Root Mean Square Speed

Q. The rms speed of oxygen molecules in a container is $V$. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed will become :

1. $V$
2. $\sqrt{2}V$
3. $2V$
4. $4V$

Q. The gas having average speed four times as that of $S{O}_2$ at same temperature is
(Molar mass of $S{O}_2=64g$)

1. $He$
2. $O_2$
3. $H_2$
4. $C{H}_4$

Q. The curve between $v_{rms}^2$ and pressure $P$ for constant volume is

1. 
2. 
3. 
4. 

Q.

Two containers are at the same temperature. The first contains a gas with pressure $P_1$, molecular mass $M_1$ and rms speed $v_{rms{}_1}$. The second contains gas with pressure $15P_1$, molecular mass $m_2$, and average speed $V_{avg2}=2.0v_{rms{}_1}$. What is the ratio $m_1:m_2$?

1. 

2. 

3. 

4. 

Q. Find the most probable speed $\left(V_{mp}\right)$ of nitrogen gas molecules at $T=560\text{K}$. (Given: Numerical value of $\sqrt{R}$ is $2.88$, where $R$ is gas constant)

1. $460\text{m/s}$
2. $500\text{m/s}$
3. $576\text{m/s}$
4. $600\text{m/s}$

Q.

The root mean square velocity of the molecules in a sample of helium is $\frac{5}{7}th$ that of the molecules in a sample of hydrogen. If the temperature of hydrogen sample is 0°C, then the temperature of the helium sample is about

1. 0°C

2. 0 K

3. 273°C

4. 100°C

Q. Average kinetic energy per mole and per molecule

Q. The rms speed of oxygen molecules in a container is $V$. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed will become :

1. $V$
2. $\sqrt{2}V$
3. $2V$
4. $4V$

Q. The mean square speed of molecules of a gas at absolute temperature T is proportional to

1. T
2. 1/T
3. T^2
4. None of these

Q. Given molecular weight of hydrogen molecule is $M=2.016\times {10}^{-3}\text{kg/mol}$. Calculate the root - mean-square speed of hydrogen molecules $\left(H_2\right)$ in km/s at $373.15K\left({100}^{\circ }C\right)$. (Answer to the nearest integer)

Q. A closed vessel contains a mixture of two diatomic gases $A$ and $B$. Molar mass of $A$ is 16 times that of $B$ and mass of gas $A$ contained in the vessel is 2 times that of $B$. Which of the following statements are correct?

1. Average kinetic energy per molecule of $A$ is equal to that of $B$.
2. Root-mean-square value of translational velocity of $B$ is four times that of $A$.
3. Pressure exerted by $B$ is eight times of that exerted by $A$.
4. Number of molecules of $B$, in the cylinder, is eight times that of $A$.

Q. At what temperature root mean square velocity of hydrogen becomes double of its value at $\text{S.T.P}$, keeping pressure constant?

1. ${273}^{\circ }\text{C}$
2. ${514}^{\circ }\text{C}$
3. ${819}^{\circ }\text{C}$
4. ${1012}^{\circ }\text{C}$

Q. Temperature at which rms speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at $-{20}^{\circ }\text{C}$ is
(Take molar mass of argon as $40\text{g}$ and for helium as $4\text{g}$)

1. $2530\text{K}$
2. $3000\text{K}$
3. $2000\text{K}$
4. $4000\text{K}$

Q. Which of the following gases has minimum $rms$ speed at a given temperature ?

1. Oxygen
2. Nitrogen
3. Hydrogen
4. Carbon dioxide.

Q. Find the temperature at which molecules of oxygen gas have the same rms speed as that of Helium atoms at $240\text{K}$.
$\{\text{Molecular mass of}{O}_2=32\text{g/mol}\&\text{He}=4\text{g/mol}\}$

1. $1920\text{K}$
2. ${2400}^{\circ }\text{C}$
3. $24\text{K}$
4. $758.95\text{K}$

Q. derive an equation for pressure for gas molecules.

Q.

Three closed vessels $A,B$ and $C$ are at the same temperature. Vessel $A$ contains only $O_2$ $B$ only $N_2$ and $C$ a mixture of equal quantities of $O_2$ and $N_2$. If the average speed of $O_2$ molecules in vessel $A$ is $v_1$, that of $O_2$ molecules is vessel C is

1. 

2. 

3. 

4. 

Q. The average translational kinetic energy and the root mean square speed of the molecules in a sample of oxygen gas at $300\text{K}$ are $6.21\times {10}^{-21}\text{J}$ and $484\text{m/s}$ respectively. The corresponding values at $600\text{K}$ are nearly (assuming ideal gas behaviour)

1. $2.42\times {10}^{-20}\text{J}$ and $968\text{m/s}$
2. $8.78\times {10}^{-20}\text{J}$ and $684\text{m/s}$
3. $6.21\times {10}^{-20}\text{J}$ and $968\text{m/s}$
4. $1.24\times {10}^{-20}\text{J}$ and $684\text{m/s}$

Q.

At what temperature would the root mean square speed of a gas molecule have twice its value at ${100}^{\circ }$C?

1. ${200}^{\circ }$C
   

2. ${273}^{\circ }$C
   

3. ${1219}^{\circ }$C
   

4. ${1492}^{\circ }$C

Q.

In a sample of an ideal gas the average momentum of a molecule depends on

1. pressure

2. mass of gas

3. number of moles

4. none of these

Q. A closed box contains an ideal gas. If temperature of gas increased then
$\left(A\right).$ Mean free path remain same.
$\left(B\right).$ Mean free path decreases.
$\left(C\right).$ Relaxation time decreases.
$\left(D\right).$ Relaxation time remain same.

Which of the following is correct?

1. $A\&C$
2. $B\&D$
3. $B\&C$
4. $A\&D$

Q. Suppose a container is evacuated to leave just one molecule of a gas in it. Let $v_{av}$ and $v_{rms}$ ​ represent the average speed and rms speed of the gas.

1. $v_{av}>v_{rms}$
2. $v_{av}<v_{rms}$
3. $v_{av}=v_{rms}$
4. $v_{rms}$ is undefined

Q. If at same pressure, the densities of two gases are ${\rho }_1$ and ${\rho }_2$ respectively, then the ratio of r.m.s. velocity of their molecules respectively are

1. ${\rho }_1:{\rho }_2$
2. $\sqrt{{\rho }_2}:\sqrt{{\rho }_1}$
3. ${\rho }_2:{\rho }_1$
4. $\sqrt{{\rho }_1}:\sqrt{{\rho }_2}$

Q. At what temperature root mean square velocity of hydrogen becomes double of its value at $\text{S.T.P}$, keeping pressure constant?

1. ${1012}^{\circ }\text{C}$
2. ${273}^{\circ }\text{C}$
3. ${514}^{\circ }\text{C}$
4. ${819}^{\circ }\text{C}$

Q. If nitrogen gas molecules goes straight up with its rms speed at $0^{\circ }\text{C}$ from the surface of the earth and there are no collision with other molecules, then it will rise to an approximate height of :
(Take $g=10m/s^2$)

1. $60\text{km}$
2. $40\text{km}$
3. $35\text{km}$
4. $12\text{km}$

Q. Suppose a container is evacuated to leave just one molecule of a gas in it. Let $v_{\alpha }$ and $v_{rms}$ represent the average speed and the rms speed of the gas.

1. $v_{\alpha }>v_{rms}$
2. $v_{\alpha }<v_{rms}$
3. $v_{\alpha }=v_{rms}$
4. $v_{rms}$ is undefined.

Q. A mixture of $1$ mole of nitrogen and $1$ mole of hydrogen is in a container at room temperature. The ratio of root mean square speed of hydrogen and nitrogen molecules is

1. $\sqrt{14}:1$
2. $\sqrt{28}:1$
3. $\sqrt{12}:1$
4. $\sqrt{15}:1$

Q. Figure shows a vessel partitioned by a fixed diathermic separation. Different ideal gases are filled in the two parts. The rms speed of the molecules in the left pat equals the mean speed of the molecules in the right part. Calculate the ratio of the mass of a molecule in the left part to the mass of a molecule in the right part.

1. $\frac{3\pi }{8}$
2. $\frac{5\pi }{8}$
3. $\frac{7\pi }{8}$
4. $\frac{9\pi }{8}$

Q. The rms speed of oxygen at room temperature is about $500\text{m/s}$. The rms speed of hydrogen at the same temperature is about

1. $125\text{m/s}$
2. $2000\text{m/s}$
3. $8000\text{m/s}$
4. $31\text{m/s}$

Q. 130.The mean square speed of gas molecules at absolute temperature T is equal to 1) 1/T 2) T 3) root T 4) T square