Chapter 3

A manometer is connected to a gas containing bulb. The open arm reads \(53.3 \mathrm{~cm}\) whereas the arm connected to the bulb reads \(15.6 \mathrm{~cm}\). If the barometric pressure is \(763 \mathrm{~mm}\) mercury, what is the pressure of gas, in atm? (a) \(1.05 \mathrm{~atm}\) (b) \(1.5 \mathrm{~atm}\) (c) \(0.51 \mathrm{~atm}\) (d) \(1.91\) atm

The pressure outside a jet plane flying at high altitude falls considerably below atmospheric pressure at sea level. The air inside the cabin must therefore be pressurized to protect the passengers. What is the pressure (in atmosphere) in the cabin if the barometer reading is \(688 \mathrm{~mm}\) of \(\mathrm{Hg}\) ? (a) \(0.905 \mathrm{~atm}\) (b) \(6.88\) atm (c) \(9.05 \mathrm{~atm}\) (d) data, insufficient

A diver ascends quickly to the surface from the bottom of a lake of depth \(H\) metre. During this period, he neither exhales nor inhales air. Assuming constant temperature, what would be the fractional increase in volume of his lungs? The atmospheric pressure is \(7 H\) metre of water. (a) \(\frac{1}{8}\) (b) \(\frac{7}{8}\) (c) \(\frac{8}{7}\) (d) \(\frac{1}{7}\)

A \(2 \mathrm{~m}\) long tube closed at one end is lowered vertically into water until the closed end is flush with the water surface. See figure. Calculate the water level height in the tube. (Barometric pressure \(=1\) atm \(=10 \mathrm{~m}\) of hydrostatic water head. Temperature \(=25^{\circ} \mathrm{C}\), Density of water \(1.00 \mathrm{~g} / \mathrm{ml}\). Neglect water vapour pressure) (a) \(1.01 \mathrm{~m}\) (b) \(0.29 \mathrm{~m}\) (c) \(1.71 \mathrm{~m}\) (d) \(0.92 \mathrm{~m}\)

At a constant temperature a gas occupies a volume of \(200 \mathrm{ml}\) at a pressure of \(0.720\) bar. It is subjected to an external pressure of \(0.900\) bar. What is the resulting volume of the gas? (a) \(160 \mathrm{ml}\) (b) \(320 \mathrm{ml}\) (c) \(80 \mathrm{~m} .\) (d) \(400 \mathrm{ml}\)

At \(0^{\circ} \mathrm{C}\) and a pressure of \(1000 \mathrm{~mm}\), a given weight of nitrogen occupies a volume of \(1.0\) 1. At \(-100^{\circ} \mathrm{C}\), the same weight of gas under the same pressure occupies a volume of \(0.61\). What is the value of absolute zero in degree celsius? (a) \(-250^{\circ} \mathrm{C}\) (b) \(250^{\circ} \mathrm{C}\) (c) \(-273^{\circ} \mathrm{C}\) (d) \(273^{\circ} \mathrm{C}\)

In the outer space, the pressure recorded is \(5 \times 10^{-4}\) torr. How much outer space could be compressed into \(1 \mathrm{dm}^{3}\) box at a pressure of 1 atm? (a) \(1.52 \times 10^{16} \mathrm{dm}^{3}\) (b) \(4.56 \times 10^{16} \mathrm{dm}^{3}\) (c) \(2.28 \times 10^{6} \mathrm{dm}^{3}\) (d) \(1.14 \times 10^{16} \mathrm{dm}^{3}\)

Two flasks \(\mathrm{A}\) and \(\mathrm{B}\) of \(\mathrm{I} 1\) capacity each contains \(\mathrm{SO}_{2}\) and \(\mathrm{Br}_{2}\) gases, respectively, maintained at \(340 \mathrm{~K}\) and pressure of \(1.5\) atm. If number of \(\mathrm{Br}_{2}\) molecules in flask \(\mathrm{B}\) is \(N\), the total number of atoms in flask A will be (a) \(\underline{N}\) (b) \(2 N\) (c) \(N / 2\) (d) \(3 N\)

A sample of gas at \(35^{\circ} \mathrm{C}\) and 1 atmospheric pressure occupies a volume of 3.75 1. At what temperature should the gas be kept, if it is required to reduce the volume to \(3.01\) at the same pressure? (a) \(-26.6^{\circ} \mathrm{C}\) (b) \(0^{\circ} \mathrm{C}\) (c) \(3.98^{\circ} \mathrm{C}\) (d) \(28^{\circ} \mathrm{C}\)

One day, when the temperature and pressure were \(300 \mathrm{~K}\) and \(760 \mathrm{~mm}\), a mass of gas had a volume of \(1200 \mathrm{ml}\). On the next day, the volume had changed to \(1218 \mathrm{ml}\) while the pressure was the same. What was the temperature on the next day? (a) \(546 \mathrm{~K}\) (b) \(304.5 \mathrm{~K}\) (c) \(31.5 \mathrm{~K}\) (d) \(300 \mathrm{~K}\)

If the pressure of a certain amount of a gas increases by \(1 \%\) on heating by \(1^{\circ} \mathrm{C}\) at constant volume, its initial temperature must be (a) \(100 \mathrm{~K}\) (b) \(100^{\circ} \mathrm{C}\) (c) \(250 \mathrm{~K}\) (d) \(250^{\circ} \mathrm{C}\)

A gas has a volume of \(V \mathrm{~cm}^{3}\) at \(10^{\circ} \mathrm{C}\). If the pressure is doubled, at what temperature will the volume still be \(V \mathrm{~cm}^{3}\) ? (a) \(273^{\circ} \mathrm{C}\) (b) \(300^{\circ} \mathrm{C}\) (c) \(283^{\circ} \mathrm{C}\) (d) \(293^{\circ} \mathrm{C}\)

A bottle of cold drink has \(200 \mathrm{ml}\) of liquid in which concentration of \(\mathrm{CO}_{2}\) is \(0.1 \mathrm{M}\). If \(\mathrm{CO}_{2}\), behaves as ideal gas, the volume of \(\mathrm{CO}_{2}^{\circ}\) at \(0^{\circ} \mathrm{C}\) and 1 atm equivalent to the one in cold drink is (a) \(0.2241\) (b) \(0.4481\) (c) \(0.1121\) (d) \(4.481\)

A pre-weighed vessel was filled with oxygen at NTP and weighed. It was then evacuated, filled with \(\mathrm{SO}_{2}\) at the same temperature and pressure, and again weighed. The mass of oxygen will be (a) the same as that of \(\mathrm{SO}_{2}\) (b) half that of \(\mathrm{SO}_{2}\) (c) twice that of \(\mathrm{SO}_{2}\) (d) one-fourth of \(\mathrm{SO}_{2}\)

According to Avogadro's hypothesis, equal volumes of all gases under the same conditions of temperature and pressure will contain (a) the same number of molecules (b) different number of molecules (c) the same number of molecules only if their molecular masses are equal (d) the same number of molecules if their densities are equal

If at top of a hill \(2000 \mathrm{~m}\) above sea level, the atmospheric pressure is \(50 \mathrm{~cm}\) of \(\mathrm{Hg}\) and at the sea level the atmospheric pressure is \(74.5 \mathrm{~cm}\) of \(\mathrm{Hg}\), and you need as much oxygen to breath at sea level as on the top of the hill, how much faster need you breathe on the hill top? (a) \(2.44\) times (b) \(1.49\) times (c) 5 times (d) 7 times

Four \(1-1\) flasks are separately filled with the gas hydrogen, helium, oxygen and ozone at the same room temperature and pressure. The ratio of total number of atoms of these gases present in the different flasks would be (a) \(1: 1: 1: 1\) (b) \(1: 2: 2: 3\) (c) \(2: 1: 2: 3\) (d) \(1: 2: 2: 1\)

At \(0^{\circ} \mathrm{C}\) the density of nitrogen at 1 atm is \(1.25 \mathrm{~kg} / \mathrm{m}^{3}\). The nitrogen which occupied \(1500 \mathrm{ml}\) at \(0^{\circ} \mathrm{C}\) and 1 atm was compressed at \(0^{\circ} \mathrm{C}\) and 575 atm and the gas volume was observed to be \(3.92 \mathrm{ml}\), in violation of Boyle's law. What was the final density of this non-ideal gas? (a) \(278 \mathrm{~kg} / \mathrm{m}^{3}\) (b) \(378 \mathrm{~kg} / \mathrm{m}^{3}\) (c) \(478 \mathrm{~kg} / \mathrm{m}^{3}\) (d) \(578 \mathrm{~kg} / \mathrm{m}^{3}\)

Reducing the pressure from \(1.0\) atm to \(0.5\) atm would change the number of molecules in one mole of ammonia to (a) \(75 \%\) of initial value (b) \(50 \%\) of initial value (c) \(25 \%\) of initial value (d) None of these

The ratio of universal gas constant and molar mass of gas is called molar gas constant. The value of molar gas constant is greater for (a) He (b) \(\mathrm{N}_{2}\) (c) \(\mathrm{H}_{2}\) (d) same for all

The pressure exerted on walls of a \(3 \mathrm{~L}\) flask when \(7 \mathrm{~g}\) of \(\mathrm{N}_{2}\) is introduced into it at \(300 \mathrm{~K}\) should be (assume ideal behaviour of gas) (a) zero (b) \(2.05 \mathrm{~atm}\) (c) \(4.10 \mathrm{~atm}\) (d) \(207.85\) atm

An amount of 1 mole of a gas is changed from its initial state \((20 \mathrm{~L}, 2 \mathrm{~atm})\) to final state (4L, \(10 \mathrm{~atm}\) ), respectively. If the change can be represented by a straight line in \(P-V\) curve, the maximum temperature achieved by the gas in the process is \((R=0.08 \mathrm{~L}-\mathrm{atm} / \mathrm{K}-\mathrm{mol})\) (a) \(900^{\circ} \mathrm{C}\) (b) \(900 \mathrm{~K}\) (c) \(627 \mathrm{~K}\) (d) \(1173^{\circ} \mathrm{C}\)

The drain cleaner, Drainex contains small bits of aluminium which react with caustic soda to produce hydrogen. What volume of hydrogen at \(27^{\circ} \mathrm{C}\) and \(0.831\) bar will be released when \(0.15 \mathrm{~g}\) of aluminium reacts? \((\mathrm{Al}=27)\) (a) \(250 \mathrm{ml}\) (b) \(150 \mathrm{~m} 1\) (c) \(500 \mathrm{ml}\) (d) \(125 \mathrm{ml}\)

A gaseous mixture of three gases \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) has a pressure of \(10 \mathrm{~atm}\). The total number of moles of all the gases is \(10 .\) If the partial pressures of \(\mathrm{A}\) and \(\mathrm{B}\) are \(3.0\) and \(1.0\) atm, respectively, and if \(C\) has molecular mass of \(2.0\), what is the mass of \(\mathrm{C}\), in \(\mathrm{g}\), present in the mixture? (a) 6 (b) 8 (c) 12 (d) 3

If air is pumped slowly but continuously into a metallic cylinder of strong wall, what would happen to the air inside the cylinder? (a) temperature of air would increase (b) pressure of air would increase (c) pressure of air would decrease (d) temperature and pressure of air would increase

At which of the following four conditions, the density of an ideal gas will be maximum? (a) \(273 \mathrm{~K}\) and \(1 \mathrm{~atm}\) (b) \(273 \mathrm{~K}\) and \(2 \mathrm{~atm}\) (c) \(546 \mathrm{~K}\) and 1 atm (d) \(546 \mathrm{~K}\) and \(2 \mathrm{~atm}\)

A vessel contains 1 mole of \(\mathrm{O}_{2}\) gas at a temperature \(T\). The pressure of the gas is \(P\). An identical vessel containing 1 mole of \(\mathrm{He}\) gas at a temperature \(2 T\) has a pressure of (a) \(P / 8\) (b) \(P\) (c) \(2 P\) (d) \(8 P\)

Suppose the inhaled air has partial pressure of water vapour of \(5 \mathrm{~mm} \mathrm{Hg}\) and exhaled air is nearly saturated at body temperature \((310 \mathrm{~K})\) with water vapour. The mass of water lost per day by a person assuming that the normal man breaths 10,000 litre per day. Saturated vapour pressure of water at \(310 \mathrm{~K}\) is \(45 \mathrm{~mm} \mathrm{Hg}\) (a) \(20.68 \mathrm{~g}\) (b) \(372.23 \mathrm{~g}\) (c) \(418.76 \mathrm{~g}\) (d) \(46.53 \mathrm{~g}\)

If the absolute temperature of an ideal gas having volume \(V \mathrm{~cm}^{3}\) is doubled and the pressure is reduced to half, the final volume of gas will be (a) \(0.25 \mathrm{~V}\) (b) \(0.50 \mathrm{~V}\) (c) \(2 V^{2}\) (d) \(4 V\)

Vapour is injected at a uniform rate in a closed vessel which was initially evacuated. The pressure in the vessel (a) increases continuously (b) decreases continuously (c) first increases and then decreases (d) first increases and then becomes constant

The rate of diffusion of two gases \(X\) and \(\mathrm{Y}\) is in the ratio \(1: 5\) and that of \(\mathrm{Y}\) and \(\mathrm{Z}\) in the ratio of \(1: 6 .\) The ratio of the rate of diffusion of \(\mathrm{Z}\) with respect to \(\mathrm{X}\) is (a) \(30 / 1\) (b) \(1 / 30\) (c) \(5 / 6\) (d) \(6 / 5\)

Pressure of \(1 \mathrm{~g}\) of an ideal gas \(\mathrm{A}\) at \(27^{\circ} \mathrm{C}\) is found to be 2 bar. When \(2 \mathrm{~g}\) of another ideal gas \(\mathrm{B}\) is introduced in the same flask at same temperature the pressure becomes 3 bar. What is the relationship between their molecular masses? (a) \(2 M_{\mathrm{B}}=M_{\mathrm{A}}\) (b) \(M_{\mathrm{B}}=M_{\mathrm{A}}\) (c) \(M_{\mathrm{B}}=4 M_{\mathrm{A}}\) (d) \(M_{\mathrm{B}}=2 M_{\mathrm{A}}\)

A compound exists in the gaseous phase both as monomer (A) and dimer (B). The molecular mass of \(\mathrm{A}\) is \(48 .\) In an experiment, \(96 \mathrm{~g}\) of the compound was confined in a vessel of volume \(33.61\) and heated to \(546 \mathrm{~K} .\) What is the pressure developed if the compound exists as dimer to the extent of \(50 \%\) by weight under these conditions? (a) \(2 \mathrm{~atm}\) (b) \(4 \mathrm{~atm}\) (c) \(3 \mathrm{~atm}\) (d) \(0.5 \mathrm{~atm}\)

Which among the following has rate of effusion less than the moist air? (a) \(\mathrm{He}\) (b) Dry air (c) \(\mathrm{NH}_{3}\) (d) heavy hydrogen

A mixture of \(\mathrm{CH}_{4}\) and \(\mathrm{HBr}\), in a vessel are allowed to effuse out through a small hole at the same temperature. What is the mole fraction of \(\mathrm{CH}_{4}\), if the initial rates of effusion are the same for both gases? (a) \(0.31\) (b) \(0.44\) (c) \(0.5\) (d) \(0.16\)

A container contains certain gas of mass \(m\) at high pressure. Some of the gas has been allowed to escape from the container. After some time, the pressure of the gas becomes half and its absolute temperature two-third. The amount of the gas escaped is (a) \(2 \mathrm{~m} / 3\) (b) \(\mathrm{m} / \mathrm{2}\) (c) \(\mathrm{m} / 4\) (d) \(m / 6\)

In a glass tube of uniform cross section, a mixture of \(\mathrm{HCl}\) and \(\mathrm{He}\) gases are sent from one end and a mixture of \(\mathrm{NH}_{3}\) and Ar gases are sent from the another end, at the same time. The white fumes of \(\mathrm{NH}_{4} \mathrm{Cl}\) will appear first (a) at the middle of the tube (b) closer to \(\mathrm{NH}_{3}\) end (c) closer to \(\mathrm{HCl}\) end (d) at the \(\mathrm{NH}_{3}\) end

A perfectly expandable balloon filled with helium gas at \(27^{\circ} \mathrm{C}\) and a pressure of \(720 \mathrm{~mm}\) of \(\mathrm{Hg}\) has a volume of \(100 \mathrm{l}\). The balloon rises to an altitude where the pressure is \(420 \mathrm{~mm}\) of \(\mathrm{Hg}\) and the temperature \(-53^{\circ} \mathrm{C}\). What is the change in the volume of the balloon? (a) 161 (b) \(25.71\) (c) 481 (d) \(15.71\)

If Avogadro's number were to tend to infinity, the phenomenon of Brownian motion would (a) remain completely unaffected (b) become more vigorous than that observed with the present finite value of Avogadro's number, for all sizes of the Brownian particles (c) become more vigorous than that observed with the present finite value of Avogadro's number, only for relatively large Brownian particles (d) become practically unobservable, as the molecular impact would tend to balance one another for practically all sizes of Brownian particles

A certain mass of an ideal gas at \(9 \mathrm{~atm}\) and \(30^{\circ} \mathrm{C}\) is first heated to \(131^{\circ} \mathrm{C}\) at constant volume and then the amount of the gas is increased by \(50 \%\) at constant volume and temperature. The final pressure of the gas becomes (a) 9 atm (b) \(4.5 \mathrm{~atm}\) (c) 18 atm (d) \(13.5 \mathrm{~atm}\)

The RMS speed of oxygen molecules in a gas is \(V .\) If the temperature is doubled and the oxygen molecules dissociated into oxygen atoms, the RMS speed will become (a) \(\bar{V}\) (b) \(\sqrt{2} V\) (c) \(2 V\) (d) \(4 V\)

When temperature is increased, the difference between most probable velocity, RMS velocity and average velocity (a) increase (b) decrease (c) remain the same (d) none of these

The partial pressures of \(\mathrm{N}_{2}, \mathrm{O}_{2}\) and \(\mathrm{CO}_{2}\) in a vessel are \(38 \mathrm{~cm}\) of \(\mathrm{Hg}, 190\) torr and \(0.5\) atm, respectively. The total pressure of the mixture at the same temperature is (a) \(0.96 \mathrm{~atm}\) (b) \(1.02 \mathrm{~atm}\) (c) \(1.64\) atm (d) \(1.25 \mathrm{~atm}\)

Assume that air is \(21 \% \mathrm{O}_{2}\) and \(79 \% \mathrm{~N}_{2}\) by volume. If the barometric pressure is \(740 \mathrm{~mm}\), the partial pressure of \(\mathrm{O}_{2}\) is closest to which one of the following (a) \(155 \mathrm{~mm}\) (b) \(310 \mathrm{~mm}\) (c) \(580 \mathrm{~mm}\) (d) \(740 \mathrm{~mm}\)

Equal masses of ethane 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) \(1: 1\) (c) \(1: 16\) (d) \(15: 16\)

Which of the following gas will have the highest value for translational K.E. per g, at the same temperature? (a) methane (b) helium (c) nitrogen (d) same for all

If for two gases of molecular weights \(M_{\mathrm{A}}\) and \(M_{\mathrm{B}}\) at temperature \(T_{\mathrm{A}}\) and \(T_{\mathrm{B}}\), \(T_{\mathrm{A}} M_{\mathrm{B}}=T_{\mathrm{B}} M_{\mathrm{A}}\), then which property has the same magnitude for both the gases? (a) density (b) pressure (c) KE per mole (d) RMS speed

A box of 11 capacity is divided into two equal compartments by a thin partition, which is filled with \(2 \mathrm{~g}\) hydrogen and \(16 \mathrm{~g}\) methane, respectively. The pressure in each compartment is recorded as \(P\) atm. The total pressure when the partition is removed will be (a) \(P\) (b) \(2 P\) (c) \(P / 2\) (d) \(P / 4\)

At what temperature does the average translational \(\mathrm{KE}\) of a molecule in a gas becomes equal to the \(\mathrm{K} . \mathrm{E}\). of an electron accelerated through a \(\mathrm{PD}\) of \(3 \mathrm{~V} ?\) (a) \(232 \mathrm{~K}\) (b) \(2320 \mathrm{~K}\) (c) \(23,200 \mathrm{~K}\) (d) \(2,32,000 \mathrm{~K}\)

A closed vessel contains equal number of nitrogen and oxygen molecules at a pressure of \(P \mathrm{~mm}\). If nitrogen is removed from the system, then the pressure will be (a) \(P\) (b) \(2 P\) (c) \(P / 2\) (d) \(P^{2}\)