Molecular Speeds & Maxwell Distribution

If '$m$' represents the mass of each molecule of a gas and '$T$' its absolute temperature respectively, then the root mean square velocity of the gaseous molecule is proportional to

Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is

When the r.m.s. velocity of a gas is denoted by '$v$' at temperature '$T$'. Out of the following relations, the true one is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: If the average kinetic energy of $\text{H}_2$ and $\text{O}_2$ molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R: The r.m.s speed of $\text{H}_2$ and $\text{O}_2$ molecules are same at same temperature. Choose the correct answer from the options given below

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^\circ$ C is (molecular weight of hydrogen and oxygen are 2 and 32 respectively)

The speeds of the seven molecules are 1, 3, 5, 7, 2, 4 and 6 km/s respectively. The ratio of their r.m.s. velocity and average velocity will be

A flask contains argon and chlorine in the ratio of $2 : 1$ by mass. The temperature of the mixture is $27^\circ\text{C}$. The ratio of root mean square speed of the molecules of the two gases $\left(\frac{V_{\text{rms}}^{\text{Ar}}}{V_{\text{rms}}^{\text{Cl}}}\right)$ is: (Atomic mass of argon $= 40.0\text{ u}$ and molecular mass of chlorine $= 70.0\text{ u}$)

The r.m.s. speed of oxygen molecules at 47 °C is equal to that of the hydrogen molecules kept at _________ °C. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)

The average transnational kinetic energy of a molecule in a gas is $E_1$. The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is $E_2$. The temperature at which $E_1 = E_2$ possible is (mass of molecule and electron is same) (N = number of molecules, V = Velocity, R = gas constant)

The temperature of an ideal gas is increased from 100 K to 400 K. If ' $x$ ' is the root mean square velocity of its molecules at 100 K, r.m.s. velocity becomes

According to the kinetic theory of gases, when two molecules of a gas collide with each other then

Six molecules of a gas in container have speeds $2\text{ m/s}, 5\text{ m/s}, 3\text{ m/s}, 6\text{ m/s}, 3\text{ m/s}$, and $5\text{ m/s}$. The r.m.s. speed is

For a gas at a particular temperature on an average, the quantity which remains same for all molecules is

The r.m.s. speed of gas molecules at 800 K will be

The temperature of an ideal gas is increased from 100 K to 400 K. If ' $x$ ' is the R.M.S. velocity of its molecules at 100 K, it becomes

The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$, then the ratio of r.m.s. velocities will be:

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at $57^\circ\text{C}$ is (molecular masses of oxygen and helium are 32 and 4 respectively.)

Select the correct statement.

If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at $47^\circ\text{C}$, the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)

Consider the sound wave travelling in ideal gases of $\text{He, CH}_4$, and $\text{CO}_2$. All the gases have the same ratio $\frac{P}{\rho}$, where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $V_{\text{He}} : V_{\text{CH}_4} : V_{\text{CO}_2}$ is given by

Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is

The absolute temperature of a gas is determined by

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2\text{ km/s}$, the root mean square velocity of oxygen at the same condition in $\text{km/s}$ is:

The parameter that remains the same for molecules of all gases at a given temperature is:

At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^\circ\text{C}$?

' $N$ ' molecules of gas $A$, each having mass ' $m$ ' and ' 2 N ' molecules of gas B, each of mass ' 2 m ' are contained in the same vessel which is at constant temperature ' T '. The mean square velocity of $B$ is $V^{2}$ and mean square of x -component of A is $\omega^{2}$. The value of $\frac{\omega^{2}}{V^{2}}$ is

The ratio of the velocity of sound in hydrogen gas $\left(\gamma = \frac{7}{5}\right)$ to that in helium gas $\left(\gamma = \frac{5}{3}\right)$ at the same temperature is

The temperature of a gas is $-80^\circ\text{C}$. To what temperature the gas should be heated so that the r.m.s. speed is increased by 2 times?

The r.m.s. velocity of gas molecules kept at temperature $27^\circ\text{C}$ in a vessel is $61\text{ m/s}$. Molecular weight of gas is nearly

$\left[R = 8.31\frac{\text{J}}{\text{mol K}}\right]$

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^\circ\text{C}$ is (Molecular weight of hydrogen and oxygen molecules are 2 and 32 respectively)

The molecular mass of a gas having r.m.s. speed four times as that of another gas having molecular mass 32 is

The temperature of a gas is measure of

If temperature of gas molecules is raised from $127^\circ\text{C}$ to $527^\circ\text{C}$, the ratio of r.m.s. speed of the molecules is respectively

The pressure exerted by an ideal gas at a particular temperature is directly proportional to

The temperature of an ideal gas is increased from $27^\circ\text{C}$ to $927^\circ\text{C}$. The r.m.s. speed of its molecules becomes

The temperature of a gas is $-50^\circ\text{C}$. To what temperature the gas should be heated so that the rms speed is increased by $3$ times?

The temperature of an ideal gas is increased from $200\text{ K}$ to $800\text{ K}$. If r.m.s. speed of gas at $200\text{ K}$ is $v_0$. Then, r.m.s. speed of the gas at $800\text{ K}$ will be:

The root mean square velocity of molecules of gas is

The temperature of a gas is $-68^\circ\text{C}$. To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?

In a vessel, the ideal gas is at a pressure $P$. If the mass of all the molecules is halved and their speed is doubled, then resultant pressure of the gas will be

The rms speed of oxygen molecule in a vessel at particular temperature is $\left(1 + \frac{5}{x}\right)^{\frac{1}{2}} v$, where $v$ is the average speed of the molecule. The value of $x$ will be:

$($ Take $\pi = \frac{22}{7})$

If the r. m.s speed of chlorine molecule is $490\text{ m/s}$ at $27^\circ\text{C}$, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon $= 39.9\text{ u}$, molecular mass of chlorine $= 70.9\text{ u}$)

The root mean square speed of molecules of nitrogen gas at $27^\circ\text{C}$ is approximately: (Given mass of a nitrogen molecule $= 4.6 \times 10^{-26}\text{ kg}$ and take Boltzmann constant $k_B = 1.4 \times 10^{-23}\text{ J K}^{-1}$)

At 300 K, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha+5}{\alpha}}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be

(used $\pi = \frac{22}{7}$)

Given below are two statements:

Statement I: The temperature of a gas is $-73^\circ$ C. When the gas is heated to $527^\circ$ C, the root mean square speed of the molecules is doubled.

Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.

In the light of the above statements, choose the correct answer from the options given below:

When the rms velocity of a gas is denoted by '$v$', which one of the following relations is true? ($T =$ Absolute temperature of the gas.)

If the r.m.s speed of oxygen at room temperature is $\sqrt{56}\text{ m/s}$. The r.m.s speed of nitrogen at the same temperature is ________.

Following statements are given:

(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced. (B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.

(C) The average kinetic energy of a gas molecule decreases with increase in volume. (D) Pressure of a gas increases with increase in temperature at constant pressure. (E) The volume of gas decreases with increase in temperature.

Choose the correct answer from the options given below:

Two monatomic ideal gases A and B of molecular masses '$m_1$' and '$m_2$' respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas A to that in gas B is given by

The root mean square speed of smoke particles of mass $5 \times 10^{-17}\text{ kg}$ in their Brownian motion in air at NTP is approximately. [Given $k = 1.38 \times 10^{-23}\text{ J K}^{-1}$ ]

Given below are two statements:

Statement I: The average momentum of a molecule in a sample of an ideal gas depends on temperature.

Statement II: The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2v$. In the light of the above statements, choose the correct answer from the options given below:

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1 : 4$, then

A. The r.m.s. velocity of gas molecules in two vessels will be the same.

B. The ratio of pressure in these vessels will be $1 : 4$.

C. The ratio of pressure will be $1 : 1$.

D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $1 : 4$. Choose the correct answer from the options given below:

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

The relation between root mean square speed (vrms) and most probable speed (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be:

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127$^\circ$ C. The amount of heat required to double the speed of its molecules is ____________ k cal.

(Take R = 2 cal mole${}^{-1}$ K${}^{-1}$)

A vessel contains $14\text{ g}$ of nitrogen gas at a temperature of $27^\circ\text{C}$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be:

Take $R = 8.32\text{ J mol}^{-1}\text{ K}^{-1}$.

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of n will be:

The rms speed of a gas molecule is '$V$' at pressure '$P$'. If the pressure is increased by two times, then the rms speed of the gas molecule at the same temperature will be

If $m$' represents the mass of each molecules of a gas and $T$' its absolute temperature then the root mean square speed of the gas molecule is proportional to

An ideal gas having molar mass '$M_0$', has r.m.s. velocity 'V' at temperature 'T'. Then

if the rms speed of oxygen molecules at 0${}^\circ$C is 160 m/s, find the rms speed of hydrogen molecules at 0${}^\circ$C.

The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are VH, VO and VC respectively then:

Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean square speeds at normal temperature and pressure is:

The molecular masses of helium and oxygen are 4 and 32 respectively. The ratio of r.m.s. speed of helium at 327${}^\circ$ to r.m.s. speed of oxygen at 27${}^\circ$ will be

Equal volumes of two gases, having their densíties in the ratio of $1 : 16$ exert equal pressures on the walls of two containers. The ratio of their rms speads ($C_1 : C_2)$ is

What is the ratio of the velocity of sound in hydrogen $\left(\gamma = \frac{7}{5}\right)$ to that in helium $\left(\gamma = \frac{5}{3}\right)$ at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.)

Equal volumes of two gases are kept in different containers having densities in the ratio 1: 16. They exert equal pressures on the wall of their respective containers. Then the ratio of their r.m.s. velocities is

Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be:

(Molecular weight of oxygen is 32g/mol; R = 8.3 J K${}^{-1}$ mol${}^{-1}$)

The root mean square speed of molecules of a given mass of a gas at 27$^\circ$C and 1 atmosphere pressure is 200 ms${}^{-1}$. The root mean square speed of molecules of the gas at 127$^\circ$C and 2 atmosphere pressure is $\frac{x}{\sqrt{3}}$ ms${}^{-1}$. The value of x will be _________.

The root mean square velocity of molecules of a gas is $200\text{ m/s}$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

Nitrogen gas is at 300oC temperature. The temperature (in K) at which the rms speed of a H2 molecule would be equal to the rms speed of a nitrogen molecule, is _______.

(Molar mass of N2 gas 28 g).

Increase in tempertaure of a gas filled in a container would lead to:

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $\left[\frac{V_{rms}(\text{helium})}{V_{rms}(\text{argon})}\right],$ is close to:

The rms speed of oxygen molecule in a gas is $u$, If the temperature is doubled and the molecules dissociates into two atoms, the rms speed will be

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $\bar{v}$, m is its mass and kB is Boltzmann constant, then its temperature will be:

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be:

If 1022 gas molecules each of mass 10–26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104 m/s, the pressure exerted by the gas molecules will be of the order of:

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to:

[Boltzmann Constant kB = 1.38 × 10–23 J/K Avogadro Number NA = 6.02 × 1026 /kg Radius of Earth: 6.4 × 106 m Gravitational acceleration on Earth = 10ms–2]

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27oC. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take R = 8.3 J/K mole]

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is: [kB =1.4 $\times$ 10-23 J/K; mHe = 7 $\times$ 10 -27 kg ]

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere?

(Given: Mass of oxygen molecule (m) = 2.76 × 10–26 kg, Boltzmann’s constant kB = 1.38 × 10–23 J K–1)

The mass of a hydrogen molecule is 3.32 $\times$ 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45° to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly:

The molecules of a given mass of a gas have r.m.s. velocity of 200 m s${}^{-1}$ at 27oC and 1.0 $\times$ 105 N m${}^{-2}$ pressure. When the temperature and pressure of the gas are respectively, 127oC and 0.05 $\times$ 105 N m${}^{-2}$, the r.m.s. velocity of its molecules in m s${}^{-1}$ is

At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms${}^{-1}$. The gas is:

In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

The speed of sound in oxygen $(\text{O}_2)$ at a certain temperature is $460\text{ m s}^{-1}.$ The speed of sound in helium $(\text{He})$ at the same temperature will be (assume both gases to be ideal)

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

At what temperature is the $r.m.s.$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^\circ\text{C}?$