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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:

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 \( R = 0.083 \; \mathrm{L\,atm\,K^{-1}\,mol^{-1}} \))

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)

\( 2\mathrm{SO_2(g)} + \mathrm{O_2(g)} \longrightarrow 2\mathrm{SO_3(g)} \)
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).

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 \( R = 0.083 \ \text{L bar mol}^{-1}\text{K}^{-1}, \ N_A = 6.023\times 10^{23} \)]

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).

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 _________.

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)

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JEE Main 2021 31st August Morning Shift

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)