Kinetic Theory of Gases

Q. What is the total translational and rotational energy of 1 mole of oxygen at $300\text{K}$ ?
$R=8.314{\text{J mol}}^{-1}{\text{K}}^{-1}$

1. $623.25\text{J}$
2. $62.325\text{J}$
3. $6.2325\text{J}$
4. $6235.5\text{J}$

Q.

What are the five basic ideas of kinetic molecular theory?

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

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

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 pressure needed to confine 1.5 mol of $N_2$ molecules to 28 L flask is 1.0 bar. Thus, root mean square velocity of the gas (assuming ideal behaviour) is

1. $370{\text{m s}}^{-1}$
2. $200{\text{m s}}^{-1}$
3. $51.5{\text{m s}}^{-1}$
4. $37.0{\text{m s}}^{-1}$

Q.

The average distance travelled by the molecule between successive collision is called _____.

1. Collision path

2. Mean free path

3. Collision diameter

4. Collision distance

Q. The vapour pressures of pure liquids A and B are 400 and 600 mm Hg, respectively at 298 K. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid B is 0.5 in the mixture. The vapour pressure of the final solution, the mole fractions of components A and B in vapour phase, respectively are:

1. 500 mm Hg, 0.5, 0.5
2. 450 mmHg, 0.5, 0.5
3. 450 mmHg, 0.4, 0.6
4. 500 mmHg, 0.4, 0.6

Q. Which of the following properties of liquids arise because of the molecular interaction and thermal energy?
I. Vapour pressure
II. Surface tension
III. Viscosity

1. I and II
2. I and III
3. II and III
4. I, II and III

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. What is the sum of translational and rotational energy of 1 mole of oxygen at $300\text{K}$ ?
$R=8.314{\text{J mol}}^{-1}{\text{K}}^{-1}$

1. $6235.5\text{J}$
2. $623.25\text{J}$
3. $62.325\text{J}$
4. $6.2325\text{J}$

Q.

The piston shown in the figure is moved downwards such that the vapour volume is decreased by 246.3cc. How many grams of $H_{2}O$ is condensed? (Assume aqueous tension at 27${}^{\circ }$C is 360 mm Hg)

1. 1.8 gm

2. 0.09 gm

3. 0.9 gm

4. 0.18 gm

Q. The compressiblity factor for an ideal gas is

1. 1.5
2. 1
3. 2
4. $\infty$

Q. If the vapour behaves ideally at 1000 K, determine the average translational kinetic energy of a molecule.

1. $1.07\times {10}^{-21}\text{J}$
2. $1.07\times {10}^{-20}\text{J}$
3. $2.07\times {10}^{-21}\text{J}$
4. $2.07\times {10}^{-20}\text{J}$

Q. Calculate the average kinetic energy in joule per molecule in 8.0 g of methane at ${27}^{\circ }\text{C}$

1. $6.21\times {10}^{-19}$
2. $6.023\times {10}^{-21}$
3. $6.21\times {10}^{-21}$
4. $6.21\times {10}^{-23}$

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. Which of the following is true about gaseous state

1. Thermal energy = Molecular attraction
2. Thermal energy >> Molecular attraction
3. Thermal energy << Molecular attraction
4. Molecular forces >> Those in liquids

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.

According to kinetic theory of gases:

1. There are intermolecular attractions

2. Molecules have considerable volume

3. There is no intermolecular attraction

4. Energy is lost during molecular collisions

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. The vapour pressures of pure liquids A and B are 400 and 600 mm Hg, respectively at 298 K. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid B is 0.5 in the mixture. The vapour pressure of the final solution, the mole fractions of components A and B in vapour phase, respectively are:

1. 450 mmHg, 0.5, 0.5
2. 500 mmHg, 0.4, 0.6
3. 450 mmHg, 0.4, 0.6
4. 500 mm Hg, 0.5, 0.5

Q. A jar contains a gas and a few drops of water at $T\text{K}$. The pressure in the jar is $830\text{mm}$ of $Hg$. The temperature of the jar is reduced by $1\%$. The vapour pressure of water at two temperatures are 30 and $25\text{mm}$ of $Hg$. Calculate the new pressure in the jar.

1. 817
2. 971
3. 771
4. 671

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.

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 valid at absolute zero

1. Kinetic energy of the gas becomes zero but the molecular motion does not become zero

2. Kinetic energy of the gas becomes zero and molecular motion also becomes zero

3. Kinetic energy of the gas decreases but does not become zero

4. None of the above

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.

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. $2$

2. $\sqrt{\frac{313}{293}}$

3. $\frac{313}{293}$

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

Q. The average kinetic energy (in joules) of molecules in $8.0\text{g}$ of methane at ${27}^{\circ }\text{C}$ is:

1. $6.21\times {10}^{-20}\text{J/molecule}$
2. $6.21\times {10}^{-21}\text{J/molecule}$
3. $6.21\times {10}^{-22}\text{J/molecule}$
4. $3.1\times {10}^{-22}\text{J/molecule}$

Q.

Anil weighed three packages on a scale. Individually, they weigh 4.2 kg, 2370 g, and 0.45 kg. Is the total weight of the packages more than or less than 7 kg?

Q. Calculate the average kinetic energy in joule per molecule in 8.0 g of methane at ${27}^{\circ }\text{C}$

1. $6.21\times {10}^{-19}$
2. $6.023\times {10}^{-21}$
3. $6.21\times {10}^{-21}$
4. $6.21\times {10}^{-23}$

Q.

If the value of Avogadro number is 6.023 $\times {10}^{23}mo{l}^{-1}$ and the value of Boltzmann constant is 1.380 $\times {10}^{-23}J{K}^{-1},$ then the number of significant digits in the calculated value of the universal gas constant is ___