Gaseous State

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JEE Advanced 2026

LEVELJEE Advanced

The cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In the first cylinder, the masses of He and Ar are $m_{1}$ and $m_{2}$ , respectively. In the second cylinder, the masses of He and Ar are $m_{2}$ and $m_{1}$ , respectively the molar mass of Ar is 10 times the molar mass of He. The external pressure applied by the piston on the first cylinder needs to be 5 times that on the second cylinder so that the volume of the gas mixtures in both the cylinders are equal at the same temperature. Assuming He and Ar behaves like ideal gases, the value of $(m_{1} / m_{2})$ is _____.

JEE Advanced 2025

LEVELJEE Main

The correct statements (s) about intermolecular forces is(are)

* Multiple Correct Options

(A)

The potential energy between two point charges approaches zero more rapidly than the potential energy between a point dipole and a point charge as the distance between them approaches infinity.

(B)

The average potential energy of two rotating polar molecules that are separated by a distance

r

has

1/ r^{3}

dependence.

(C)

The dipole-induced dipole average interaction energy is independent of temperature.

(D)

Nonpolar molecules attract one another even though neither has a permanent dipole moment.

JEE Advanced 2025

LEVELJEE Main

Molar volume ( $V_{m}$ ) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_{m}$ as the variable. The ratio (in $mol dm^{- 3}$ ) of the coefficient of $V_{m}^{2}$ to the coefficient of $V_{m}$ for a gas having van der Waals constants $a = 6.0 dm^{6} atm mol^{- 2}$ and $b = 0.060 dm^{3} mol^{- 1}$ at $300 K$ and $300 atm$ is _______. Use: Universal gas constant (R) = $0.082 dm^{3} atm mol^{- 1} K^{- 1}$

LEVELJEE Main

For one mole of a van der Waals gas when b = 0 and T=300K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm. liter² mol⁻²) is

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 roots mean square speeds, respectively, is

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 2015

LEVELJEE Main

A closed vessel with rigid walls contains 1 mol of $_{92}^{238} U$ and 1 mol of air at 298 K. Considering complete decay of $_{92}^{238} U$ to $_{82}^{206} Pb$ , the ratio of the final pressure to the initial pressure of the system at 298 K is -

JEE Advanced 2014

LEVELJEE Advanced

Comprehension Passage

X and Y are two volatile liquids with molar weights of

10 g mol^{- 1}

and

40 g mol^{- 1}

respectively. Two cotton plugs, one soaked in X and the other soaked in Y, are simultaneously placed at the ends of a tube of length

L = 24 cm

, as shown in the figure. The tube is filled with an inert gas at

1 atmosphere

pressure and a temperature of

300 K

. Vapours of X and Y react to form a product which is first observed at a distance

d cm

from the plug soaked in X. Take X and Y to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.

Question 1:

The value of $d$ in cm (shown in the figure), as estimated from Graham's law, is - [JEE(Advanced) 2014]

The experimetnal value of $d$ is found to be smaller than the estimate obtained using Graham's law. This is due to - [JEE(Advanced) 2014]

(A)

Larger mean free path for X as compared to that of Y

(B)

Larger mean free path for Y as compared to that of X

(C)

Increased collision frequency of Y with the inert gas as compared to that of X with the inert gas

(D)

Increased collision frequency of X with the inert gas as compared to that of Y with the inert gas

JEE Advanced 2023

LEVELJEE Main

A gas has a compressibility factor of 0.5 and a molar volume of $0.4 dm^{3} mol^{- 1}$ at a temperature of 800 K and pressure x atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be y $dm^{3} mol^{- 1}$ . The value of x/y is ______. [Use: Gas constant, $R = 8 \times 1 0^{- 2} L atm K^{- 1} mol^{- 1}$ ]

JEE Advanced 2018

LEVELJEE Advanced

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in $m^{3}$ ) of the compartment A after the system attains equilibrium is_______.

JEE Advanced 2015

LEVELJEE Main

One mole of a monoatomic real gas satisfied the equation $p (V - b) = R T$ where $b$ is a constant. The relationship of interatomic potential $V (r)$ and interatomic distance $r$ for the gas is given by –

For which of the following parameters, the structural isomers $C_{2} H_{5} O H$ and $C H_{3} O C H_{3}$ would be expected to have the same values? (Assume ideal behaviour)

(A)

Heat of vaporisation

(B)

Vapour pressure at the same temperature

(C)

Boiling points

(D)

Gaseous densities at the same temperature and pressure

JEE Main 2019

LEVELJEE Main

0.5 moles of gas A and $x$ moles of gas B exert a pressure of $200 Pa$ in a container of volume $10 m^{3}$ at $1000 K$ . Given $R$ is the gas constant in $J K^{- 1} mol^{- 1}$ , $x$ is

(A)

\frac{2 R}{4 - R}

(B)

\frac{4 - R}{2 R}

(C)

\frac{4 + R}{2 R}

(D)

\frac{2 R}{4 + R}

JEE Main 2021

LEVELJEE Main

An LPG cylinder contains gas at a pressure of $300 kPa$ at $2 7^{\circ} C$ . The cylinder can withstand the pressure of $12 \times 1 0^{6} Pa$ . The room in which the cylinder is kept catches fire. The minimum temperature at which the bursting of cylinder will take place is ……… $^{\circ} C$ . (Nearest integer)

LEVELJEE Main

When $r$ , $p$ and $M$ represent rate of diffusion, pressure and molecular mass, respectively, then the ratio of the rates of diffusion $(r_{A} / r_{B})$ of two gases $A$ and $B$ , is given as

(A)

(p_{A} / p_{B})^{1/2} (M_{A} / M_{B})

(B)

(p_{A} / p_{B}) (M_{B} / M_{A})^{1/2}

(C)

(p_{A} / p_{B})^{1/2} (M_{B} / M_{A})

(D)

(p_{A} / p_{B}) (M_{A} / M_{B})^{1/2}

JEE Main 2019

LEVELJEE Main

The volume of gas $A$ is twice than that of gas $B$ . The compressibility factor of gas $A$ is thrice than that of gas $B$ at same temperature. The pressures of the gases for equal number of moles are

(A)

p_{A} = 2 p_{B}

(B)

2 p_{A} = 3 p_{B}

(C)

p_{A} = 3 p_{B}

(D)

3 p_{A} = 2 p_{B}

LEVELJEE Main

If $1 0^{- 4} dm^{3}$ of water is introduced into a $1.0 dm^{3}$ flask at $300 K$ , then how many moles of water are in the vapour phase when equilibrium is established? (Given, vapour pressure of $H_{2} O$ at $300 K$ is $3170 Pa$ ; $R = 8.314 J K^{- 1} mol^{- 1}$ )

(A)

5.56 \times 1 0^{- 3} mol

(B)

1.53 \times 1 0^{- 2} mol

(C)

4.46 \times 1 0^{- 2} mol

(D)

1.27 \times 1 0^{- 3} mol

JEE Main 2019

LEVELJEE Main

Consider the van der Waals' constants, $a$ and $b$ , for the following gases. \begin{array}{|c|c|c|c|c|} \hline \textbf{Gas} & \textbf{Ar} & \textbf{Ne} & \textbf{Kr} & \textbf{Xe} \\ \hline \mathbf{a / (atm\ dm^6\ mol^{-2})} & 1.3 & 0.2 & 5.1 & 4.1 \\ \hline \mathbf{b / (10^{-2}\ dm^3\ mol^{-1})} & 3.2 & 1.7 & 1.0 & 5.0 \\ \hline \end{array} Which gas is expected to have the highest critical temperature ?

Which one of the following statements is not true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

(A)

The area under the distribution curve remains the same as under the lower temperature

(B)

The distribution becomes broader

(C)

The fraction of the molecules with the most probable speed increases

(D)

The most probable speed increases

LEVELBoard

For an ideal gas, number of moles per litre in terms of its pressure $p$ , temperature $T$ and gas constant $R$ is

(A)

\frac{pT}{R}

(B)

pR T

(C)

\frac{p}{R T}

(D)

\frac{R T}{p}

JEE Main 2020

LEVELJEE Main

Identify the correct labels of $A$ , $B$ and $C$ in the following graph from the options given below : Root mean square speed ( $v_{rms}$ ); most probable speed ( $v_{mp}$ ); Average speed ( $v_{av}$ )

(A)

A - v_{rms}; B - v_{mp}; C - v_{av}

(B)

A - v_{mp}; B - v_{rms}; C - v_{av}

(C)

A - v_{mp}; B - v_{av}; C - v_{rms}

(D)

A - v_{av}; B - v_{rms}; C - v_{mp}

LEVELJEE Main

$a$ and $b$ are van der Waals' constants for gases. Chlorine is more easily liquefied than ethane because

(A)

a

and

b

for

Cl_{2} > a

and

b

for

C_{2} H_{6}

(B)

a

and

b

for

Cl_{2} < a

and

b

for

C_{2} H_{6}

(C)

a

for

Cl_{2} > a

for

C_{2} H_{6}

but

b

for

Cl_{2} > b

for

C_{2} H_{6}

(D)

a

for

Cl_{2} > a

for

C_{2} H_{6}

but

b

for

Cl_{2} < b

for

C_{2} H_{6}

LEVELJEE Main

According to the kinetic theory of gases, in an ideal gas, between two successive collisions a gas molecule travels

in a straight line path

(D)

with an accelerated velocity

LEVELJEE Main

Based on kinetic theory of gases following laws can be proved

A home owner uses $4.00 \times 1 0^{3} m^{3}$ of methane ( $CH_{4}$ ) gas, (assume $CH_{4}$ is an ideal gas) in a Year to heat his home. Under the pressure of $1.0 atm$ and $300 K$ , mass of gas used is $x \times 1 0^{5} g$ . The value of $x$ is ...... . (Nearest integer) (Given, $R = 0.083 L atm K^{- 1} mol^{- 1}$ )

The correct statements (s) about intermolecular forces is(are)

For one mole of a van der Waals gas when b = 0 and T=300K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm. liter² mol⁻²) is

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 roots mean square speeds, respectively, is

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

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of d in cm (shown in the figure), as estimated from Graham's law, is - [JEE(Advanced) 2014]

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The experimetnal value of d is found to be smaller than the estimate obtained using Graham's law. This is due to - [JEE(Advanced) 2014]

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For which of the following parameters, the structural isomers C2​H5​OH and CH3​OCH3​ would be expected to have the same values? (Assume ideal behaviour)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume 10 m3 at 1000 K. Given R is the gas constant in J K−1mol−1, x is

Which one of the following statements is not true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For an ideal gas, number of moles per litre in terms of its pressure p, temperature T and gas constant R is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } a and b are van der Waals' constants for gases. Chlorine is more easily liquefied than ethane because

According to the kinetic theory of gases, in an ideal gas, between two successive collisions a gas molecule travels

Based on kinetic theory of gases following laws can be proved

The value of $d$ in cm (shown in the figure), as estimated from Graham's law, is - [JEE(Advanced) 2014]

The experimetnal value of $d$ is found to be smaller than the estimate obtained using Graham's law. This is due to - [JEE(Advanced) 2014]

For which of the following parameters, the structural isomers $C_{2} H_{5} O H$ and $C H_{3} O C H_{3}$ would be expected to have the same values? (Assume ideal behaviour)

0.5 moles of gas A and $x$ moles of gas B exert a pressure of $200 Pa$ in a container of volume $10 m^{3}$ at $1000 K$ . Given $R$ is the gas constant in $J K^{- 1} mol^{- 1}$ , $x$ is

For an ideal gas, number of moles per litre in terms of its pressure $p$ , temperature $T$ and gas constant $R$ is

$a$ and $b$ are van der Waals' constants for gases. Chlorine is more easily liquefied than ethane because