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

\( 100 \, \text{g} \) of an ideal gas is kept in a cylinder of \( 416 \, \text{L} \) volume at \( 27^\circ \mathrm{C} \) under \( 1.5 \, \text{bar} \) pressure. The molar mass of the gas is ________ \( \text{g mol}^{-1} \). (Nearest integer)
(Given : \( R = 0.083 \, \text{L bar K}^{-1} \, \text{mol}^{-1} \) )

A home owner uses \( 4.00 \times 10^{3} \; \mathrm{m^{3}} \) of methane \( \mathrm{(CH_4}) \) 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 \( x \) is __________. (Nearest integer)
(Given \( R = 0.083 \; \mathrm{L\,atm\,K^{-1}\,mol^{-1}} \))

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Amongst He, Ne, Ar and Kr. \( 1 \,\mathrm{g} \) of activated charcoal adsorbs more of Kr.
Reason R: The critical volume \( V_c \left( \mathrm{cm^3 \, mol^{-1}} \right) \) and critical pressure \( P_c \) \( \left( \mathrm{atm} \right) \) 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:

Arrange the following gases in increasing order of vander Waals constant \( 'a' \)
A. \( \mathrm{Ar} \) B. \( \mathrm{CH_4} \) C. \( \mathrm{H_2O} \) D. \( \mathrm{C_6H_6} \)
Choose the correct option from the following:

For a real gas at \( 25^\circ \mathrm{C} \) temperature and high pressure (\( 99 \) bar) the value of compressibility factor is \( 2 \), so the value of Vander Waal’s constant ‘b’ should be ______ \( \times 10^{-2} \, \mathrm{L \, mol^{-1}} \) (Nearest integer)
(Given \( R = 0.083 \, \mathrm{L \, bar \, K^{-1} \, mol^{-1}} \) )

A selected flask with a capacity of \( 2 \, \text{dm}^3 \) contains \( 11 \, \text{g} \) of propane gas. The flask is so weak that it will burst if the pressure becomes \( 2 \, \text{MPa} \). The minimum temperature at which the flask will burst is ________ \( ^\circ\text{C} \). [Nearest integer]
(Given : \( R = 8.3 \, \text{J K}^{-1} \text{ mol}^{-1} \), Atomic masses of C and H are \( 12u \) and \( 1u \), respectively) (Assume that propane behaves as an ideal gas)

The volume occupied by \\( 4.75 \, \text{g} \\) of acetylene gas at \\( 50^\circ \text{C} \\) and \\( 740 \, \text{mmHg} \\) pressure is ______ \\( \text{L} \\). (Rounded off to the nearest integer)
[Given \\( R = 0.0826 \, \text{L atm K}^{-1} \text{mol}^{-1} \\)]

An empty LPG cylinder weights \( 14.8 \, \text{kg} \). When full, it weights \( 29.0 \, \text{kg} \) and shows a pressure of \( 3.47 \, \text{atm} \). In the course of use at ambient temperature, the mass of the cylinder is reduced to \( 23.0 \, \text{kg} \). The final pressure inside the cylinder is ____ \( \text{atm} \). (Assume LPG to be an ideal gas)

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

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

\( 2\mathrm{SO_2(g)} + \mathrm{O_2(g)} \longrightarrow 2\mathrm{SO_3(g)} \)
The above reaction is carried out in a vessel starting with partial pressures \( P_{\mathrm{SO_2}} = 250 \, \mathrm{m\,bar} \), \( P_{\mathrm{O_2}} = 750 \, \mathrm{m\,bar} \) and \( P_{\mathrm{SO_3}} = 0 \, \mathrm{bar} \). When the reaction is complete, the total pressure in the reaction vessel is ___________ \( \mathrm{m\,bar} \). (Round off to the Nearest Integer).

Three bulbs are filled with \( \mathrm{CH_4} \), \( \mathrm{CO_2} \) and \( \mathrm{Ne} \) as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout, the pressure of the system is found to be ________ \( \text{atm} \). (Nearest integer)

The number of chlorine atoms in \( 20 \ \text{mL} \) of chlorine gas at STP is ________ \( \times 10^{21} \). (Round off to the Nearest Integer) [Assume chlorine is an ideal gas at STP \( R = 0.083 \ \text{L bar mol}^{-1}\text{K}^{-1}, \ N_A = 6.023\times 10^{23} \)]

At constant temperature, a gas is at a pressure of \( 940.3 \, \text{mm Hg} \). The pressure at which its volume decreases by \( 40\% \) is ________ \( \text{mm Hg} \). (Nearest integer)

Which one of the following is the correct \( PV \) vs \( P \) plot at constant temperature for an ideal gas? (\( P \) and \( V \) stand for pressure and volume of the gas respectively)

At \( 363 \, \text{K} \), the vapour pressure of A is \( 21 \, \text{kPa} \) and that of B is \( 18 \, \text{kPa} \). One mole of A and \( 2 \) moles of B are mixed. Assuming that this solution is ideal, the vapour pressure of the mixture is _______ \( \text{kPa} \). (Round off to the Nearest Integer).

Based on the given figure, the number of correct statement/s is/are ________.

A. Surface tension is the outcome of equal attractive and repulsive forces acting on the liquid molecule in bulk.
B. Surface tension is due to uneven forces acting on the molecules present on the surface.
C. The molecule in the bulk can never come to the liquid surface.
D. The molecules on the surface are responsible for vapour pressure if the system is a closed system.

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

An evacuated glass vessel weighs \( 40.0 \, \text{g} \) when empty, \( 135.0 \, \text{g} \) when filled with a liquid of density \( 0.95 \, \text{mL}^{-1} \) and \( 40.5 \, \text{g} \) when filled with an ideal gas at \( 0.82 \, \text{atm} \) at \( 250 \, \text{K} \). The molar mass of the gas in \( \text{g mol}^{-1} \) is: (Given: \( R = 0.082 \, \text{L atm K}^{-1} \, \text{mol}^{-1} \))

At \( 300 \, \mathrm{K} \), a sample of \( 3.0 \, \mathrm{g} \) of gas A occupies the same volume as \( 0.2 \, \mathrm{g} \) of hydrogen at \( 200 \, \mathrm{K} \) at the same pressure. The molar mass of gas A is _______ \( \mathrm{g \, mol^{-1}} \). (nearest integer) Assume that the behavior of gases as ideal. (Given: The molar mass of hydrogen (\( \mathrm{H_2} \)) gas is \( 2.0 \, \mathrm{g \, mol^{-1}} \).)

The formula of a gaseous hydrocarbon which requires \( 6 \) times of its own volume of \( \mathrm{O}_2 \) for complete oxidation and produces \( 4 \) times its own volume of \( \mathrm{CO}_2 \) is \( \mathrm{C}_x \mathrm{H}_y \). The value of \( y \) is _________.

A \( 10 \, \text{g} \) mixture of hydrogen and helium is contained in a vessel of capacity \( 0.0125 \, \text{m}^3 \) at \( 6 \, \text{bar} \) and \( 27^\circ \text{C} \). The mass of helium in the mixture is ______ g. (nearest integer) Given : \( R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} \) (Atomic masses of H and He are \( 1u \) and \( 4u \), respectively)

A mixture of hydrogen and oxygen contains \( 40\% \) hydrogen by mass when the pressure is \( 2.2 \, \mathrm{bar} \). The partial pressure of hydrogen is _______ bar. (Nearest Integer)

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

Geraniol, a volatile organic compound, is a component of rose oil. The density of the vapour is \( 0.46 \, \text{g L}^{-1} \) at \( 257^\circ \text{C} \) and \( 100 \, \text{mm Hg} \). The molar mass of geraniol is ________ \( \text{g mol}^{-1} \) (Nearest Integer)
[Given : \( R = 0.082 \, \text{L atm K}^{-1} \text{ mol}^{-1} \)]

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JEE Main 2022 26th July Morning Shift

A mixture of hydrogen and oxygen contains \( 40\% \) hydrogen by mass when the pressure is \( 2.2 \, \mathrm{bar} \). The partial pressure of hydrogen is _______ bar. (Nearest Integer)