Chapter 3

A gas, which obeys Boyle's law, Charle's law, Avogadro's law etc., or ideal gas equation \(\mathrm{PV}=\mathrm{nRT}\) under all conditions of temperature and pressure, is called ideal gas. No gas is ideal. All gases are real gases. The real gas obeys these gas laws only when the temperature is high or pressure is low. The extent of derivations of a real gas form ideal behaviour is expressed in terms of compressibility factor \(Z\) defined as \(\mathrm{Z}=\frac{\mathrm{PV}}{\mathrm{nRT}}\) Real gases have characteristic temperatures like critical temperature, inversion temperature and Boyle temperature. These temperatures can be calculated using van der Waal constants. Density of two gases of same molecular weight are in the ratio \(1: 3\) and their temperatures are in the ratio \(3: 2 .\) The ratio of respective pressures is (a) \(2: 1\) (b) \(2: 3\) (c) \(3: 2\) (d) \(1: 2\)

In the given sample of a gas all molecules do not possess same speed. Due to frequent molecular collisions, the molecules move with ever changing speeds and also with changing direction. There are three types of velocities (i) root mean square velocity (ii) average velocity and (iii) most probable velocity. Relation between the three types of velocities, i.e., most probable velocity : average velocity: root mean square velocity is (a) \(\sqrt{3}: \sqrt{2}: \sqrt{\frac{8}{\pi}}\) (b) \(\sqrt{3}: \sqrt{2}: \sqrt{8}\) (c) \(\sqrt{2}: \sqrt{(8 / \pi)}: \sqrt{3}\) (d) \(1: 2: 3\)

In the given sample of a gas all molecules do not possess same speed. Due to frequent molecular collisions, the molecules move with ever changing speeds and also with changing direction. There are three types of velocities (i) root mean square velocity (ii) average velocity and (iii) most probable velocity. Oxygen has a density of \(1.429 \mathrm{gm} / \mathrm{L}\) at STP. The RMS velocity of \(\mathrm{O}_{2}\) molecules in \(\mathrm{cms}_{-1}\) (a) \(4.61 \times 10_{3}\) (b) \(4.16 \times 10_{3}\) (c) \(46.1 \times 10_{3}\) (d) \(6.41 \times 10_{3}^{3}\)

In the given sample of a gas all molecules do not possess same speed. Due to frequent molecular collisions, the molecules move with ever changing speeds and also with changing direction. There are three types of velocities (i) root mean square velocity (ii) average velocity and (iii) most probable velocity. By how may folds the temperature of the gas would increase when the RMS velocity of gas molecules in a container of fixed volume is increased from \(5 \times 10^{4} \mathrm{~cm}\) \(\sec ^{-1}\) to \(10 \times 10^{4} \mathrm{~cm} \sec -1 ?\) (a) 6 times (b) 4 times (c) 2 times (d) 8 times

Match the following Column-I (A) \(U_{r x}\) (B) \(U_{m}\) (C) \(U_{w v}^{m}\) (D) \(\sqrt{P}\) Column-II (p) \(\frac{\mathrm{dRT}}{\mathrm{M}}\) (q) \(\sqrt{\frac{2.5 \mathrm{RT}}{\mathrm{M}}}\) (r) \(\sqrt{\frac{3 \mathrm{P}}{\mathrm{d}}}\) (s) \(\sqrt{\frac{8 \mathrm{P}}{\pi \mathrm{d}}}\) (t) \(\sqrt{\frac{2 \mathrm{RT}}{\mathrm{M}}}\)

Match the following Column-I (a) Boyle's law (b) Charles' law (c) Graham's law (d) Ideal gas Column-II (p) \(\log \mathrm{P}=-\log \mathrm{V}+\) constant (q) \(\mathrm{r}=\frac{\mathrm{K} \cdot \mathrm{P}}{\sqrt{\mathrm{M}}}\) (r) \(\mathrm{d}=\frac{\mathrm{PM}}{\mathrm{RT}}\)

Match the following Column-I (a) Compressibility factor, \(\mathrm{Z}=1\) (b) Compressibility factor, \(Z>1\) (c) Compressibility factor, \(Z<1\) (d) Boyle temperature Column-II (p) Attractive forces dominate (q) \(\mathrm{PV}=\mathrm{nRT}\) (r) Repulsive forces dominate (s) Attractive force and repulsive forces cancel each other (t) Gas is less compressible

A man weigh \(72.15 \mathrm{~kg}\) and want to fly in the sky with the aid of balloons itself weighing \(20 \mathrm{~kg}\) and each containing 50 moles of \(\mathrm{H}_{2}\) gas at \(0.05 \mathrm{~atm}\) and \(27^{\circ} \mathrm{C}\). If the density of air at the given conditions is \(1.25 \mathrm{~g} / \mathrm{L}\), how many such types of balloons he is needed to fly in the sky.

The ration between the r.m.s velocity of \(\mathrm{H}_{2}\) at \(50 \mathrm{~K}\) ad that of \(\mathrm{O}_{2}\) at \(800 \mathrm{~K}\) is

A gas at \(350 \mathrm{~K} 15\) atm has a molar volume 12 percent smaller than that calculated from the perfect gas law. Compressibility factor under these conditions can be expressed in scientific notation as \(88 \times 10^{-\mathrm{x}}\). The value of \(x\) is

Ar and He are both gases at room temperature. The average molecular velocity of He atoms is \(x\) times of the average molecular velocity of Ar atoms at this temperature. The numerical value of \(x\) is

If a mixture of 3 mole of \(\mathrm{H}_{2}\) and 1 mole of \(\mathrm{N}_{2}\) is completely converted into \(\mathrm{NH}_{3}\), what would be the ratio of the initial and final volume at same temperature and pressure?

For an ideal gas, number of mole per litre in terms of its pressure \(\mathrm{P}\), temperature \(\mathrm{T}\) and gas constant \(\mathrm{R}\) is [2002] (a) \(\mathrm{PT} / \mathrm{R}\) (b) PRT (c) \(\mathrm{P} / \mathrm{RT}\) (d) \(\mathrm{RT} / \mathrm{P}\)

Based on kinetic theory of gases following laws can be proved: [2002] (a) Boyle's law (b) Charles law (c) Avogadro's law (d) All of these

According to the kinetic theory of gases, in an ideal gas, between two successive collisions the gas molecules travels (a) in a circular path (b) in a wavy path (c) in a straight line path (d) with an accelerated velocity

As the temperature is raised from \(20^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\), the average kinetic energy of neon atoms changes by a factor of which of the following? [2004] (a) \(1 / 2\) (b) 2 (c) \(\sqrt{3} 13 / 293\) (d) \(313 / 293\)

In van der Waals equation of state of the gas law, the constant 'b' is a measure of (a) intermolecular attraction (b) intermolecular repulsions (c) intermolecular collision per unit volume (d) volume occupied by the molecules

For which of the following parameters the structural isomers \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) and \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) would be expected to have the same vaules? (assume ideal behaviour) [2004] (a) gaseous densities at the same temperature and pressure (b) heat of vaporization (c) boiling points (d) vapour pressure at the same temperature

Which one of the following statement is not true about the effect of an increase in temperature on the distribution molecular speeds in a gas? (a) the most probable speed increases (b) the fraction of the molecules with the most probable speed increases (c) the distribution becomes broader (d) the area under the distribution curve remains the same as the under the lower temperature

Equal masses of methane and oxygen are mixed in an empty container at \(25^{\circ} \mathrm{C}\). The fraction of the total pressure exerted by oxygen is [2007] (a) \(1 / 3 \times 273 / 298\) (b) \(1 / 3\) (c) \(1 / 2\) (d) \(2 / 3\)

'a' and 'b' are van der Wall's constants for gases. Chlorine is more easily liquefied than ethane because [2011] (a) a for \(\mathrm{Cl}_{2}<\mathrm{a}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\) but \(\mathrm{b}\) for \(\mathrm{Cl}_{2}>\mathrm{b}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\) (b) a and \(\mathrm{b}\) for \(\mathrm{Cl}_{2}<\mathrm{a}\) and \(\mathrm{b}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\) (c) a and \(\mathrm{b}\) for \(\mathrm{Cl}_{2}>\mathrm{a}\) and \(\mathrm{b}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\) (d) a for \(\mathrm{Cl}_{2}>\mathrm{a}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\) but \(\mathrm{b}\) for \(\mathrm{Cl}_{2}<\mathrm{b}\) for \(\mathrm{C}_{2} \mathrm{H}_{6}\)

The compressibility factor for a real gas at high pressure is - (a) \(1+\mathrm{Pb} / \mathrm{RT}\) (b) \(1+\mathrm{RT} / \mathrm{Pb}\) (c) 1 (d) \(1-\mathrm{Pb} / \mathrm{RT}\)

For gaseous state if most probable speed is denoted \(\mathrm{C}^{*}\), average speed by \(\overline{\mathrm{C}}\) and and mean square speed by C, then for a large number of molecules the ratios of these speeds are: (a) \(C^{*}: \overline{\mathrm{C}}: \mathrm{C}=1: 128: 1.225\) (b) \(\mathrm{C}^{*}: \overline{\mathrm{C}}=1: 1.225: 1.128\) (c) \(\mathrm{C}^{*}: \overline{\mathrm{C}}: \mathrm{C}=1.225: 1.128: 1\) (d) \(\mathrm{C}^{*}: \overline{\mathrm{C}}: \mathrm{C}=1.128: 1.225: 1\)

If \(Z\) is a compressibility factor, van der Waals equation at low pressure can be written as: [2014] (a) \(\mathrm{Z}=1-\frac{\mathrm{Pb}}{\mathrm{RT}}\) (b) \(\mathrm{Z}=1+\frac{\mathrm{Pb}}{\mathrm{RT}}\) (c) \(\mathrm{Z}=1+\frac{\mathrm{RT}}{\mathrm{Pb}}\) (d) \(Z=1+\frac{a}{V R T}\)

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is \(1: 4\). The ratio of number of their molecule is: (a) \(1: 8\) (b) \(3: 16\) (c) \(1: 4\) (d) \(7: 32\)

The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is \([2015]\) (a) Ion-ion interaction (b) Ion-dipole interaction (c) London force (d) Hydrogen bond

Two closed bulbs of equal volume \((V)\) containing an ideal gas initially at pressure \(P\) and temperature \(T_{1}\) are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to \(T_{2}\). The final pressure \(p_{f}\) is [2016] (a) \(2 p_{i}\left(\frac{T_{1}}{T_{1}+T_{2}}\right)\) (b) \(2 p_{i}\left(\frac{T_{2}}{T_{1}+T_{2}}\right)\) (c) \(2 p_{i}\left(\frac{T_{1} T_{2}}{T_{1}+T_{2}}\right)\) (d) \(p_{i}\left(\frac{T_{1} T_{2}}{T_{1}+T_{2}}\right)\)