States of Matter

1 L closed flask contains a mixture of 4 g of methane and 4.4 g of carbon dioxide. The pressure inside the flask at \({27}^{\mathrm{o}}\mathrm{C}\) is (Assume ideal behaviour of gases)

At the sea level, the dry air mass percentage composition is given as nitrogen gas : \(70.0\), oxygen gas : \(27.0\) and argon gas : \(3.0\). If total pressure is \(1.15\) atm, then calculate the ratio of followings respectively :
(i) partial pressure of nitrogen gas to partial pressure of oxygen gas
(ii) partial pressure of oxygen gas to partial pressure of argon gas
(Given : Molar mass of N, O and Ar are \(14,16,\) and \(40\mathrm{g}{\mathrm{mol}}^{-1}\) respectively)

[JEE Main 2025, 7 Apr (Shift 1)]

At the sea level, the dry air mass percentage composition is given as nitrogen gas : \(70.0\), oxygen gas : \(27.0\) and argon gas : \(3.0\). If total pressure is \(1.15\) atm, then calculate the ratio of followings respectively :
(i) partial pressure of nitrogen gas to partial pressure of oxygen gas
(ii) partial pressure of oxygen gas to partial pressure of argon gas
(Given : Molar mass of N, O and Ar are \(14,16,\) and \(40\mathrm{g}{\mathrm{mol}}^{-1}\) respectively)

[JEE Main 2025, 7 Apr (Shift 1)]

1 L closed flask contains a mixture of 4 g of methane and 4.4 g of carbon dioxide. The pressure inside the flask at \({27}^{\mathrm{o}}\mathrm{C}\) is (Assume ideal behaviour of gases)

Molar volume ( \({V}_{\mathrm{m}}\) ) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with \({V}_{\mathrm{m}}\) as the variable. The ratio (in \({\mathrm{moldm}}^{-3}\) ) of the coefficient of \({V}_{\mathrm{m}}^{2}\) to the coefficient of \({V}_{\mathrm{m}}\) for a gas having van der Waals constants \(a=6.0{\mathrm{dm}}^{6}\mathrm{atm}{\mathrm{mol}}^{-2}\) and \(b=0.060\) \(\mathrm{dm}^3 \mathrm{~mol}^{-1}\) at 300 K and 300 atm is (nearest integer) ______(consider magnitude)

Use: Universal gas constant \((R)=0.082{\mathrm{dm}}^{3}\mathrm{atm}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}\)

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

A closed vessel contains \(10\mathrm{g}\) of an ideal gas X at \(300\mathrm{K}\), which exerts \(2\mathrm{atm}\) pressure. At the same temperature, \(80\mathrm{g}\) of another ideal gas Y is added to it and the pressure becomes \(6\mathrm{atm}\). The ratio of root mean square velocities of X and Y at \(300\mathrm{K}\) is

[JEE Advanced 2024, Paper-1]

A closed vessel contains \(10\mathrm{g}\) of an ideal gas X at \(300\mathrm{K}\), which exerts \(2\mathrm{atm}\) pressure. At the same temperature, \(80\mathrm{g}\) of another ideal gas Y is added to it and the pressure becomes \(6\mathrm{atm}\). The ratio of root mean square velocities of X and Y at \(300\mathrm{K}\) is

A mixture of one mole each of \( \mathrm{H}_{2}, \mathrm{He} \) and \( \mathrm{O}_{2} \) each are enclosed in a cylinder of volume \( \mathrm{V} \) at temperature \( \mathrm{T} \). If the partial pressure of \( \mathrm{H}_{2} \) is \( 2 \mathrm{~atm} \), the total pressure of the gases in the cylinder is

[JEE Main 2020, 3 Sep (Shift 2)]

Arrange the following gases in increasing order of vander Waal's constant ' a '.

(A) Ar
(B) \({\mathrm{CH}}_{4}\)
(C) \({\mathrm{H}}_{2}\mathrm{O}\)
(D) \({\mathrm{C}}_{6}{\mathrm{H}}_{6}\)

Choose the correct option from the following :

[JEE Main 2023, 8 Apr (Shift 2)]

At constant temperature, a gas is at a pressure of 940.3 mm Hg. The pressure at which its volume decreases by 40% is______mm Hg. (Nearest Integer)

[JEE Main 2023, 10 Apr (Shift 1)]

Assertion (A): Amongst \(\mathrm{He},\mathrm{Ne},\mathrm{Ar}\) and \(\mathrm{Kr};1\mathrm{g}\) of activated charcoal adsorbs more of Kr.

Reason (R): The critical volume \({\mathrm{V}}_{\mathrm{c}}\left({\mathrm{cm}}^{3}{\mathrm{mol}}^{-1}\right)\) and critical pressure \({\mathrm{P}}_{\mathrm{c}}(\mathrm{atm})\) is highest for Krypton but the compressibility factor at critical point \({Z}_{c}\) is lowest for Krypton.

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

[JEE Main 2023, 1 Feb (Shift 1)]

A car tyre is filled with nitrogen gas at \(35\mathrm{psi}\) at \(27^\circ \mathrm{C}\). It will burst if pressure exceeds 40 psi. The temperature in \({}^{∘}\mathrm{C}\) at which the car tyre will burst is____.(Round off to the nearest integer)

[JEE Main 2021, 25 Feb (Shift 1)]

At 600 K, the root mean square (rms) speed of gas X (molar mass =40 ) is equal to the most probable speed of gas Y at 90 K. The molar mass of the gas Y is_______ \({\mathrm{gmol}}^{-1}\). (Nearest integer)

[JEE Main 2023, 12 Apr (Shift 1)]

A home owner uses \( 4.00 \times 10^{3} \mathrm{~m}^{3} \) of methane \( \left(\mathrm{CH}_{4}\right) \) gas, (assume \( \mathrm{CH}_{4} \) is an ideal gas) in a year to heat his home. Under the pressure of \( 1.0 \mathrm{~atm} \) and \( 300 \mathrm{~K} \), mass of gas used is \( x \times 10^{5} \mathrm{~g} \). The value of \( \mathrm{x} \) is ____________(Nearest integer) (Given \( \mathrm{R}=0.083 \mathrm{Latm} \mathrm{K}^{-1} \mathrm{~mol}^{-1} \) )

Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Sharp glass edge becomes smooth on heating it upto its melting point.

Reason (R): The viscosity of glass decreases on melting.

Choose the most appropriate answer from the options given below

[JEE Main 2021, 20 Jul (Shift 1)]

The unit of the van der Waals gas equation parameter ' a ' in \(\left(\mathrm{P}+\frac{{\mathrm{an}}^{2}}{{\mathrm{V}}^{2}}\right)(\mathrm{V}-\mathrm{nb})=\mathrm{nRT}\) is

[JEE Main 2021, 27 Aug (Shift 1)]

Two vessels of volumes 16.4 L and 5 L contain two ideal gases of molecular existence at the respective temperature of 27 °C and 227 °C and exert 1.5 and 4.1 atmospheres respectively. The ratio of the number of molecules of the former to that of the later is

X mL of \({\mathrm{H}}_{2}\) gas effuses through a hole in a container in 5 seconds. The time taken for the effusion of the same volume of the gas specified below under identical conditions is:

An empty LPG cylinder weighs \( 14.8 \mathrm{~kg} \). When full, it weighs \( 29.0 \mathrm{~kg} \) and shows a pressure of \( 3.47 \mathrm{~atm} \). In the course of use at ambient temperature, the mass of the cylinder is reduced to \( 23.0 \mathrm{~kg} \). The final pressure inside of the cylinder is ___atm. (Nearest integer)

(ASSUME LPG of be an ideal gas)

[JEE Main 2021, 1 Sep (Shift 2)]

An LPG cylinder contains gas at a pressure of \( 300 \mathrm{~kPa} \) at \( 27^{\circ} \mathrm{C} \). The cylinder can withstand the pressure of \( 1.2 \times 10^{6} \mathrm{~Pa} \). The room in which the cylinder is kept catches fire. The minimum temperature at which the bursting of cylinder will take place is ______ \( { }^{\circ} \mathrm{C} \). (Nearest integer)

[JEE Main 2021, 25 Jul (Shift 2)]

A spherical ballon of radius 3 cm containing helium gas has a pressure of
48 × 10^-3 bar. At the same temperature, the pressure of a spherical ballon of radius 12 cm containing the same amount of gas will be ______ × 10^-6 bar.

Match the type of interaction in column A with the distance dependence of their interaction energy in column B :

[JEE Main 2020, 2 Sep (Shift 2)]

A certain quantity of a real gas occupies a volume of 0.15 \({\mathrm{dm}}^{3}\) at 100 atm and 500 K when its compressibility factor is 1.07 . Its volume at 300 atm and 300 K (when its compressibility factor is 1.4) is _______\(\times {10}^{-4}{\mathrm{dm}}^{3}\)

[JEE Main 2023, 13 Apr (Shift 1)]

The pressure exerted by a non- reactive gaseous mixture of \(6.4\mathrm{g}\) of methane and \(8.8\mathrm{g}\) of carbon dioxide in a \(10\mathrm{L}\) vessel at \(27^\circ \mathrm{C}\) is ______kPa (Round off to the nearest integer)

[Assume gases are ideal, \(\mathrm{R}=8.314\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}\)

Atomic masses: C: \(12.0\mathrm{u},\mathrm{H}:1.0\mathrm{u},\mathrm{O}:16.0\mathrm{u}\) ]

[JEE Main 2021, 17 Mar (Shift 1)]

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 32 g/mol; R = 8.3 JK^–1 mol^–1)

[JEE Main 2021, 18 Mar (Shift 2)]

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Sharp glass edge becomes smooth on heating it upto its melting point.
Reason R: The viscosity of glass decreases on melting.
Choose the most appropriate answer from the options given below.

[JEE Main 2021, 20 Jul (Shift 1)]

The volume occupied by \(4.75\mathrm{g}\) of acetylene gas at \(50^\circ \mathrm{C}\) and 740 mmHg pressure is_______L. (Rounded off to the nearest integer)

[Given \(\mathrm{R}=0.0826\mathrm{L}\mathrm{atm}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}\) ]

[JEE Main 2021, 24 Feb (Shift 2)]

A certain quantity of a real gas occupies a volume of 0.15 \({\mathrm{dm}}^{3}\) at 100 atm and 500 K when its compressibility factor is 1.07 . Its volume at 300 atm and 300 K (when its compressibility factor is 1.4) is _______\(\times {10}^{-4}{\mathrm{dm}}^{3}\)

The predominant intermolecular forces present in acetone, a liquid, are :

An evacuated glass vessel weighs \(40.0\mathrm{g}\) when empty, \(135.0\mathrm{g}\) when filled with a liquid of density \(0.95\mathrm{g}{\mathrm{mL}}^{-1}\) and \(40.5\mathrm{g}\) when filled with an ideal gas at \(0.82\mathrm{atm}\) at 250 K. The molar mass of the gas in \({\mathrm{gmol}}^{-1}\) is_______.

(Given: \(\mathrm{R}=0.082\mathrm{L}\mathrm{atm}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}\) )

[JEE Main 2022, 26 Jun (Shift 1)]

The number of chlorine atoms in 20 mL of chlorine gas (Cl₂) at STP is____×10²¹ (Round off to the nearest integer).

[Assume chlorine is an ideal gas at STP

\(\left.\mathrm{R}=0.083\mathrm{L}\mathrm{bar}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1},{\mathrm{N}}_{\mathrm{A}}=6.023\times {10}^{23}\right]\)

[JEE Main 2021, 17 Mar (Shift 2)]

A certain gas obeys \(P\left({V}_{m}-b\right)=RT\). The value of \({\left(\frac{\partial Z}{\partial P}\right)}_{T}\) is \(\frac{\mathrm{xb}}{\mathrm{RT}}\). The value of x is_________. (Integer answer) (Z : compressibility factor)

The relative strength of interionic/intermolecular forces in decreasing order is:

[JEE Main 2020, 7 Jan (Shift 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 K and pressure x atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be y \({\mathrm{dm}}^{3}\) \({\mathrm{mol}}^{-1}\). The value of \(\mathrm{x}/\mathrm{y}\) is_____.

[Use: Gas constant, \(\mathrm{R}=8\times {10}^{-2}\mathrm{L}\mathrm{atm}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}\) ]