Practice free NEET NEET multiple-choice questions online with instant answers and detailed explanations. No login required.
At a given temperature the rms velocity of molecules of the gas is
$ \nu _{rms } = \sqrt {3RT \over M_o } \Rightarrow \nu _{rms} \alpha { 1 \over \sqrt {M_o} } $
According to the kinetic theroy of gases the r.m.s velocity of gas molecules is directly proportional to
$ \nu_{rms } \alpha \sqrt T $
The speeds of 5 molecules of a gas (in arbitrary units) are as follows: 2, 3, 4, 5, 6, The root mean square speed for these molecules is
$ \nu_{rms} = \sqrt { \nu_1^2 + \nu_2^2 + \nu_3^2 + \nu_4^2 + \nu_5^2 \over 5 } = 4.24 $
To what temperature should the hydrogen at room temperature ($ 27 ^\circ C$ ) be heated at constant pressure so that the rms velocity of its molecule becomes double of its previous value
$ \nu_{rms } \alpha \sqrt T \Rightarrow { (\nu_{rms})_2 \over (\nu_{rms})_1} = \sqrt {T_2 \over T_1} $
Root mean square velocity of a molecule is $ \nu $ at pressure P. If pressure is increased two times, then the rms velocity becomes
rms velocity does not depend on pressure.
The rms speed of gas molecules is given by
$ \nu _{rms } = \sqrt { 3RT \over M_o} = \sqrt {3} \sqrt { RT \over M_o } = 1.73 \sqrt { RT \over M_o} $
A sample of gas is at $ 0 ^\circ C$ . To what temperature it must be raised in order to double the rms speed of molecule.
$ \nu_{rms} \alpha \sqrt T $ To double the rms speed temperature should be made four times i.e. $ \therefore T_2 = 4 T_1 $
If the ratio of vapour density for hydrogen and oxygen is 1/ 16 , then under constant pressure the ratio of their rms velocities will be
$ \nu _ {rms} =\sqrt { 3P \over \rho } \Rightarrow { \nu_1 \over \nu_2 } = \sqrt { \rho_2 \over \rho_1} = \sqrt { 16 \over 1} = 4:1 $
The molecules of a given mass of a gas have a rms velocity of 200 m /s at $ 27 ^\circ C$ and $ 1.0 \times 10^5 Nm^{-2} $ pressure when the temperature is $ 127 ^\circ C$ and pressure is $ 0.5 \times 10^5 Nm^{-2} $ , the rms velocity in m s will be
rms velocity doesn't depend on pressure, it depends upon temperature only $ \nu_{rms} = \sqrt { 3RT \over Mo } \Rightarrow \nu_{rms} \alpha \sqrt T $ $ \therefore T \alpha \nu_{rms}^2 \Rightarrow { \nu_1 \over \nu_2 } = \sqrt { T_1 \over T_2 } $
If the molecular weight of two gases are $ M_1$ and $M_2$ , then at a given temperature the ratio of root mean square velocity $ \nu _1 $ and $ \nu _2 $ will be
$ \nu_{rms} = \sqrt { 3RT \over Mo } \Rightarrow \nu_1 \alpha \sqrt { 1 \over M_1 } and \nu_2 \alpha \sqrt { 1 \over M_2} \Rightarrow { \nu_1 \over \nu_2 } = \sqrt { M_2 \over M_1 } $
Ready to ace NEET?
Free access · No credit card required
Yes. You can attempt every NEET question on this page for free without logging in, and check the correct answer with a detailed explanation instantly.
No account is required to attempt questions and view answers. A free account adds bookmarks, personal notes, and progress tracking.
The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.