Root Mean Square Velocity

Q. Which of the following options is/are correct with respect to $C{H}_4$ and $S{O}_2$? (Equal mass of $C{H}_4$ and $S{O}_2$ are contained in a 2 L container at same temperature)

1. $C{H}_4$ will diffuse 4 times faster than $S{O}_2$
2. Average speed of $C{H}_4$ is 2 times that of $S{O}_2$
3. Both have the same average kinetic energy per mol
4. $C{H}_4$ has double the partial pressure of $S{O}_2$

Q. The root mean square speed of molecules of nitrogen gas is $v$ at a certain temperature. When the temperature is doubled, the molecules dissociate into individual atoms. The new rms speed of the atom is:

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

Q. At $298\text{K}$, which of the following gases has the lowest average molecular speed ?

1. $C{H}_4$ at $0.80\text{atm}$
2. $He$ at $0.40\text{atm}$
3. $C{O}_2$ at $0.20\text{atm}$
4. $NO$ at $1.00\text{atm}$

Q. For $C{O}_2$, given that average velocity at $T_1$ is equal to most probable velocity at $T_2$. Thus, $\frac{T_1}{T_2}$

1. 2.26
2. 1.27
3. 0.78
4. 1.13

Q. The root mean square speed of $8g$ of $He$ is $300{\text{ms}}^{-1}$. Total kinetic energy of $He$ gas is:

1. $120J$
2. $240J$
3. $360J$
4. None of these

Q.

The R.M.S. velocity of hydrogen is $\sqrt{7}$ times the R.M.S. velocity of Nitrogen. If T is the temperature of the Gas, then

1. 

2. 

3. 

4. 

Q. The mass of molecule $A$ is twice that of molecule $B$. The root mean square velocity of molecule $A$ is twice that of molecule $B$. If two containers of equal volume have same number of molecules, the ratio of pressure $\frac{P_A}{P_B}$ will be:

1. 8 : 1
2. 1 : 8
3. 4 : 1
4. 1 : 4

Q.

The R.M.S. velocity of hydrogen is $\sqrt{7}$ times the R.M.S. velocity of Nitrogen. If T is the temperature of the Gas, then

1. $T_{H_2}=T_{N_2}$

2. $T_{H_2}>T_{N_2}$

3. $T_{H_2}<T_{N_2}$

4. $T_{H_2}=\sqrt{7}\times T_{N_2}$

Q.

The R.M.S. velocity of hydrogen is $\sqrt{7}$ times the R.M.S. velocity of Nitrogen. If T is the temperature of the Gas, then

1. $T_{H_2}=T_{N_2}$

2. $T_{H_2}>T_{N_2}$

3. $T_{H_2}<T_{N_2}$

4. $T_{H_2}=\sqrt{7}\times T_{N_2}$

Q. The ratio of the root mean square speed of $H_2$ gas at $50\text{K}$ and that of $O_2$ gas at $800\text{K}$ is:

1. 4
2. 2
3. 1
4. 0.25

Q. For gaseous state, if most probable speed is denoted by C*, average speed by $\overrightarrow{C}$ and root mean square speed by C, then for a large number of molecules, the ratios of these speeds are

1. C* : $\overline{C}$ : C = 1.225 : 1.128 : 1
2. C* : $\overline{C}$ : C = 1.128 : 1.225 : 1
3. C* : $\overline{C}$ : C = 1 : 1.128 : 1.225
4. C* : $\overline{C}$ : C = 1 : 1.225 : 1.128

Q. Let, the average molar mass of air is $24.9g$. An open vessel at $27{}^{o}C$ is heated upto $t{}^{o}C$ until $1/3^{rd}$ of the air measured at final temperature excapes out. The rms velocity of air molecules at $t{}^{o}C$ is: (Take $R=8.3J{K}^{-1}mo{l}^{-1}$)

1. $340.12mse{c}^{-1}$
2. $420.35mse{c}^{-1}$
3. $515.25mse{c}^{-1}$
4. $632.45mse{c}^{-1}$