Chapter 3

The number of collisions of \(\mathrm{Ar}\) atoms with the walls of container per unit time (a) increases when the temperature increases. (b) remains the same when \(\mathrm{CO}_{2}\) is added to the container at constant temperature. (c) increases when \(\mathrm{CO}_{2}\) is added to the container at constant temperature. (d) decreases, when the average kinetic energy per molecule is decreased.

The volumes of the two vessels are in the ratio of \(2: 1\). One contains nitrogen and the other oxygen at \(800 \mathrm{~mm}\) and \(680 \mathrm{~mm}\) pressure, respectively. Determine the resulting pressure when they are connected together. (a) \(760 \mathrm{~mm}\) (b) \(670 \mathrm{~mm}\) (c) \(1140 \mathrm{~mm}\) (d) \(1480 \mathrm{~mm}\)

How many times the average speed of the molecules in a gas becomes when the temperature is raised from \(27^{\circ} \mathrm{C}\) to \(159^{\circ} \mathrm{C}\) ? (a) \(1.2\) (b) \(1.44\) (c) \(5.89\) (d) \(2.43\)

A sample of air contains only \(\mathrm{N}_{2}, \mathrm{O}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} .\) It is saturated with water vapour and pressure is 640 torr. The vapour pressure of water is 40 torr and the molar ratio of \(\mathrm{N}_{2}: \mathrm{O}_{2}\) is \(3: 1\). The partial pressure of \(\mathrm{N}_{2}\) in the sample is (a) 540 torr (b) 900 torr (c) 1080 torr (d) 450 torr

Oxygen gas is collected by downward displacement of water in a jar. The level of water inside the jar is adjusted to the height of water outside the jar. When the adjustment is made, the pressure exerted by the oxygen is (a) equal to the atmospheric pressure (b) equal to the vapour pressure of oxygen at that temperature (c) equal to atmospheric pressure plus aqueous tension at that temperature (d) equal to atmospheric pressure minus aqueous tension at that temperature

The most probable kinetic energy of gas molecule is (a) \(k T / 2\) (b) \(3 \mathrm{kT} / 2\) (c) \(k T\) (d) \(k T / 4\)

If the concentration of water vapour in the air is \(1 \%\) and the total atmospheric pressure equals 1 atm, then the partial pressure of water vapour is (a) \(0.1\) atm (b) \(1 \mathrm{~mm} \mathrm{Hg}\) (c) \(7.6 \mathrm{~mm} \mathrm{Hg}\) (d) \(100 \mathrm{~atm}\)

The assumptions of the kinetic theory of gases are most likely to be incorrect for gases under which of the following conditions? (a) High temperature and high pressure (b) High temperature and low pressure (c) Low temperature and low pressure (d) Low temperature and high pressure

A volume of \(190.0 \mathrm{ml}\) of \(\mathrm{N}_{2}\) was collected in a jar over water at some temperature, water level inside and outside the jar standing at the same height. If barometer reads \(740 \mathrm{~mm} \mathrm{Hg}\) and aqueous tension at the temperature of the experiment is \(20 \mathrm{~mm} \mathrm{Hg}\), the volume of the gas at 1 atm pressure and at the same temperature would be (a) \(185.0 \mathrm{ml}\) (b) \(180.0 \mathrm{ml}\) (c) \(195.0 \mathrm{ml}\) (d) \(200 \mathrm{ml}\)

If helium and methane are allowed to diffuse out of the container under the similar conditions of temperature and pressure, then the ratio of rate of diffusion of helium to methane is (a) \(2.0\) (b) \(1.0\) (c) \(0.5\) (d) \(4.0\)

An unknown gas ' \(\mathrm{X}\) ' has rate of diffusion measured to be \(0.88\) times that of \(\mathrm{PH}_{3}\) at the same conditions of temperature and pressure. The gas may be (a) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (b) \(\mathrm{CO}\) (c) \(\mathrm{NO}_{2}\) (d) \(\mathrm{N}_{2} \mathrm{O}\)

In the case of positive deviation from an ideal gas (a) interactions in molecules, \(\frac{P V}{n R T}>1\) (b) interactions in molecules, \(\frac{P V}{n R T}<1\) (c) finite size of molecules, \(\frac{P V}{n R T}>1\) (d) finite size of molecule, \(\frac{P V}{n R T}<1\)

A gas with formula \(\mathrm{C}_{n} \mathrm{H}_{2 n+2}\) diffuses through the porous plug at a rate onesixth of the rate of diffusion of hydrogen gas under similar conditions. The formula of gas is (a) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (b) \(\mathrm{C}_{10} \mathrm{H}_{22}\) (c) \(\mathrm{C}_{5} \mathrm{H}_{12}\) (d) \(\mathrm{C}_{6} \mathrm{H}_{14}\)

One mole of each gases \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and \(\mathrm{D}\) with van der Waal's constant \(\left(\mathrm{atm} 1^{2} \mathrm{~mol}^{-2}\right)\) \(1.348,6.823,4.390\) and \(2.438\), respec- tively, are kept separately in four different vessels of equal volumes at identical temperature. Their pressures are observed to be \(P_{A}, P_{\mathrm{B}}, P_{\mathrm{C}}\) and \(P_{\mathrm{D}}\), respectively. On the basis of this data alone, the order of pressure of gases is (assume other van der Waal's constant to be nearly same for all gases) (a) \(P_{\mathrm{A}}

A balloon is filled with \(\mathrm{N}_{2} \mathrm{O}\) is pricked with a sharp point and quickly plunged into a tank of \(\mathrm{CO}_{2}\) under the same pressure and temperature. The balloon will (a) be enlarged (b) shrink (c) remain unchanged in size (d) collapse completely

When the pressure of a sample of gas is increased from \(0.50\) to \(100 \mathrm{~atm}\) at constant temperature, its volume decreases from \(2.01\) to \(13 \mathrm{ml}\). What could cause the deviation from Boyle's law? (a) Volume of the gas molecules is a significant fraction of the volume of container at higher pressure. (b) The force of attraction between the gas molecules is greater when the pressure is higher. (c) The molecules are dimerized at the higher pressure. (d) The collision of the molecules on the walls of the container are no longer elastic at higher pressure.

A volume of \(180 \mathrm{~m}\) of hydrocarbon takes \(15 \mathrm{~min}\) to diffuse. Under the same conditions \(120 \mathrm{ml}\) of sulphur dioxide takes 20 min. The molecular weight of hydrocarbon is (a) 16 (b) 32 (c) 48 (d) 64

The ratio of root mean square speed of \(\mathrm{H}_{2}\) at \(50 \mathrm{~K}\) and that of \(\mathrm{O}_{2}\) at \(800 \mathrm{~K}\) is (a) 4 (b) 2 (c) 1 (d) \(1 / 4\)

The virial form of van der Waal's gas equation is \(P V=R T\left(1+\frac{B}{V}+\frac{C}{V^{2}}+\ldots\right)\) \(=R T\left(1+B^{\prime} P+C^{\prime} P^{2}+\ldots\right) .\) The sec- ond virial coefficient of argon gas at \(262.5 \mathrm{~K}\) is \(-11 \mathrm{~mol}^{-1}\). What is the density of argon gas at \(262.5 \mathrm{~K}\) and \(1 \mathrm{~atm}\) ? Neglect all the terms after second term in the virial forms, under these condition. \((R=0.08 \mathrm{~L}-\mathrm{atm} / \mathrm{K}-\mathrm{mol}, \mathrm{Ar}=40)\) (a) \(2.0 \mathrm{~g} / 1\) (b) \(1.905 \mathrm{~g} / \mathrm{l}\) (c) \(1.818 \mathrm{~g} / 1\) (d) \(1.964 \mathrm{~g} / \mathrm{l}\)

The molecules of a given mass of a gas have RMS speed of \(200 \mathrm{~m} / \mathrm{s}\) at \(300 \mathrm{~K}\) and \(1,00,000\) bar pressure. When the absolute temperature is doubled and the pressure is halved, the RMS speed of molecules will become (a) \(200 \mathrm{~m} / \mathrm{s}\) (b) \(400 \mathrm{~m} / \mathrm{s}\) (c) \(100 \mathrm{~m} / \mathrm{s}\) (d) \(200 \sqrt{2} \mathrm{~m} / \mathrm{s}\)

At moderate pressure, the compressibility factor for a gas is given as: \(Z=1+0.35 P\) \(-\frac{168}{T} \cdot P\), where \(P\) is in bar and \(T\) is in Kelvin. What is the Boyle's temperature of the gas? (a) \(168 \mathrm{~K}\) (b) \(480 \mathrm{~K}\) (c) \(58.8 \mathrm{~K}\) (d) \(575 \mathrm{~K}\)

At STP, the order of the RMS speed of molecules of \(\mathrm{H}_{2}, \mathrm{~N}_{2}, \mathrm{O}_{2}\) and HBr gases is (a) \(\mathrm{H}_{2}>\mathrm{N}_{2}>\mathrm{O}_{2}>\mathrm{HBr}\) (b) \(\mathrm{HBr}>\mathrm{O}_{2}>\mathrm{N}_{2}>\mathrm{H}_{2}\) (c) \(\mathrm{HBr}>\mathrm{H}_{2}>\mathrm{O}_{2}>\mathrm{N}_{2}\) (d) \(\mathrm{N}_{2}>\mathrm{O}_{2}>\mathrm{H}_{2}>\mathrm{HBr}\)

Two gases \(\mathrm{X}\) and \(\mathrm{Y}\) have their molecular speed in ratio of \(3: 1\) at certain temperature. The ratio of their molecular masses \(M_{x}: M_{y}\) is (a) \(1: 3\) (b) \(3: 1\) (c) \(1: 9\) (d) \(9: 1\)

At what temperature will the total translational kinetic energy of \(0.30\) mole of He gas be the same as the total translational kinetic energy of \(0.40 \mathrm{~mol}\) of \(\overline{\mathrm{Ar}}\) at \(400 \mathrm{~K} ?\) (a) \(533 \mathrm{~K}\) (b) \(400 \mathrm{~K}\) (c) \(300 \mathrm{~K}\) (d) \(266 \mathrm{~K}\)

Critical temperatures of for \(\mathrm{NO}, \mathrm{CO}_{2}\) and \(\mathrm{CCl}_{4}\) are \(177 \mathrm{~K}, 304\) and \(550 \mathrm{~K}\), respectively. Which gas is more close to ideal behaviour at \(300 \mathrm{~K}\) ? (a) NO (b) \(\mathrm{CO}_{2}\) (c) \(\mathrm{CCl}_{4}\) (d) Unpredictable

Gases do not liquefy above the critical temperature because above critical temperature (a) the gases become ideal. (b) the intermolecular attraction vanishes. (c) the kinetic energy of molecules become so large that the attractive forces become unable to hold the molecules together. (d) the repulsive forces dominates in the molecules.

Consider three identical flasks with differ- ent gases: Flask A: \(\mathrm{CO}\) at 760 torr and \(273 \mathrm{~K}\) Flask \(\mathrm{B}: \mathrm{N}_{2}\) at 250 torr and \(273 \mathrm{~K}\) Flask \(\mathrm{C}: \mathrm{H}_{2}\) at 100 torr and \(273 \mathrm{~K}\) In which flask will the molecules have the greatest average kinetic energy per mole? (a) \(\overline{\mathrm{A}}\) (b) \(\underline{B}\) (c) \(\mathrm{C}\) (d) same in all

A gas can never be liquefied at (a) \(T=T_{C}\) and \(P=P_{c}\) (b) \(TT_{C}\) and \(P \gg P_{\mathrm{c}}\)

A gas container observes Maxwellian distribution law of speed. If the number of molecules between the speed \(5.0\) and \(5.1 \mathrm{~km}\) per sec at \(298 \mathrm{~K}\) is \(N\), what would be number of molecules between this range of speed if the total number of molecules in the vessel are doubled? (a) \(2 N\) (b) \(N\) (c) \(2 N^{2}\) (d) \(N^{2} / 2\)

A real gas obeying van der Waal's equation will resemble ideal gas if the constants (a) \(a\) and \(b\) are small (b) \(a\) is large and \(b\) is small (c) \(a\) is small and \(b\) is large (d) \(a\) and \(b\) are large

The behaviour of a real gas is usually depicted by plotting compressibility factor \(Z\) versus \(P\) at a constant temperature. At high temperature and high pressure, \(Z\) is usually more than \(1 .\) This fact can be explained by van der Waal's equation when (a) the constant \(a\) is negligible and not \(b\) (b) the constant \(b\) is negligible and not \(a\) (c) both constants \(a\) and \(b\) are negligible (d) both constants \(a\) and \(b\) arenot negligible

The van der Waal's equation for \((1 / 2)\) mole of a gas (a) \(\left(P+\frac{a}{V^{2}}\right)(V-b)=R T\) (b) \(\left(P+\frac{a}{4 V^{2}}\right)\left(V-\frac{b}{2}\right)=\frac{R T}{2}\) (c) \(\left(P+\frac{a}{4 V^{2}}\right)\left(\frac{V-b}{2}\right)=R T\) (d) \(\left(P+\frac{a}{4 V^{2}}\right)\left(\frac{V-b}{2}\right)=2 R T\)

The \(P V-P\) isotherms of 1 mole of different gases at \(273 \mathrm{~K}\), if the limit of pressure tending to zero, converge to a value of \(P V=\) (a) \(11.21\) -atm (b) \(22.41\) -atm (c) zero (d) \(22.41\)

Only the vapours of a liquid exist (a) below boiling point (b) below critical temperature (c) below inversion temperature (d) above critical temperature

The correct order of the values of critical temp, \(T_{\mathrm{c}}\); Boyle temp, \(T_{\mathrm{B}}\) and inversion temp, \(T_{i}\) of a real gas is (a) \(T_{\mathrm{C}}