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QUESTION: 1

The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is:

Solution:

QUESTION: 2

The temperature at which a real gas obeys the ideal gas laws over a wide range of pressure is:

Solution:

- The temperature at which the
**real or non-ideal gas behaves as an ideal gas**over a wide range of pressure is known as Boyle temperature. - Boyle temperature (T
_{B}) is related to the Vander Waal’s constant a, b as given below. At this temperature, the attractive and repulsive forces acting on the gas particles arrive at a balance for a real gas. - T
_{B }= a/Rb

QUESTION: 3

Equal weights of methane and oxygen and mixed in an empty container at 25°C. The fraction of the total pressure exerted by oxygen is:

Solution:

Let the mass of methane and oxygen be m gm.

Mole fraction of oxygen, x_{O2} = m/32/(m/32 +m/16) = 1/3

Let the total pressure be P.

Partial pressure of O_{2}, p_{O2} = P × x_{O2} = P x 1/3 = P/3

QUESTION: 4

Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is:

Solution:

Kinetic energy of gas molecule depends on temperature and does not depend upon the nature of gas.

K.E =(3/2)kT.

Thus hydrogen and helium have same K.E at same temperature

QUESTION: 5

No cooling occurs, when an ideal gas undergoes unrestrained expansion, because the molecules:

Solution:

Ideal gas has no attractive force between the particles

QUESTION: 6

A liquid is in equilibrium with its vapour at it’s boiling point. On the average, the molecules in the two phases have equal:

Solution:

When a liquid is in equilibrium with its vapout at its boiling point, the molecules in the two phases have equal kinetic energy.

At equilibrium, the rate of molecules going from the liquid to the gaseous phase equal to the rate of molecules going from the gaseous phase to the liquid surface and hence they have equal kinetic energy.

QUESTION: 7

Rate of diffusion of a gas is:

Solution:

**Graham's law **states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight.

**Rate of Diffusion is proportional to 1/ √M**

QUESTION: 8

The average velocity of an ideal gas molecule at 27°C is 0.3 m/s. The average velocity at 927°C will be

Solution:

QUESTION: 9

In van der Waals’ equation of state for a non-ideal gas, the term that accounts for intermolecular forces is:

Solution:

__In van der Waals’ equation of state:__

(p + a/V^{2}) (V - b) = RT (for 1 mole)

The first factor **(p + a/V _{2}) correct** for

QUESTION: 10

A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends the white ammonium chloride ring first formed will be:

Solution:

__According to Graham's law of effusion:__

Rate of effusion = √(1/Molar mass)

i.e.**Gas of higher molar mass will effuse slowly**, therefore, move a shorter distance.- NH
_{3}molar mass is 17 and HCl molar mass is 36.5. So, HCl effuses slowly and the formation of NH_{4}Cl white rings are formed near the HCl

QUESTION: 11

The value of van der Waals’ constant ‘a’ for the gases O_{2}, N_{2}, NH_{3} and CH_{4} are 1.360, 1.390, 4.170 and 2.253 L^{2} atm mol^{–2} respectively. The gas which can most easily be liquefied is:

Solution:

- The
**ease of liquification of a gas depends on their intermolecular force of attraction**which in turn is measured in terms of van der Waals’ constant ‘a’. - Hence, the higher the value of ‘a’, the greater the intermolecular force of attraction, the easier the liquification.
- In the present case, NH
_{3}has the highest ‘a’, can most easily be liquefied.

QUESTION: 12

The density of neon will be highest at:

Solution:

__According to the ideal gas equation:__

P = dRT/M i.e. d = PM/RT- As per the above equation at
**high pressure and low-temperature**, density is maximum.

QUESTION: 13

The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight of X is:

Solution:

The rate of diffusion of methane at a given temperature is twice that of gas X i.e. r_{CH4 }= 2r_{X}

∵ The rate of diffusion is inversely proportional to the square root of its molar mass.

Therefore,

Thus, molecular mass of gas X is M_{X }= 64.0 g/mol

QUESTION: 14

According to kinetics theory of gases, for a diatomic molecule:

Solution:

__As we know__: KE = (3/2) RT

⇒ **KE ∝ T**

i.e. mean transitional kinetic energy of the molecules is proportional to the absolute temperature.

QUESTION: 15

At constant volume, for a fixed number of moles of a gas the pressure of the gas increases with rise of temperature due to:

Solution:

QUESTION: 16

Equal weights of ethane and hydrogen are mixed in an empty container at 25°C. The fraction of the total pressure exerted by hydrogen is:

Solution:

Partial pressure of hydrogen/total pressure = mole fraction of hydrogen =15:16

QUESTION: 17

The ratio between the root mean square speed of H_{2} at 50 K and that of O_{2} at 800 K is:

Solution:

The rms velocity is directly proportional to the square root of temperature and inversely proportional to the square root of molecular weight.

The ratio between the root mean square velocity of H_{2} at 50K and that of O_{2} at 800K is

QUESTION: 18

The compressibility factor for an ideal gas is:

Solution:

The deviation of ideal behaviour is introduced by compressibility factor Z.

i.e.** Z = PV/nRT**

for ideal gas PV = nRT, therefore, Z is 1.

QUESTION: 19

The critical temperature of water is higher than that of O_{2} because the H_{2}O molecule has:

Solution:

QUESTION: 20

According to Graham’s law, at a given temperature the ratio of the rates of diffusionof gases A and B is given by (where, p and M are pressure and molecular weights of gases A and B respectively)

Solution:

**Hence C is correct.**

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