Chapter 3

\(6.4 \mathrm{~g} \mathrm{SO}_{2}\) at \(0^{\circ} \mathrm{C}\) and \(0.99 \mathrm{~atm}\) pressure occupies a volume of \(2.241 \mathrm{~L}\). Predict which of the following is correct? (a) the gas is ideal (b) the gas is real with intermolecular attraction (c) the gas is real without intermolecular repulsion (d) the gas is real with intermolecular repulsion greater than intermolecular attraction

If increase in temperature and volume of an ideal gas is two times, then the initial pressure \(\mathrm{P}\) changes to (a) \(4 \mathrm{P}\) (b) \(2 \mathrm{P}\) (c) \(\mathrm{P}\) (d) \(3 \mathrm{P}\)

What is the ratio of kinetic energies of \(3 \mathrm{~g}\) of hydrogen and 4 grams of oxygen at \(\mathrm{T}(\mathrm{K}) ?\) (a) \(12: 1\) (b) \(6: 1\) (c) \(1 ; 6\) (d) \(24: 1\)

The van der Waals equation of state is $$ \mathrm{P}+\frac{(\mathrm{V}-\mathrm{nb})}{\mathrm{V}^{2}}=\mathrm{nRT} $$ The pressure exerted by individual gas molecules on the walls of the container depends upon the (a) frequency of the collisions of the molecules with the walls as well as the momentum imparted by the molecules to the walls (b) frequency of molecular collision (c) mean free path of the molecules (d) momentum and critical pressure of the gas molecules

The density of a gas is \(1.964 \mathrm{~g} \mathrm{dm}^{-3}\) at \(273 \mathrm{~K}\) and \(76 \mathrm{~cm} \mathrm{Hg}\). The gas is (a) \(\mathrm{CH}_{4}\) (b) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (c) \(\mathrm{CO}_{2}\) (d) \(\mathrm{Xe}\)

Two gas bulbs \(\mathrm{A}\) and \(\mathrm{B}\) are connected by a tube having a stopcock. Bulb A has a volume of \(100 \mathrm{~mL}\) and contains hydrogen. After opening the gas from \(A\). to the evacuated bulb \(\mathrm{B}\), the pressure falls down by \(40 \%\). The volume \((\mathrm{mL}\) ) of \(\mathrm{B}\) must be (a) 75 (b) 150 (c) 125 (d) 200

At \(27^{\circ} \mathrm{C}, 500 \mathrm{~mL}\) of helium diffuses in 30 minutes. What is the time (in hours) taken for \(1000 \mathrm{~mL}\) of \(\mathrm{SO}_{2}\) to diffuse under same experimental conditions? (a) 240 (b) 340 (c) 200 (d) 440

If two moles of an ideal gas at a temperature \(546 \mathrm{~K}\), occupy a volume of \(44.8\) litres its pressure must be (a) \(4 \mathrm{~atm}\) (b) \(3 \mathrm{~atm}\) (c) \(2 \mathrm{~atm}\) (d) 1 atm

Containers A and B have same gases. Pressure, volume and temperature of \(\mathrm{A}\) are all twice that of \(\mathrm{B}\), then the ratio of number of molecules of \(\mathrm{A}\) and \(\mathrm{B}\) are (a) \(1: 2\) (b) 2 (c) \(1: 4\) (d) 4

In Haber's process, \(30 \mathrm{~L}\) of dihydrogen and \(30 \mathrm{~L}\) of dinitrogen were taken for reaction which yielded only \(50 \%\) of expected product. What is the composition of the gaseous mixture under afore-said conditions in the end? (a) \(20 \mathrm{~L} \mathrm{NH}_{3}, 25 \mathrm{~L} \mathrm{~N}_{2}, 15 \mathrm{~L} \mathrm{H}_{2}\) (b) \(20 \mathrm{~L} \mathrm{NH}_{3}, 20 \mathrm{~L} \mathrm{~N}_{2}, 20 \mathrm{~L} \mathrm{H}_{2}\) (c) \(10 \mathrm{~L} \mathrm{NH}_{3}, 25 \mathrm{~L} \mathrm{~N}_{2}, 15 \mathrm{~L} \mathrm{H}_{2}\) (d) \(20 \mathrm{~L} \mathrm{NH}_{3}, 10 \mathrm{~L} \mathrm{~N}_{2}, 30 \mathrm{~L} \mathrm{H}_{2}\)

If the rms velocity of a gas at \(100 \mathrm{~K}\) is \(10^{4} \mathrm{~cm} \mathrm{sec}^{-1}\), what is the temperature (in \({ }^{\circ} \mathrm{C}\) ) at which the rms velocity will be \(3 \times 10^{4} \mathrm{~cm} \sec ^{-1} ?\) (a) 900 (b) 627 (c) 327 (d) 1217

A solution has a 1: 4 mole ratio of pentane to hexane. The vapour pressures of the pure hydrocarbons at \(20^{\circ} \mathrm{C}\) are \(400 \mathrm{~mm} \mathrm{Hg}\) for pentane and \(120 \mathrm{~mm} \mathrm{Hg}\) for hexane. The mole fraction of pentane in the vapour phase would be (a) \(0.200\) (b) \(0.549\) (c) \(0.786\) (d) \(0.478\)

At what temperature, the rate of diffusion of \(\mathrm{N}_{2}\) would be \(1.625\) times the rate of effusion of \(\mathrm{SO}_{2}\) at \(50^{\circ} \mathrm{C}\) ? (a) \(110 \mathrm{~K}\) (b) \(173 \mathrm{~K}\) (c) \(373 \mathrm{~K}\) (d) \(273 \mathrm{~K}\)

\(0.24 \mathrm{~g}\) of a volatile gas upon vaporization gives \(45 \mathrm{~mL}\) vapour at NTP. What will be the vapour density of the substances? (density of \(\mathrm{H}_{2}=1\) ) (a) \(95.39\) (b) \(5.973\) (c) \(95.93\) (d) \(59.73\)

A monoatomic ideal gas undergoes a process in which the ratio of \(\mathrm{P}\) to \(\mathrm{V}\) at any instant is constant and equals to 1 . What is the molar heat capacity of the gas? (a) \(4 \mathrm{R} / 2\) (b) \(3 \mathrm{R} / 2\) (c) \(5 \mathrm{R} / 2\) (d) 0

\(\mathrm{X} \mathrm{mL}\) of \(\mathrm{H}_{2}\) has effused through a hole in a container in 5 seconds. The time taken for the effusion of the same volume of the gas specified below under identical conditions is (a) 10 seconds : \(\mathrm{He}\) (b) 20 seconds : \(\mathrm{O}_{2}\) (c) 25 seconds : \(\mathrm{CO}\) (d) 55 seconds : \(\mathrm{CO}_{2}\)

The ratio between the root mean square velocity 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) \(\frac{1}{4}\)

If \(\mathrm{C}_{1}, \mathrm{C}_{2}, \mathrm{C}_{3} \ldots \ldots \ldots\) represents the speed of \(\mathrm{n}_{1}\), \(\mathrm{n}_{2}, \mathrm{n}_{3}, \ldots\) molecules, then the root mean square of speed is (a) \(\left(\frac{\mathrm{n}_{1} \mathrm{C}_{1}^{2}+\mathrm{n}_{2} \mathrm{C}_{2}^{2}+\mathrm{n}_{3} \mathrm{C}_{3}^{2}+\ldots}{\mathrm{n}_{1}+\mathrm{n}_{2}+\mathrm{n}_{3}+\ldots}\right)^{1 / 2}\) (b) \(\left(\frac{n_{1} C_{1}^{2}+n_{2} C_{2}^{2}+n_{3} C_{3}^{2}+\ldots}{n_{1}+n_{2}+n_{3}+\ldots}\right)^{2}\) (c) \(\frac{\left(\mathrm{n}_{1} \mathrm{C}_{1}^{2}\right)^{1 / 2}}{\mathrm{n}_{1}}+\frac{\left(\mathrm{n}_{2} \mathrm{C}_{2}^{2}\right)^{1 / 2}}{\mathrm{n}_{2}}+\frac{\left(\mathrm{n}_{3} \mathrm{C}_{3}^{2}\right)^{1 / 2}}{\mathrm{n}_{3}}+\ldots\) (d) \(\left[\frac{\left(\mathrm{n}_{1} \mathrm{C}_{1}+\mathrm{n}_{2} \mathrm{C}_{2}+\mathrm{n}_{3} \mathrm{C}_{3}+\ldots\right)^{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}+\mathrm{n}_{3}+\ldots}\right]^{1 / 2}\)

If Vrms of \(\mathrm{H}_{2}\) at \(300 \mathrm{~K}\) is \(1.9 \times 10^{3} \mathrm{~m} / \mathrm{s}\). What is the value of Vrms of \(\mathrm{O}_{2}\) at \(1200 \mathrm{~K} ?\) (a) \(1.9 \times 10^{3}\) (b) \(3.8 \times 10^{3} \mathrm{~m} / \mathrm{s}\) (c) \(0.475 \times 10^{3} \mathrm{~m} / \mathrm{s}\) (d) \(0.95 \times 10^{3} \mathrm{~m} / \mathrm{s}\)

The average velocity of ideal gas molecules at \(27^{\circ} \mathrm{C}\) is \(0.3 \mathrm{~m} / \mathrm{sec}\). The average velocity at \(927^{\circ} \mathrm{C}\) will be (a) \(0.6 \mathrm{~m} / \mathrm{sec}\) (b) \(0.3 \mathrm{~m} / \mathrm{sec}\) (c) \(0.9 \mathrm{~m} / \mathrm{sec}\) (d) \(3.0 \mathrm{~m} / \mathrm{sec}\)

The rate of diffusion of methane at a given temperature is twice that of a gas \(\mathrm{X}\). The molecular weight of \(\mathrm{X}\) is (a) \(64.0\) (b) \(32.0\) (c) \(4.0\) (d) \(8.0\)

Equal masses of methane and hydrogen are mixed in an empty container at \(25^{\circ} \mathrm{C}\). The fraction of the total pressure exerted by hydrogen is (a) \(1 / 2\) (b) \(8 / 9\) (c) \(1 / 9\) (d) \(16 / 17\)

Helium atom is two times heavier than a hydrogen molecule. At \(298 \mathrm{~K}\), the average kinetic energy of a helium atom is (a) same as that of a hydrogen molecule (b) half that of a hydrogen molecule (c) two times that of a hydrogen molecule (d) four times that of a hydrogen molecule

A \(2.24\) L cylinder of oxygen at NTP is found to develop a leakage. When the leakage was plugged the pressure dropped to \(570 \mathrm{~mm}\) of \(\mathrm{Hg}\). The number of moles of gas that escaped will be (a) \(0.050\) (b) \(0.025\) (c) \(0.075\) (d) \(0.01\)

A balloon having weight \(50 \mathrm{~kg}\) is filled with \(685.2 \mathrm{~kg}\) of helium gas at \(760 \mathrm{~mm}\) pressure and \(25^{\circ} \mathrm{C}\). What will be its pay load if it displaces \(5108 \mathrm{~kg}\) of air? (a) \(4372.8 \mathrm{~kg}\) (b) \(4392.6 \mathrm{~kg}\) (c) \(4444.4 \mathrm{~kg}\) (d) \(3482.9 \mathrm{~kg}\)

For non-zero value of force of attraction between gas molecules, gas equation will be (a) \(\mathrm{PV}=\mathrm{n} \mathrm{RT}-\frac{\mathrm{n}^{2}}{\mathrm{~V}} \mathrm{a}\) (b) \(\mathrm{PV}=\mathrm{nRT}+\mathrm{nbP}\) (c) \(\mathrm{P}=\frac{\mathrm{nRT}}{\mathrm{V}-\mathrm{b}}\) (d) \(\mathrm{PV}=\mathrm{nRT}\)

Four rubber tubes are respectively filled with \(\mathrm{H}_{2}\), He, \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2} .\) Which tube will be reinflated first? (a) \(\mathrm{H}_{2}\) filled tube (b) \(\mathrm{N}_{2}\) filled tube (c) He filled tube (d) \(\mathrm{O}_{2}\) filled tube

One litre of gas \(\mathrm{A}\) at 2 atm pressure at \(27^{\circ} \mathrm{C}\) and two litres of gas \(\mathrm{B}\) at \(3 \mathrm{~atm}\) pressure at \(127^{\circ} \mathrm{C}\) are mixed in a 4 litre vessel. The temperature of the mixture is maintained at \(327^{\circ} \mathrm{C}\). What is the total pressure of the gaseous mixture? (a) \(3.93 \mathrm{~atm}\) (b) \(3.25 \mathrm{~atm}\) (c) \(4.25 \mathrm{~atm}\) (d) \(6.25 \mathrm{~atm}\)

The maximum number of molecules is present in (a) \(15 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas at STP (b) \(5 \mathrm{~L}\) of \(\mathrm{N}\), gas at \(\mathrm{STP}\) (c) \(0.5 \mathrm{~g}\) of \(\mathrm{H}_{2}\) gas (d) \(10 \mathrm{~g}\) of \(\mathrm{O}_{2}\) gas

The root mean square velocity of one mole of a monoatomic gas having molar mass \(\mathrm{M}\) is \(u_{\mathrm{rms}}\). The relation between the average kinetic energy (E) of the gas and \(u_{r m}\) is (a) \(\mathrm{u}_{\mathrm{rm}}=\sqrt{(3 \mathrm{E} / 2 \mathrm{M})}\) (b) \(\mathrm{u}_{\mathrm{ms}}=\sqrt{(2 \mathrm{E} / 3 \mathrm{M})}\) (c) \(\mathrm{u}_{\mathrm{mas}}=\sqrt{(2 \mathrm{E} / \mathrm{M})}\) (d) \(u_{\operatorname{me}}=\sqrt{(E / 3 M)}\)

Positive deviation from ideal behaviour takes place because of (a) molecular interaction between atoms and \(\frac{\mathrm{PV}}{\mathrm{nRT}}>1\) (b) molecular interaction between atoms and \(\frac{\mathrm{PV}}{\mathrm{nRT}}<1\) (c) finite size of atoms and \(\frac{\mathrm{PV}}{\mathrm{nRT}}>1\) (d) finite size of atoms and \(\frac{\mathrm{PV}}{\mathrm{nRT}}<1\)

At a certain temperature for which \(\mathrm{RT}=25 \mathrm{~L}\) atm. \(\mathrm{mol}^{-1}\), the density of a gas, in \(\mathrm{g} \mathrm{L}^{-1}\), is \(\mathrm{d}=2.00 \mathrm{P}+\) \(0.020 \mathrm{P}^{2}\), where \(\mathrm{P}\) is the pressure in atmosphere. The molecular weight of the gas in \(\mathrm{g} \mathrm{mol}-1\) is (a) 60 (b) 75 (c) 50 (d) 35

At \(100^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\), if the density of liquid water is \(1.0 \mathrm{~g} \mathrm{~cm}^{-3}\) and that of water vapour is \(0.0006 \mathrm{~g} \mathrm{~cm}^{-3}\), then the volume occupied by water molecules in 1 litre of steam at that temperature (a) \(6 \mathrm{~cm}^{3}\) (b) \(60 \mathrm{~cm}^{3}\) (c) \(0.6 \mathrm{~cm}^{3}\) (d) \(0.06 \mathrm{~cm}^{3}\)

The compressibility factor of a gas is less than unity at STP. Therefore (a) \(\mathrm{V}_{\mathrm{m}}>22.4 \mathrm{~L}\) (b) \(\mathrm{V}_{=}<22.4 \mathrm{~L}\) (c) \(\mathrm{V}_{\mathrm{m}}=22.4 \mathrm{~L}\) (d) \(\mathrm{V}_{\mathrm{a}}=44.8 \mathrm{~L}\)

The rms velocity of hydrogen is \(\sqrt{7}\) times the rms velocity of nitrogen. If \(T\) is the temperature of the gas (a) \(\mathrm{T}\left(\mathrm{H}_{2}\right)=\mathrm{T}\left(\mathrm{N}_{2}\right)\) (b) \(\mathrm{T}\left(\mathrm{H}_{2}\right)>\mathrm{T}\left(\mathrm{N}_{2}\right)\) (c) \(\mathrm{T}\left(\mathrm{H}_{2}\right)<\mathrm{T}\left(\mathrm{N}_{2}\right)\) (d) \(\mathrm{T}\left(\mathrm{H}_{2}\right)=\sqrt{7} \mathrm{~T}\left(\mathrm{~N}_{2}\right)\)

The following statement (s) is (are) correct (1) A plot of log KP versus \(1 / \mathrm{T}\) is linear (2) A plot of log \((\mathrm{X})\) versus time is linear for a first order reaction \(\mathrm{X} \longrightarrow \mathrm{P}\) (3) A plot of log P versus \(1 / \mathrm{T}\) is linear at constant volume (4) A plot of P versus \(1 / V\) is linear at constant temperature. (a) 1,2 (b) 2,4 (c) 2,3 (d) 1,4

Equal weights of ethane and hydrogen are mixed in an empty container at \(25^{\circ} \mathrm{C}\). The fraction to total pressure exerted by hydrogen is (a) \(1: 2\) (b) \(1: 1\) (c) \(1: 16\) (d) \(15: 16\)

The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is (a) \(1: 1.086\) (b) \(2: 1.086\) (c) \(1.086: 1\) (d) \(1.086: 2\)

Equal weights 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 (a) \(1 / 2\) (b) \(2 / 3\) (c) \(1 / 3 \times 273 / 298\) (d) \(1 / 3\)

An L.PG. cylinder contains \(15 \mathrm{~kg}\) of butane gas at \(27^{\circ} \mathrm{C}\) and 10 atmospheric pressure. It was leaking and its pressure fell down to 8 atmospheric pressure after one day. The gas leaked in 5 days is (a) \(10 \mathrm{~kg}\) (b) \(3 \mathrm{~kg}\) (c) \(15 \mathrm{~kg}\) (d) \(12 \mathrm{~kg}\)

The partial pressure of oxygen in a flask containin \(16 \mathrm{~g} \mathrm{O}_{2}\) and \(32 \mathrm{~g} \mathrm{SO}_{2}\) is (a) \(1 / 16\) of total pressure (b) \(1 / 2\) of total pressure (c) \(2 / 3\) of total pressure (d) none of the above

Match the following: List I List II 1\. Critical temperature (i) \(\mathrm{a} / \mathrm{R}_{\mathrm{b}}\) 2\. Boyle's temperature (ii) \(2 \mathrm{a} / \mathrm{R}_{\mathrm{b}}\) 3\. Inversion temperature (iii) \(\mathrm{T} / \mathrm{T}_{4}\) 4\. Reduced temperature (iv) \(8 a / 27 \mathrm{R}\) The correct matching is 1 2 4 (a) (ii) (iv) (i) (iii) (b) (iv) (i) (ii) (iii) (c) (iii) (ii) (i) (iv) (d) (iv) (iii) (ii) (i)

A gas cylinder has \(370 \mathrm{~g}\) of oxygen at \(298 \mathrm{~K}\) and 30 atm pressure. If the cylinder was heated upto \(348 \mathrm{~K}\) then the valve were held open until the gas pressure was 1 atm and the temperature remains \(348 \mathrm{~K}\). What mass of oxygen would escape in this condition? (a) \(349 \mathrm{~g}\) (b) \(359 \mathrm{~g}\) (c) \(329 \mathrm{~g}\) (d) \(339 \mathrm{~g}\)

A \(200 \mathrm{~mL}\) flask having oxygen at \(220 \mathrm{~mm}\) and a \(300 \mathrm{~mL}\) flask having nitrogen at \(100 \mathrm{~mm}\) are connected in such a way that \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\) may combine in their volumes, if temperature is kept constant. Find the total pressure of the gaseous mixture. (a) \(158 \mathrm{~mm}\) (b) \(138 \mathrm{~mm}\) (c) \(148 \mathrm{~mm}\) (d) \(168 \mathrm{~mm}\)

Pick out the correct statements of the following about liquids? (a) The intermolecular forces of attraction in a liquid are high. (b) All liquids suffer cooling on evaporation. (c) Lower the boiling point of a liquid, greater the vapour pressure at room temperature. (d) At higher altitudes water boils at a higher temperature than at the sea level.

Kinetic energy per mole of an ideal gas is (a) Zero at zero Kelvin temperature (b) Independent of temperature (c) Proportional to the absolute temperature of the gas (d) Proportional to pressure at constant temperature

Mark the correct statements (a) At low pressure, the van der Waal's equation is written as $$ \left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^{2}}\right) \times \mathrm{V}=\mathrm{RT} $$ (b) When \(\mathrm{Z}>1\), at STP, \(\mathrm{V}_{\text {ral }}>\mathrm{V}_{\text {iddal }}\) (c) Mean free path of \(\mathrm{O}_{2}\) is greater than that of \(\mathrm{H}_{2}\). (d) At \(273 \mathrm{~K}\), the total kinetic energy of \(\mathrm{O}_{2}\) will be eight times that of one mole of \(\mathrm{He}\).

Which of the following statement(s) is/are incorrect? (a) A gas can be liquefied at a temperature ' \(\mathrm{T}\) ' such that \(\mathrm{T}<\mathrm{T}_{c}\) and \(\mathrm{p}=\mathrm{P}_{\mathrm{C}}-\mathrm{T}_{\mathrm{c}}\) and \(\mathrm{P}_{\mathrm{c}}\) are critical tem- perature and pressure. (b) Rise in the compressibility factor with increasing pressure is due to equal contribution of both a and b (Van der Waal's parameter). (c) The fraction of molecules having speeds in the range of \(\mathrm{u}\) to \(\mathrm{u}+\) du of a gas of molar mass ' \(\mathrm{M}\) ' at temperature ' \(\mathrm{T}\) ' is the same as that of gas of molar mass ' \(2 \mathrm{M}^{\prime}\) at temperature ' \(\mathrm{T} / 2^{\prime}\) (d) The product of pressure and volume of a fixed amount of a gas is independent of temperature.

If a real gas follows equation \(\mathrm{P}(\mathrm{V}-\mathrm{nb})=\mathrm{RT}\) at low pressure, then for a graph between d/P vs. P, (where \(\mathrm{d}\) is the density of gas) (a) Intercept is \(\frac{\mathrm{MR}}{\mathrm{T}}\) (b) Intercept is \(\frac{\mathrm{M}}{\mathrm{RT}}\) (c) Slope is \(-\frac{b}{M(R T)^{2}}\) (d) Slope is \(-\frac{\mathrm{Mb}}{(\mathrm{RT})^{2}}\)

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) \(1: 2\)