Gaseous State · Chemistry · JEE Advanced
MCQ (Single Correct Answer)
1
A closed vessel contains $10 \mathrm{~g}$ of an ideal gas $\mathbf{X}$ at $300 \mathrm{~K}$, which exerts $2 \mathrm{~atm}$ pressure. At the same temperature, $80 \mathrm{~g}$ of another ideal gas $\mathbf{Y}$ is added to it and the pressure becomes $6 \mathrm{~atm}$. The ratio of root mean square velocities of $\mathbf{X}$ and $\mathbf{Y}$ at $300 \mathrm{~K}$ is
JEE Advanced 2024 Paper 1 Online
2
If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is
JEE Advanced 2020 Paper 1 Offline
3
For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm L2 mol$$-$$2) is
IIT-JEE 2012 Paper 1 Offline
4
The term that corrects for the attractive forces present in a real gas in the van der Waals equation is
IIT-JEE 2009 Paper 1 Offline
5
The average velocity of an ideal gas molecule at 27oC is 0.3m/sec. The average velocity at 927oC will be
IIT-JEE 1986
6
Rate of diffusion of a gas is
IIT-JEE 1985
7
Equal weights of methane and hydrogen are mixed in an empty container at 25oC. The fraction of the total pressure exerted by hydrogen is
IIT-JEE 1984
8
Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is
IIT-JEE 1982
9
Equal weights of methane and oxygen are mixed in an empty container at 25oC. The fraction of the total pressure exerted by oxygen is
IIT-JEE 1981
10
The temperature at which a real gas obeys the ideal gas aws over a wide range of pressure is
IIT-JEE 1981
11
The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is
IIT-JEE 1981
Numerical
1
A gas has a compressibility factor of 0.5 and a molar volume of $0.4 ~\mathrm{dm}^3 \mathrm{~mol}^{-1}$ at a temperature of $800 \mathrm{~K}$ and pressure $\mathbf{x}$ atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be $\mathbf{y} ~\mathrm{dm}^3 \mathrm{~mol}^{-1}$. The value of $\mathbf{x} / \mathbf{y}$ is __________.
[Use: Gas constant, $\mathrm{R}=8 \times 10^{-2} \mathrm{~L}$ atm $\mathrm{K}^{-1} \mathrm{~mol}^{-1}$ ]
[Use: Gas constant, $\mathrm{R}=8 \times 10^{-2} \mathrm{~L}$ atm $\mathrm{K}^{-1} \mathrm{~mol}^{-1}$ ]
JEE Advanced 2023 Paper 1 Online
2
Aluminium reacts with sulphuric acid to form aluminium sulphate and hydrogen. What is the volume of hydrogen gas in litre (L) produced at 300 K and 1.0 atm pressure, when 5.4 g of aluminium and 50.0 mL of 5.0 M sulphuric acid are combined for the reaction?
(Use molar mass of aluminium as 27.0 g mol$$-$$1, R = 0.082 atm L mol$$-$$1 K$$-$$1)
(Use molar mass of aluminium as 27.0 g mol$$-$$1, R = 0.082 atm L mol$$-$$1 K$$-$$1)
JEE Advanced 2020 Paper 1 Offline
3
The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute
temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the
diffusion coefficient of this gas increases x times. The value of x is ___________:
JEE Advanced 2016 Paper 1 Offline
4
To an evacuated vessel with movable piston under external pressure of 1 atm, 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm, at 0oC) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0oC is close to
IIT-JEE 2011 Paper 1 Offline
5
At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is ___________.
IIT-JEE 2009 Paper 2 Offline
6
At 27oC, hydrogen is leaked through a tiny hole into a vessel for 20 minutes. Another unknown gas at the same temperature and pressure as that of H2 is leaked through the same hole for 20 minutes After the effusion of the gases the mixture exerts a pressure of 6 atmosphere. The hydrogen content of the mixture is 0.7 mole. If the volume of ther container is 3 litres, what is the molecular weight of the unknown gas?
IIT-JEE 1992
7
A spherical balloon of 21 cm diameter is to be filled up with hydrogen at N.T.P from a cylinder containing the gas at 20 atmospheres at 27oC. If the cylinder can hold 2.82 litres of water, calculate the number of balloons that can be filled up.
IIT-JEE 1987
8
The value of PV for 5.6 litres of an ideal gas is ________ RT, at NTP.
IIT-JEE 1987
9
The total energy of one mole of an ideal monatomic gas at 27o is _______ calories.
IIT-JEE 1984
MCQ (More than One Correct Answer)
1
One mole of a monoatomic real gas satisfies the equation p(V $$-$$ b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by
JEE Advanced 2015 Paper 2 Offline
2
An ideal gas in thermally insulated vessel at internal pressure = p1, volume = V1 and absolute temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram.
The final internal pressure, volume and absolute temperature of the gas are p2, V2 and T2, respectively. For this expansion
JEE Advanced 2014 Paper 1 Offline
3
According to kinetic theory of gases
IIT-JEE 2011 Paper 1 Offline
4
A gas described by van Der Waals equation
IIT-JEE 2008 Paper 1 Offline
Subjective
1
One mole of nitrogen gas at 0.8 atm takes 38 s to diffuse through a pinhole. whereas one mole of an unknown compound of xenon with flourine at 1.6 atm takes 57 s to diffuse through the same hole. Calculate the molecular formula of the compound.
IIT-JEE 1999
2
An LPG (liquefied petroleum gas) cylinder weighs 14.8 kg when empty. When full, it weighs 29.0 kg and shows a pressure of 2.5 atm. In the course of use at 27o C, the weight of the full cylinder reduces to 23.2 kg. Find out the volume of the gas in cubic meters used up at the normal usage conditions find the final pressure inside the cylinder. Assume LPG to be n-butane with normal boiling point of 0o C.
IIT-JEE 1994
3
A 4 : 1 molar mixture of He and CH4 is contained in a vessel at 20 bar pressure. Due to a hole in the vessel the gas mixture leaks out. What is the composition of the mixture effusing out initially?
IIT-JEE 1994
4
A gas bulb of 1 litre capacity contains 2.0 $$\times$$ 1021 molecules of nitrogen exerting a pressure of 7.57 $$\times$$ 103 Nm-2. Calculate the root mean square (r.m.s) speed and the temparature of the gas molecules. If the ratio of the most probable speed to the root mean square speed is 0.82, calculate the most probable speed for these molecules at this temparature.
IIT-JEE 1993
5
At room temperature the following reacton is procedd nearly to completion:
2NO + O2 $$\to$$ 2NO2 $$\to$$ N2O4
The dimer, N2O4, solidifies at 262 K. A 250 ml flask and a 100 ml flask are separated by a stop-cock. At 300 K, the nitric oxide in the larger flask exerts a pressure of 1.053 atm. and the smaller one contains oxygen at 0.789 atm. The gases are mixed by the opening stopcock and after the end of raction the flasks are cooled at 220K. Neglecting the vapour pressure of the dimer, find out the pressure and composition of the gas remaining at 220 K. (Assume the gases to behave ideally)
2NO + O2 $$\to$$ 2NO2 $$\to$$ N2O4
The dimer, N2O4, solidifies at 262 K. A 250 ml flask and a 100 ml flask are separated by a stop-cock. At 300 K, the nitric oxide in the larger flask exerts a pressure of 1.053 atm. and the smaller one contains oxygen at 0.789 atm. The gases are mixed by the opening stopcock and after the end of raction the flasks are cooled at 220K. Neglecting the vapour pressure of the dimer, find out the pressure and composition of the gas remaining at 220 K. (Assume the gases to behave ideally)
IIT-JEE 1992
6
Calculate the volume occupied by 5.0 g of acetylene gas at 50oC and 740 mm pressure.
IIT-JEE 1991
7
Calculate the root mean square velocity of ozone kept in a closes vessel at 20oC and 82 cm mercury pressure.
IIT-JEE 1985
8
At room temparature, ammonia gas at 1 atm pressure and hydrogen chloride gas at P atm pressure are allowed to effuse through identical pin holes from opposite ends of a glass tube of one metre length and of uniform cross-section. Ammonium chloride is first formed at a distance of 60 cm from the end through which HCL gas is sent in. What is the value of P?
IIT-JEE 1982
True or False
1
A mixture of ideal gas is cooled upto liquid helium temperature (4.22K) to form an ideal solution
IIT-JEE 1996
2
In the van der Waal's equation (P + $${{{n^2}a} \over {{V^2}}}$$)(V - nb) = nRT the constant 'a' reflects the actual volume of the gas molecules.
IIT-JEE 1993
3
Kinetic Energy of a Molecule is zero at 0oC.
IIT-JEE 1985
4
A gas in a closed container will exert much higher pressure due to gravity at the bottom than at the top.
IIT-JEE 1985