The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is:
The temperature at which a real gas obeys the ideal gas laws over a wide range of pressure is:
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:
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
Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is:
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
No cooling occurs, when an ideal gas undergoes unrestrained expansion, because the molecules:
Ideal gas has no attractive force between the particles
A liquid is in equilibrium with its vapour at it’s boiling point. On the average, the molecules in the two phases have equal:
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.
Rate of diffusion of a gas is:
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
The average velocity of an ideal gas molecule at 27°C is 0.3 m/s. The average velocity at 927°C will be
In van der Waals’ equation of state for a nonideal gas, the term that accounts for intermolecular forces is:
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 intermolecular force while the second term (V  b) correct for molecular volume.
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:
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:
The density of neon will be highest at:
The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight of X is:
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
According to kinetics theory of gases, for a diatomic molecule:
As we know: KE = (3/2) RT
⇒ KE ∝ T
i.e. mean transitional kinetic energy of the molecules is proportional to the absolute temperature.
At constant volume, for a fixed number of moles of a gas the pressure of the gas increases with rise of temperature due to:
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:
Partial pressure of hydrogen/total pressure = mole fraction of hydrogen =15:16
The ratio between the root mean square speed of H_{2} at 50 K and that of O_{2} at 800 K is:
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
The compressibility factor for an ideal gas is:
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.
The critical temperature of water is higher than that of O_{2} because the H_{2}O molecule has:
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)
Hence C is correct.
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