States of Matter

Two 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 behave like ideal gases, the value of $(m_1/m_2)$ is ____.

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 $\mathrm{mol\,dm^{-3}}$) of the coefficient of $V_m^2$ to the coefficient of $V_m$ for a gas having van der Waals constants $a = 6.0\ \mathrm{dm^6\,atm\,mol^{-2}}$ and $b = 0.060\ \mathrm{dm^3\,mol^{-1}}$ at 300 K and 300 atm is _____.

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

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

A gas has a compressibility factor of 0.5 and a molar volume of $0.4\,\mathrm{dm^3\,mol^{-1}}$ 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 $\mathrm{dm^3\,mol^{-1}}$. The value of $\mathbf{x}/\mathbf{y}$ is _____.

[Use: Gas constant, $R = 8\times10^{-2}\,\mathrm{L\,atm\,K^{-1}\,mol^{-1}}$]

At 300 K, a sample of 3.0 g of gas A occupies the same volume as 0.2 g of hydrogen at 200 K at the same pressure. The molar mass of gas A is ______ g mol$^{-1}$. (nearest integer) Assume that the behaviour of gases as ideal.

(Given: The molar mass of hydrogen ($\mathrm{H_2}$) gas is 2.0 g mol$^{-1}$.)

A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature is 27 °C. At 03:00 pm, when the temperature is 45°C, the pressure in the tank will be ______ atm. [nearest integer]

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

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

2.0 g of $\mathrm{H_2}$ gas is adsorbed on 2.5 g of platinum powder at 300 K and 1 bar pressure. The volume of the gas adsorbed per gram of the adsorbent is ______ mL.

(Given : $R=0.083$ L bar K$^{-1}$ mol$^{-1}$)

Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas?

100 g of an ideal gas is kept in a cylinder of 416 L volume at 27°C under 1.5 bar pressure. The molar mass of the gas is ______ g mol$^{-1}$. (Nearest integer)

(Given : R = 0.083 L bar K$^{-1}$ mol$^{-1}$)

Geraniol, a volatile organic compound, is a component of rose oil. The density of the vapour is 0.46 gL$^{-1}$ at 257°C and 100 mm Hg. The molar mass of geraniol is ______ g mol$^{-1}$. (Nearest Integer)

[Given : R = 0.082 L atm K$^{-1}$ mol$^{-1}$]

A box contains 0.90 g of liquid water in equilibrium with water vapour at 27°C. The equilibrium vapour pressure of water at 27°C is 32.0 Torr. When the volume of the box is increased, some of the liquid water evaporates to maintain the equilibrium pressure. If all the liquid water evaporates, then the volume of the box must be ______ litre. [nearest integer]

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

(Ignore the volume of the liquid water and assume water vapours behave as an ideal gas.)

The pressure of a moist gas at 27°C is 4 atm. The volume of the container is doubled at the same temperature. The new pressure of the moist gas is ______ $\times10^{-1}$ atm. (Nearest integer)

(Given : The vapour pressure of water at 27°C is 0.4 atm.)

A sealed flask with a capacity of 2 dm$^3$ contains 11 g of propane gas. The flask is so weak that it will burst if the pressure becomes 2 MPa. The minimum temperature at which the flask will burst is ______ °C. [Nearest integer]

(Given: R = 8.3 J K$^{-1}$ mol$^{-1}$, Atomic masses of C and H are 12u and 1u, respectively.) (Assume that propane behaves as an ideal gas.)

A mixture of hydrogen and oxygen contains 40% hydrogen by mass when the pressure is 2.2 bar. The partial pressure of hydrogen is ______ bar. (Nearest Integer)

A 10 g mixture of hydrogen and helium is contained in a vessel of capacity 0.0125 m$^3$ at 6 bar and 27°C. The mass of helium in the mixture is ______ g. (nearest integer)

Given: R = 8.3 J K$^{-1}$ mol$^{-1}$ (Atomic masses of H and He are 1 u and 4 u, respectively)

For a real gas at 25°C temperature and high pressure (99 bar) the value of compressibility factor is 2, so the value of Vander Waal's constant 'b' should be ______ $\times10^{-2}$ L mol$^{-1}$ (Nearest integer)

(Given R = 0.083 L bar K$^{-1}$mol$^{-1}$)

'x' g of molecular oxygen (O$_2$) is mixed with 200 g of neon (Ne). The total pressure of the non-reactive mixture of O$_2$ and Ne in the cylinder is 25 bar. The partial pressure of Ne is 20 bar at the same temperature and volume. The value of 'x' is _______.

[Given: Molar mass of O$_2$ = 32 g mol$^{-1}$. Molar mass of Ne = 20 g mol$^{-1}$]

Combination of temperature and pressure causing the greatest deviation from ideal gas behaviour is;