}^{\prime }{N}^{\prime }$ molecules of $H_2$ is $3J$ at $-{73}^{\circ }C$. The kinetic energy of the same sample of $H_2$ at $-{127}^{\circ }C$ is ___.

1. $12J$

2. $2.19J$

3. $9J$

4. $3J$