## PRACTICE SET-1 STATE OF MATTERS

### STATE OF MATTERS

#### EXERCISE-1

#### BOYLE'S LAW, CHARLE'S LAW AVOGADRO'S LAW AND GAY-LUSSAC'S LAW

Q.1 An open flask containing air is heated from \(300 \mathrm{~K}\) to \(500 \mathrm{~K}\). What percentage of air will be escaped to the atmosphere, if pressure is keeping constant?

(1) 80

(2) 40

(3) 60

(4) 20

Q.2 At \(27^{\circ} \mathrm{C}\) a sample of ammonia gas exerts a pressure of \(5.3 \mathrm{~atm}\). What is the pressure when the volume of the gas is reduced to one-tenth of the original value at the same temperature ?

(1) \(0.53 \mathrm{~atm}\)

(2) \(5.3 \mathrm{~atm}\)

(3) \(53 \mathrm{~atm}\)

(4) None of these

Q.3 Three flasks of equal volumes contain \(\mathrm{CH}_{4}, \mathrm{CO}_{2}\) and \(\mathrm{Cl}_{2}\) gases respectively. They will contain equal number of molecules if -

(1) the mass of all the gases is same

(2) the moles of all the gas is same but temperature is different

(3) temperature and pressure of all the flasks are same

(4) temperature, pressure and masses same in the flasks

Q.4 If \(500 \mathrm{ml}\) of a gas 'A' at 1000 torr and \(1000 \mathrm{ml}\) of gas \(\mathrm{B}\) at 800 torr are placed in a \(2 \mathrm{~L}\) container, the final pressure will be-(Assume \(\mathrm{T}\) is constant)

(1) 100 torr

(2) 650 torr

(3) 1800 torr

(4) 2400 torr

Q.5 At \(0^{\circ} \mathrm{C}\), the density of a gaseous oxide at 2 bar is same as that of nitrogen at 5 bar. What is the molecular mass of the oxide ?

(1) 70

(2) 210

(3) 35

(4) 52

Q.6 V versus T curves at constant pressure \(\mathrm{P}_{1}\) and \(\mathrm{P}_{2}\) for a fixed amount of an ideal gas are shown in fig. Which is correct -

(1) \(\mathrm{P}_{1}>\mathrm{P}_{2}\)

(2) \(P_{1}<P_{2}\)

(3) \(P_{1}=P_{2}\)

(4) All

**THE IDEAL GAS EQUATION**

Q.7 8.2 L of an ideal gas weight \(9.0\) gm at \(300 \mathrm{~K}\) and 1 atm pressure. The molecular mass of gas is-

(1) 9

(2) 27

(3) 54

(4) 81

Q.8 When the pressure of \(5 \mathrm{~L}\) of \(\mathrm{N}_{2}\) is doubled and its temperature is raised from \(300 \mathrm{~K}\) to \(600 \mathrm{~K}\), the final volume of the gas would be-

(1) \(10 \mathrm{~L}\)

(2) \(5 \mathrm{~L}\)

(3) \(15 \mathrm{~L}\)

(4) \(20 \mathrm{~L}\)

Q.9 At \(100^{\circ} \mathrm{C}\) a gas has 1 atm. pressure and \(10 \mathrm{~L}\) volume. Its volume at NTP would be -

(1) 10 litres

(2) Less than 10 litres

(3) More than 10 litres

(4) None Q.10 The density of oxygen gas at \(25^{\circ} \mathrm{C}\) is \(1.458 \mathrm{mg} /\) litre at one atmosphere. At what pressure will oxygen have the density twice the value-

(1) \(0.5 \mathrm{~atm} / 25^{\circ} \mathrm{C}\)

(2) \(2 \mathrm{~atm} / 25^{\circ} \mathrm{C}\)

(3) \(4 \mathrm{~atm} / 25^{\circ} \mathrm{C}\)

(4) None

Q.11 The density of the gas is equal to

(1) P/RT

(2) \(\mathrm{nP}\)

(3) \(\mathrm{MP} / \mathrm{RT}\)

(4) M/V

**DALTON'S LAW OF PARTIAL PRESSURE**

Q.12 Thepartialpressureofhydrogen in a flask containing 2gm of H_{2} & 32gm of SO_{2}
is -

(1) \(\frac{1}{16}\) of total pressure

(2) \(\frac{1}{2}\) of total pressure

(3) \(\frac{2}{3}\) of total pressure

(4) \(\frac{1}{8}\) of total pressure.

Q.13 A closed vessel contains equal number of oxygen and hydrogen molecules at a total pressure of \(740 \mathrm{~mm}\). If oxygen is removed from the system, the pressure -

(1) Becomes half of \(740 \mathrm{~mm}\).

(3) Becomes \(1 / 9\) th of \(740 \mathrm{~mm}\).

(2) Remains unchanged

(4) Becomes double of \(740 \mathrm{~mm}\).

Q.14 A cylinder is filled with a gaseous mixture containing equal masses of \(\mathrm{CO}\) and \(\mathrm{N}_{2}\). The ratio of their partial pressure is-

(1) \(\mathrm{P}_{\mathrm{N}_{2}}=\mathrm{P}_{\mathrm{CO}}\)

(2) \(\mathrm{P}_{\mathrm{CO}}=0.875 \mathrm{P}_{\mathrm{N} 2}\)

(3) \(\mathrm{P}_{\mathrm{CO}}=2 \mathrm{P}_{\mathrm{N}_{2}}\)

(4) \(\mathrm{P}_{\mathrm{CO}}=\frac{1}{2} \mathrm{P}_{\mathrm{N}_{2}}\)

Q.15 At room temperature Dalton's law of partial pressure is not applicable to -

(1) \(\mathrm{H}_{2}\) and \(\mathrm{N}_{2}\) mixture

(3) \(\mathrm{H}_{2}\) and \(\mathrm{CO}_{2}\) mixture

(2) \(\mathrm{H}_{2}\) and \(\mathrm{Cl}_{2}\) mixture

(4) None

**GRAHAM'S LAW**

Q.16 Which of the following gases will have the highest rate of diffusion?

(1) \(\mathrm{O}_{2}\)

(2) \(\mathrm{NH}_{3}\)

(3) \(\mathrm{CO}_{2}\)

(4) \(\mathrm{N}_{2}\)

Q.17 A gas 'A' having molecular weight 4 diffuses thrice as fast as the gas \(\mathrm{B}\). The molecular weight of gas B is-

(1) 36

(2) 12

(3) 18

(4) 24

Q.18 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 -

(1) 64

(2) 32

(3) 4

(4) 8

Q.19 A gas \(\mathrm{X}\) diffuses three times faster than another gas \(\mathrm{Y}\) at same temperature and pressure the ratio of their densities i.e., \(\mathrm{D}_{\mathrm{x}}: \mathrm{D}_{\mathrm{y}}\) is-

(1) \(\frac{1}{3}\)

(2) \(\frac{1}{9}\)

(3) \(\frac{1}{6}\)

(4) \(\frac{1}{12}\)

Q.20 The increasing order of effusion among the gases, \(\mathrm{H}_{2}, \mathrm{O}_{2}, \mathrm{NH}_{3}\) and \(\mathrm{CO}_{2}\) is-

(1) \(\mathrm{H}_{2}, \mathrm{CO}_{2}, \mathrm{NH}_{3}, \mathrm{O}_{2}\)

(2) \(\mathrm{H}_{2}, \mathrm{NH}_{3}, \mathrm{O}_{2}, \mathrm{CO}_{2}\)

(3) \(\mathrm{H}_{2}, \mathrm{O}_{2}, \mathrm{NH}_{3}, \mathrm{CO}_{2}\)

(4) \(\mathrm{CO}_{2}, \mathrm{O}_{2}, \mathrm{NH}_{3}, \mathrm{H}_{2}\)

Q.21 \(4 \mathrm{gm}\) of sulphur dioxide gas diffuses from a container in \(8 \mathrm{~min}\). Mass of helium gas diffusing from the same container over the same time interval is :

(1) \(0.5 \mathrm{gm}\)

(2) \(1 \mathrm{gm}\)

(3) \(2 \mathrm{gm}\)

(4) None of these

**K.T.G, K.E. \& DIFFERENT VELOCITIES OF GASEOUS MOLECULES**

Q.22 If a gas is expanded at constant temperature-

(1) Number of molecules of the gas decreases

(2) The kinetic energy of the molecule decreases

(3) The kinetic energy of the molecules remains the same

(4) The kinetic energy of the molecules increases

Q.23 The root mean square velocity of hydrogen is \(\sqrt{5}\) times than that of nitrogen. If \(\mathrm{T}\) is the temperature of the gas, then :

(1) \(\mathrm{T}_{\mathrm{H}_{2}}=\mathrm{T}_{\mathrm{N}_{2}}\)

(2) \(\mathrm{T}_{\mathrm{H}_{2}}>\mathrm{T}_{\mathrm{N}_{2}}\)

(3) \(\mathrm{T}_{\mathrm{H}_{2}}<\mathrm{T}_{\mathrm{N}_{2}}\)

(4) \(\mathrm{T}_{\mathrm{H}_{2}}=\sqrt{7} \mathrm{~T}_{\mathrm{N}_{2}}\)

Q.24 Which is not correct in terms of kinetic theory of gases-

(1) Gases are made up of small particles called molecules

(2) The molecules are in random motion

(3) When molecules collide, they lose energy

(4) When the gas is heated, the molecules moves faster

Q.25 The translational kinetic energy of 1 mole of gas is equal to -

(1) \(\frac{3}{2} \mathrm{RT}\)

(2) \(\frac{3}{2} \mathrm{KT}\)

(3) \(\frac{R T}{2}\)

(4) \(\frac{2 R}{3}\)

Q.26 The root mean square speed of \(8 \mathrm{~g}\) of \(\mathrm{He}\) is \(300 \mathrm{~ms}^{-1}\). Total kinetic energy of He gas is :

(1) \(120 \mathrm{~J}\)

(2) \(240 \mathrm{~J}\)

(3) \(360 \mathrm{~J}\)

(4) None of these

Q.27 If the r.m.s. velocity of nitrogen molecules is \(5.15 \mathrm{~ms}^{-1}\) at \(298 \mathrm{~K}\), then a velocity of \(10.30 \mathrm{~ms}^{-1}\) will be possessed at a temp-

(1) \(149 \mathrm{~K}\)

(2) \(172.6 \mathrm{~K}\)

(3) \(596 \mathrm{~K}\)

(4) \(1192 \mathrm{~K}\)

Q.28 Among the following gases which one has the lowest root mean square velocity at \(25^{\circ} \mathrm{C}-\)

(1) \(\mathrm{SO}_{2}\)

(2) \(\mathrm{N}_{2}\)

(3) \(\mathrm{O}_{2}\)

(4) \(\mathrm{Cl}_{2}\)

Q.29 Most probable speed, average speed and rms speed are related as -

(1) \(1: 1.128: 1.224\)

(2) \(1: 1.128: 1.424\)

(3) \(1: 2.128: 1.224\)

(4) \(1: 1.428: 1.442\)

Q.30 Suppose a gas sample having \(6 \times 10^{23}\) molecules. Each \(1 / 3 \mathrm{rd}\) of the molecules have rms speed \(10^{4} \mathrm{~cm} /\) sec, \(2 \times 10^{4} \mathrm{~cm} / \mathrm{sec}\) and \(3 \times 10^{4} \mathrm{~cm} / \mathrm{sec}\). Calculate the rms speed of gas molecules in sample.

(1) \(4.32 \times 10^{4} \mathrm{~cm} / \mathrm{sec}\)

(3) \(2.16 \times 10^{4} \mathrm{~cm} / \mathrm{sec}\)

(2) \(2.16 \times 10^{4} \mathrm{~m} / \mathrm{sec}\)

(4) None

Q.31 The root mean square speed of gas molecules at a temperature \(27 \mathrm{~K}\) and pressure \(1.5\) bar is \(1 \times 10^{4} \mathrm{~cm} /\) sec. If both temperature and pressure are raised three times, calculate the new rms speed of gas molecules.

(1) \(1.73 \times 10^{4} \mathrm{~cm} / \mathrm{sec}\)

(2) \(1.98 \times 10^{4} \mathrm{~cm} / \mathrm{sec}\)

(3) \(2.56 \times 10^{4} \mathrm{~cm} / \mathrm{sec}\)

(4) \(1.32 \times 10^{4} \mathrm{~cm} / \mathrm{sec}\)

Q.32 The average speed of an ideal gas molecule at \(27^{\circ} \mathrm{C}\) is \(0.3 \mathrm{~m} \mathrm{sec}^{-1}\). Calculate average speed at \(927^{\circ} \mathrm{C}\).

(1) \(0.15 \mathrm{~m} / \mathrm{sec}\)

(2) \(1.2 \mathrm{~m} / \mathrm{sec}\)

(3) \(2.4 \mathrm{~m} / \mathrm{sec}\)

(4) \(0.6 \mathrm{~m} / \mathrm{sec}\)

Q.33 Temperature at which most probable speed of \(\mathrm{O}_{2}\) becomes equal to root mean square speed of \(\mathrm{N}_{2}\) is [Given : \(\mathrm{N}_{2}\) at \(427^{\circ} \mathrm{C}\) ]

(1) \(732 \mathrm{~K}\)

(2) \(1200 \mathrm{~K}\)

(3) \(927 \mathrm{~K}\)

(4) \(800 \mathrm{~K}\)

Q.34 The velocity possessed by most of the gaseous molecules is -

(1) Average velocity

(3) R.M.S. velocity

(2) Most probable velocity

(4) None of these.

Q.35 Helium atom is two times heavier than a hydrogen molecule. At \(25^{\circ} \mathrm{C}\) the average K.E. of helium atom is -

(1) Twice that of hydrogen molecule

(2) Same as that of hydrogen molecule

(3) Four times that of hydrogen molecule

(4) Half that of hydrogen molecule

**VANDER WALL EQUATION AND CRITICAL CONSTANTS**

Q.36 The term that accounts for intermolecular force in vander Waal's equation for non ideal gas is -

(1) RT

(2) \(\mathrm{V}-\mathrm{b}\)

(3) \(\left(\mathrm{P}+\mathrm{a} / \mathrm{V}^{2}\right)\)

(4) \([\mathrm{RT}]^{-1}\)

Q.37 The critical temperature of a substance is -

(1) The temperature above which the substance undergoes decomposition

(2) The temperature above which a substance can exist only as a gas

(3) Boiling point of the substance

(4) All are wrong

Q.38 Critical temperature of the gas is the temperature-

(1) Below which it cannot be liquified

(2) Above which it cannot be liquified

(3) At which it occupies \(22.4\) Lof volume

(4) At which one mole of itoccupies volume of \(22.4 \mathrm{~L}\)

Q.39 The units of the Van der Waal's constant ' \(a\) ' are -

(1) \(\operatorname{atm} \mathrm{L}^{2} \mathrm{~mol}^{-2}\)

(2) \(\operatorname{atm} \mathrm{L}^{-2} \mathrm{~mol}^{-2}\)

(3) \(\operatorname{atm~} \mathrm{L} \mathrm{mol}^{-1}\)

(4) \(\operatorname{atm} \mathrm{mol} \mathrm{L}^{-2}\)

Q.40 The units of the van der Waal's constant ' \(b\) ' are -

(1) atmosphere

(2) joules

(3) \(\mathrm{L} \mathrm{mol}^{-1}\)

(4) \(\mathrm{mol} \mathrm{L}^{-1}\) Q.41 The Van der Waal's parameters for gases W, X, Y and Z are -

Q.41 The Van der Waal’s parameters for gases W, X, Y and Z are -

Which one of these gases has the highest critical temperature?

(1) W

(2) X

(3) \(\mathrm{Y}\)

(4) \(Z\)

Q.42 Which of the following expressions between the van der Waals constant \(\mathrm{b}\) and the radius \(r\) of spherical molecules is correct -

(1) \(b=\left(\frac{4}{3} \pi r^{3}\right) N_{A}\)

(2) \(b=\left(\frac{4}{3} \pi r^{3}\right)\)

(3) \(b=2\left(\frac{4}{3} \pi r^{3}\right) N_{A}\)

(4) \(b=4\left(\frac{4}{3} \pi r^{3}\right) N_{A}\)

Q.43 van der Waal's constant 'a' and 'b' are related with respectively.

(1) Attractive force and bond energy of molecules

(2) Attractive force and volume of molecules

(3) volume and repulsive force of molecules

(4) shape and repulsive force of molecules

Q.44 An ideal gas obeying kinetic theory of gases can not be liquefied, because :

(1) It solidifies before becoming a liquid.

(2) Force acting between its molecules are negligible.

(3) Its critical temperature is above \(0^{\circ} \mathrm{C}\)

(4) Its molecules are relatively small in size.

Q.45 Van der Waal's real gas acts as an ideal gas, at which conditions?

(1) High temperature, low pressure

(2) Low temperature, high pressure

(3) High temperature, high pressure

(4) Low temperature, low pressure

Q.46 The critical temperature, Boyle's temperature and inversion temperature respectively are given as:

(1) \(\frac{\mathrm{a}}{\mathrm{Rb}}, \frac{8 \mathrm{a}}{27 \mathrm{Rb}}, \frac{2 \mathrm{a}}{\mathrm{Rb}}\)

(2) \(\frac{8 \mathrm{a}}{27 \mathrm{Rb}}, \frac{\mathrm{a}}{\mathrm{Rb}}, \frac{2 \mathrm{a}}{\mathrm{Rb}}\)

(3) \(\frac{8 \mathrm{a}}{\mathrm{Rb}}, \frac{\mathrm{a}}{\mathrm{Rb}}, \frac{2 \mathrm{a}}{\mathrm{Rb}}\)

(4) \(\frac{\mathrm{a}}{\mathrm{Rb}}, \frac{\mathrm{a}}{27 \mathrm{Rb}}, \frac{2 \mathrm{a}}{\mathrm{Rb}}\)

Q.47 Temperature above which gas behave ideally over a wide range of pressure is called as :

(1) Boyle's temperature

(2) Inversion temperature

(3) Critical temperature

(4) Kraft temperature

**COMPRESSIBILITY**

Q.48 The value of compression factor at the critical state of a van der Waals gas is -

(1) \(3 / 8\)

(2) \(8 / 3\)

(3) 1

(4) \(5 / 8\)

Q.49 Compressibility factor \((\mathrm{Z})\) for \(\mathrm{N}_{2}\) at \(-50^{\circ} \mathrm{C}\) and 800 atm pressure is \(1.95\) Calculate mole of \(\mathrm{N}_{2}\) gas required to fill a gas cylinder of \(100 \mathrm{~mL}\) capacity under the given conditions.

(1) \(2.24 \times 10^{3}\)

(2) \(22.4\)

(3) \(44.8\)

(4) 2296

Q.50 The compressibility factor for an ideal gas is :

(1) \(1.5\)

(2) \(1.0\)

(3) \(2.0\)

(4) \(\infty\)