A Complete Resource Book in Chemistry for JEE Main

A.K. Singhal

Chapter 3

Energetics - all with Video Answers

Educators

Chapter Questions

Problem 1

Which one of the following statements is wrong for gases?
(a) gases do not have a definite shape and volume
(b) volume of the gas is equal to volume of container the confining the gas
(c) confirmed gas exerts uniform pressure on the walls of its container in all directions
(d) mass of gas cannot be determined by weighing a container in which it is enclosed

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

Which of the following mixture of gases does not obey Dalton's law of partial pressure?
(a) $\mathrm{O}_{2}$ and $\mathrm{CO}_{2}$
(b) $\mathrm{N}_{2}$ and $\mathrm{O}_{2}$
(c) $\mathrm{Cl}_{2}$ and $\mathrm{SO}_{2}$
(d) $\mathrm{NH}_{3}$ and $\mathrm{HCl}$

Narayan Hari

Numerade Educator

Problem 3

In which of the following pairs, the critical temperature of latter gascous species is higher than the first?
(a) $\mathrm{CO}_{2}, \mathrm{H}_{2}$
(b) $\mathrm{H}_{2}, \mathrm{NH}_{3}$
(c) $\mathrm{NH}_{3}, \mathrm{He}$
(d) $\mathrm{CO}_{2}, \mathrm{He}$

Narayan Hari

Numerade Educator

Problem 4

The dimensions of pressure are same as that of
(a) energy
(b) energy per unit volume
(c) force per unit area
(d) force per unit volume

Narayan Hari

Numerade Educator

Problem 5

Ideal gas obeying kinetic theory of gases can be liquefied if
(a) $\mathrm{T}>\mathrm{T}_{s}$
(b) $\mathrm{P}>\mathrm{P}$
(c) $\mathrm{P}>\mathrm{P}_{\varepsilon}$ and $\mathrm{T}<\mathrm{T}_{e}$
(d) it cannot be liquefied at any value of $\mathrm{P}$ and $\mathrm{T}$.

Narayan Hari

Numerade Educator

Problem 6

An ideal gas, obeying kinetic theory of gases cannot be liquefied, because
(a) its critical temperature is above $0^{\circ} \mathrm{C}$
(b) its molecules are relatively small in size
(c) it solidifies before becoming a liquid
(d) forces acting between its molecules are negli-gible.

Narayan Hari

Numerade Educator

Problem 7

Which of the following expressions correctly represents the relationship between the average molar kinetic energy, K.E. of $\mathrm{CO}$ and $\mathrm{N}_{2}$ molecules at the same temperature?
(a) $\overline{\mathrm{K} . \mathrm{E}_{\mathrm{c}} \mathrm{CO}}<\overline{\mathrm{K} \cdot \mathrm{E}}_{\mathrm{N}_{2}}$
(b) $\overline{\mathrm{K} . \mathrm{E}}_{\mathrm{CO}}>\overline{\mathrm{K}} \cdot \mathrm{E}_{\mathrm{N}_{2}}$
(c) $\mathrm{K} \cdot \mathrm{E}_{\mathrm{C} O}=\mathrm{K} \cdot \mathrm{E}_{\mathrm{N}_{2}}$
(d) cannot be predicted unless volumes of the gases are given.

Narayan Hari

Numerade Educator

Problem 8

Which of the following law leads us to arrive at the conclusion that 1 g-molecule of each gas at STP occupies a volume of $22.4 \mathrm{~L}$ ?
(a) Dalton's law
(b) Law of combining volumes
(c) Avogadro's law
(d) Boyle's law

Narayan Hari

Numerade Educator

Problem 9

$0.1$ mole of gas absorbs $41.75 \mathrm{~J}$ of heat, the rise in temperature oecurs $20^{\circ} \mathrm{C}$, the gas must be
(a) triatomic
(b) diatomic
(c) monoatomic
(d) (b) and (c) both

Narayan Hari

Numerade Educator

Problem 10

Which pair of the gases diffuses with the same rate at same temperature and pressure?
(a) $\mathrm{CO}$ and $\mathrm{NO}$
(b) $\mathrm{NO}_{2}$ and $\mathrm{CO}_{2}$
(c) $\mathrm{NH}_{3}$ and $\mathrm{PH}_{3}$
(d) $\mathrm{NO}$ and $\mathrm{C}_{2} \mathrm{H}_{6}$

Narayan Hari

Numerade Educator

Problem 11

Van der Waals real gas, act as an ideal gas, at which condition?
(a) high temperature, low pressure
(b) low temperature, high pressure
(c) high temperature, high pressure
(d) low temperature, low pressure

Narayan Hari

Numerade Educator

Problem 12

The compressibility factor of an ideal gas is
(a) 1
(b) 2
(c) 4
(d) 0

Narayan Hari

Numerade Educator

Problem 13

The temperature below which a gas can be made to liquefy by variation in pressure is called its
(a) inversion temperature
(b) critical temperature
(c) neutral temperature
(d) curie point

Narayan Hari

Numerade Educator

Problem 14

By the ideal gas law the pressure of $0.60 \mathrm{~mol} \mathrm{NH}_{3}$ gas in a $3.00$ litre vessel at $25^{\circ} \mathrm{C}$ is
(a) $48.9 \mathrm{~atm}$
(b) $4.89 \mathrm{~atm}$
(c) $0.489 \mathrm{~atm}$
(d) $489 \mathrm{~atm}$

Narayan Hari

Numerade Educator

Problem 15

At what Centigrade temperature will be the volume of a gas at $0^{\circ} \mathrm{C}$ double of itself, when pressure remains constant?
(a) $0^{\circ} \mathrm{C}$
(b) $273^{\circ} \mathrm{C}$
(c) $273 \mathrm{~K}$
(d) $546 \mathrm{~K}$

Narayan Hari

Numerade Educator

Problem 16

Pressure of a mixture of $4 \mathrm{~g}$ of $\mathrm{O}_{2}$ and $2 \mathrm{~g}$ of $\mathrm{H}_{2}$ confined in a bulb of $1.0 \mathrm{~L}$ capacity at $0^{\circ} \mathrm{C}$ is
(a) $25.18 \mathrm{~atm}$
(b) $31.205$ atm
(c) $40.215 \mathrm{~atm}$
(d) $15.210 \mathrm{~atm}$

Narayan Hari

Numerade Educator

Problem 17

A closed container contains equal number of oxygen and hydrogen molecules at a total pressure of $740 \mathrm{~mm}$. If oxygen is removed from the system then pressure will
(a) become double of $740 \mathrm{~mm}$
(b) become half of $740 \mathrm{~mm}$
(c) become $1 / 9$ of $740 \mathrm{~mm}$
(d) remain unchanged

Narayan Hari

Numerade Educator

Problem 18

The volume occupied by $9.0 \mathrm{~g}$ of nitrogen gas at $300 \mathrm{~K}$ and $750 \mathrm{mmHg}$ pressure is
(a) $5.854$
(b) $6.7432$
(c) $8.8462$
(d) $8.0225$

Narayan Hari

Numerade Educator

Problem 19

What are the conditions under which the relation between volume $(\mathrm{V})$ and number of moles $(\mathrm{n})$ of gas is plotted? ( $\mathrm{P}=$ pressure; $\mathrm{T}=$ temperature $)$
(a) constant $\mathrm{P}$ and $\mathrm{T}$
(b) constant $\mathrm{T}$ and $\mathrm{V}$
(c) constant $\mathrm{P}$ and $\mathrm{V}$
(d) constant $\mathrm{n}$ and $\mathrm{V}$

Narayan Hari

Numerade Educator

Problem 20

The rms velocity of $\mathrm{CO}_{2}$ at a temperature $\mathrm{T}$ (in Kelvin) is $\times \mathrm{cm} \sec ^{-1} .$ At what temperature (in Kelvin), the rms velocity of nitrous oxide would be $4 \times \mathrm{cm} \mathrm{sec}^{-1} ?$ (Atomic weights of $\mathrm{C}, \mathrm{N}$ and $\mathrm{O}$ are respectively 12,14 and 16 )
(a) $16 \mathrm{~T}$
(b) $2 \mathrm{~T}$
(c) $4 \mathrm{~T}$
(d) $32 \mathrm{~T}$

Narayan Hari

Numerade Educator

Problem 21

"n' moles of an ideal gas at temperature $\mathrm{T}$ (in Kelvin) occupy ' $\mathrm{V}$ ' litres of volume, exerting a pressure of ' $\mathrm{P}^{*}$ atomospheres. What is its concentration (in $\mathrm{mol} \mathrm{L}^{-1}$ )? $(\mathbb{R}=$ gas constant $)$
(a) $\mathrm{P} / \mathrm{RT}$
(b) $\mathrm{PT} / \mathrm{R}$
(c) $\mathrm{RT} / \mathrm{P}$
(d) $\mathrm{R} / \mathrm{PT}$

Narayan Hari

Numerade Educator

Problem 22

7.5 grams of gas occupy $5.6$ litres of volume at STP. The gas is ......... (Atomic weight of $\mathrm{C}, \mathrm{N}$, and $\mathrm{O}$ are 12,14 and 16 respectively)
(a) $\mathrm{NO}$
(b) $\mathrm{N}_{2} \mathrm{O}$
(c) $\mathrm{CO}$
(d) $\mathrm{CO}_{2}$

Narayan Hari

Numerade Educator

Problem 23

A gas diffuses four times as quickly as oxygen. The molar weight of gas is
(a) 2
(b) 4
(c) 8
(d) 16

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 24

Compressibility factor for 1 mol of a van der Waals gas at $0^{\circ} \mathrm{C}$ and 100 atmospheric pressure is found to be $0.5$, the volume of gas molecule is
(a) $2.0224 \mathrm{~L}$
(b) $1.4666 \mathrm{~L}$
(c) $0.8542 \mathrm{~L}$
(d) $0.1119 \mathrm{~L}$

Narayan Hari

Numerade Educator

Problem 25

The density of air is $0.001293 \mathrm{~g} / \mathrm{cc}$ at STP. Its vapour density is
(a) $0.001293$
(b) $8.2786$
(c) $14.48$
(d) $6.2706$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 26

At $27^{\circ} \mathrm{C}$, a closed vessel contains a mixture of equal weights of helium (mol. wt $=4$ ), methane (mol. wt $=16$ ) and sulphur dioxide (mol. wt $=64$ ). The pressure exerted by the mixture is $210 \mathrm{~mm}$. If the partial pressures of helium, methane and sulphur dioxide are $\mathrm{P}_{1}, \mathrm{P}_{2}$ and $\mathrm{P}_{3}$ respectively, which one of the following is correct?
(a) $\mathrm{P}_{3}>\mathrm{P}_{2}>\mathrm{P}_{1}$
(b) $\mathrm{P}_{1}>\mathrm{P}_{2}>\mathrm{P}_{3}$
(c) $\mathrm{P}_{1}>\mathrm{P}_{3}>\mathrm{P}_{2}$
(d) $\mathrm{P}_{2}>\mathrm{P}_{3}>\mathrm{P}_{1}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 27

4 grams of an ideal gas occupies $5.6035$ litres of volume at $546 \mathrm{~K}$ and 2 atm pressure. What is its molecular weight?
(a) 4
(b) 16
(c) 32
(d) 64

Narayan Hari

Numerade Educator

Problem 28

The kinetic energy of 4 moles of nitrogen gas at $127^{\circ} \mathrm{C}$ is ....... Kcals. $\left(\mathrm{R}=2 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)$
(a) 4400
(b) 3200
(c) 4800
(d) 1524

Narayan Hari

Numerade Educator

Problem 29

If a gas contains only three molecules that move with velocities of $100,200,500 \mathrm{~ms}^{-1}$, what is the $\mathrm{rms}$ velocity of the gas is $\mathrm{ms}^{-1 ?}$
(a) $100 \sqrt{8 / 3}$
(b) $100 \sqrt{30}$
(c) $100 \vee 0$
(d) $800 / 3$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 30

A gaseous mixture contains $56 \mathrm{~g}$ of $\mathrm{N}_{2}, 44 \mathrm{~g}$ of $\mathrm{CO}_{2}$ and $16 \mathrm{~g}$ of $\mathrm{CH}_{4}$. The total pressure of mixture is $720 \mathrm{~mm}$ of $\mathrm{Hg}$. The partial pressure of methane is
(a) $75 \mathrm{~mm}$
(b) $160 \mathrm{~mm}$
(c) $180 \mathrm{~mm}$
(d) $215 \mathrm{~mm}$

Narayan Hari

Numerade Educator

Problem 31

At $25^{\circ} \mathrm{C}$ and $730 \mathrm{~mm}$ pressure, $380 \mathrm{~mL}$ of dry oxygen was collected. If the temperature is constant, what volume will the oxygen occupy at $760 \mathrm{~mm}$ pressure?
(a) $365 \mathrm{~mL}$
(b) $2 \mathrm{~mL}$
(c) $10 \mathrm{~mL}$
(d) $20 \mathrm{~mL}$

Narayan Hari

Numerade Educator

Problem 32

The density of an ideal gas is $0.03 \mathrm{~g} \mathrm{~cm}^{-3}$, Its pressure is $106 \mathrm{~g} \mathrm{~cm}^{-1} \mathrm{sec}^{-2}$. What is its $\mathrm{ms}$ velocity (in $\left.\mathrm{cm} \sec ^{-1}\right)$ ?
(a) $10^{3}$
(b) $3 \times 10^{4}$
(c) $10^{2}$
(d) $10^{4}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 33

At a certain pressure, volume of a gas at $27^{\circ} \mathrm{C}$ is 20 litre. If the pressure and temperature are doubled, its volume will be
(a) 20 litre
(b) 40 litre
(c) $8.2$ litre
(d) $10.9$ litre

Narayan Hari

Numerade Educator

Problem 34

$\mathrm{A}$ and $\mathrm{B}$ are ideal gases. The molecular weights of $\mathrm{A}$ and $\mathrm{B}$ are in the ratio of $1: 4$. The pressure of a gas mixture containing equal weights of $\mathrm{A}$ and $\mathrm{B}$ is $\mathrm{P}$ atm. What is the partial pressure (in atm) of B in the mixture?
(a) $\mathrm{P} / 5$
(b) $\mathrm{P} / 2$
(c) $\mathrm{P} / 2.5$
(d) $3 \mathrm{P} / 4$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 35

A gas has double the average velocity of $\mathrm{SO}_{2}$ gas at any temperature. The gas may be
(a) $\mathrm{CO}_{2}$
(b) $\mathrm{C}_{2} \mathrm{H}_{4}$
(c) $\mathrm{CH}_{4}$
(d) $\mathrm{O}_{3}$

Narayan Hari

Numerade Educator

Problem 36

If two moles of ideal gas at $540 \mathrm{~K}$ has volume $44.8 \mathrm{~L}$, then its pressure will be
(a) $1 \mathrm{~atm}$
(b) $2 \mathrm{~atm}$
(c) $3 \mathrm{~atm}$
(d) $4 \mathrm{~atm}$

Narayan Hari

Numerade Educator

Problem 37

The densities of two gases are in the ratio of $1: 16$. The ratio of their rates of diffusion is
(a) $16: 1$
(b) $4: 1$
(c) $1: 4$
(d) $1: 16$

Narayan Hari

Numerade Educator

Problem 38

The critical temperature of water is higher than that of $\mathrm{O}_{2}$ because the $\mathrm{H}_{2} \mathrm{O}$ molecule has
(a) fewer electrons than $\mathrm{O}_{2}$
(b) two covalent bonds
(c) V-shape
(d) dipole moment

Narayan Hari

Numerade Educator

Problem 39

If pressure of $2 \mathrm{~mol}$ of an ideal gas at $546 \mathrm{~K}$ having volume $44.8$ litre is
(a) $2 \mathrm{~atm}$
(b) $3 \mathrm{~atm}$
(c) $4 \mathrm{~atm}$
(d) $1 \mathrm{~atm}$

Narayan Hari

Numerade Educator

Problem 40

56 g of nitrogen and $96 \mathrm{~g}$ of oxygen are mixed isothermally and at a total pressure of $10 \mathrm{~atm}$. The partial pressures of oxygen and nitrogen (in atm) are respectively
(a) 4,6
(b) 5,5
(c) 6,4
(d) 8,2

Narayan Hari

Numerade Educator

Problem 41

At constant volume and temperature conditions, the rates of diffusion $\mathrm{D}_{A}$ and $\mathrm{D}_{\mathrm{B}}$ of gases $\mathrm{A}$ and $\mathrm{B}$ having densities $\rho_{A}$ and $\rho_{n}$ are related by the expression
(a) $\mathrm{D}_{\mathrm{A}}=\left[\mathrm{D}_{\mathrm{a}} \rho_{\mathrm{A}} / \rho_{\mathrm{h}}\right]^{1 / 2}$
(b) $\mathrm{D}_{\mathrm{A}}=\left[\mathrm{D}_{\mathrm{B}} \rho_{\mathrm{B}} / \rho_{A}\right]^{1 / 2}$
(c) $D_{A}=D_{B}\left[\rho_{A} / \rho_{B}\right]^{1 / 2}$
(d) $\mathrm{D}_{\mathrm{A}}=\mathrm{D}_{\mathrm{B}}\left[\rho_{\mathrm{B}} / \rho_{\mathrm{A}}\right]^{12}$

Narayan Hari

Numerade Educator

Problem 42

The term that accounts for intermolecular force in van der Waals equation for non ideal gas is
(a) $\mathrm{RT}$
(b) $\mathrm{V}-\mathrm{b}$
(c) $\left(\mathrm{P}+\alpha \mathrm{V}^{2}\right)$
(d) $(\mathrm{RT})^{-1}$

Narayan Hari

Numerade Educator

Problem 43

A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends, the white ammonium chloride ring first formed will be
(a) at the centre of the tube
(b) near the hydrogen chloride bottle
(c) near the ammonia bottle
(d) throughout the length of the tube

Narayan Hari

Numerade Educator

Problem 44

If a gas expands at constant temperature
(1) the pressure decreases
(2) the kinetic energy of the molecules remains the same
(3) the kinetic energy of the molecules decreases
(4) the number of molecules of the gas increase
(a) 1,2
(b) $1,2,3$
(c) $1,2,4$
(d) 2,3

Narayan Hari

Numerade Educator

Problem 45

At what temperature the rms velocity of gas shown at $50^{\circ} \mathrm{c}$ will be doubled?
(a) $626 \mathrm{~K}$
(b) $1019^{\circ} \mathrm{C}$
(c) $218 \mathrm{~K}$
(d) $1019 \mathrm{~K}$

Narayan Hari

Numerade Educator

Problem 46

An ideal gas cannot be liquefied because
(a) it solidifies before becoming a liquid
(b) forces operative between its molecules are neglgible
(c) its molecules are relatively smaller in size
(d) its critical temperature is always above $0^{\circ} \mathrm{C}$

Narayan Hari

Numerade Educator

Problem 47

According to Boyle's law
(a) $(\mathrm{dP} / \mathrm{dV})_{\mathrm{T}}=-\mathrm{K} / \mathrm{P}^{2}$
(b) $(\mathrm{dP} / \mathrm{dV})_{\mathrm{T}}=\mathrm{K} / \mathrm{V}$
(c) $(\mathrm{d} \mathrm{V} / \mathrm{dP})_{\mathrm{T}}=-\mathrm{K} / \mathrm{P}^{2}$
(d) $(\mathrm{dV} / \mathrm{dP})_{\mathrm{T}}=-\mathrm{K} / \mathrm{P}$

Narayan Hari

Numerade Educator

Problem 48

The values of van der Waals constant ' $\alpha$ ' for the gases $\mathrm{O}_{2}, \mathrm{~N}_{2}, \mathrm{NH}_{3}$ and $\mathrm{CH}_{4}$ are $1.360,1.390,4.170$ and $2.253$
L atm. mol $^{2}$ respectively. The gas which can most easily be liquefied is
(a) $\mathrm{O}_{2}$
(b) $\mathrm{N}_{2}$
(c) $\mathrm{NH}_{3}$
(d) $\mathrm{CH}_{4}$

Narayan Hari

Numerade Educator

Problem 49

The density of gas $\mathrm{A}$ is twice of that of $\mathrm{B}$ and mol. wt. of $\mathrm{A}$ is half of that of $\mathrm{B}$. The Ratio of partial pressures of $P_{A}$ and $P_{n}$ is
(a) $\frac{1}{4}$
(b) $\frac{4}{1}$
(c) $\frac{2}{1}$
(d) $\frac{1}{2}$

Narayan Hari

Numerade Educator

Problem 50

The ratio of rate of diffusion of helium with respect to methane under similar conditions of constant temperature and pressure
(a) $\underline{2}$
(b) $0.5$
(c) 16
(d) 4

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 51

The density of neon will be highest at
(a) STP
(b) $0^{\circ} \mathrm{C}, 2 \mathrm{~atm}$
(c) $273^{\circ} \mathrm{C}, 1 \mathrm{~atm}$
(d) $273^{\circ} \mathrm{C}, 2 \mathrm{~atm}$

Narayan Hari

Numerade Educator

Problem 52

At constant volume for a fixed number of a moles of gas, the pressure of the gas increases with the rise in temperature due to
(a) increase in average molecular speed
(b) increase in rate of collisions
(c) increase in molecular attraction
(d) increase in mean free path

Narayan Hari

Numerade Educator

Problem 53

Four one litre flasks are separately filled with the gases $\mathrm{O}_{2}, \mathrm{~F}_{2}, \mathrm{CH}_{4}$ and $\mathrm{CO}_{2}$ under same conditions. The ratio of the number of molecules in these gases are
(a) $2: 2: 4: 3$
(b) $1: 1: 1: 1$
(c) $1: 2 ; 3 ; 4$
(d) $2: 2 ; 3: 4$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 54

An ideal gas expands according to $\mathrm{PV}=$ constant. On expansion, the temperature of gas
(a) will rise
(b) will drop
(c) will remain constant
(d) cannot be determined because the external pressure is not known

Narayan Hari

Numerade Educator

Problem 55

Which of the following is true about $u_{n=}, 0, \alpha ?$
(a) $\mathrm{u}_{\mathrm{h}}>\mathrm{a}>\alpha$
(b) urms $<\mathbf{0}<\boldsymbol{\alpha}$
(c) $u_{r=}>a<\alpha$
(d) urms $<\mathrm{a}>\alpha$

Narayan Hari

Numerade Educator

Problem 56

According to the kinetic theory of gases
(a) the pressure exerted by a gas is proportional to mean square velocity of the molecules
(b) the pressure exerted by the gas is proportional to the root mean square velocity of the molecules
(c) the root mean square velocity is inversely proportional to the temperature
(d) the mean translational K.E. of the molecule is directly proportional to the absolute temperature.

Narayan Hari

Numerade Educator

Problem 57

$6.4 \mathrm{~g} \mathrm{SO}_{2}$ 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

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 58

$\mathrm{V}$ vs $\mathrm{T}$ curves at constant pressure $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ for an ideal gas are shown below.
Which of the following is correct?
(a) $\mathrm{P}_{1}>\mathrm{P}_{2}$
(b) $\mathrm{P}_{1}<\mathrm{P}_{2}$
(c) $\mathrm{P}_{\mathrm{t}}=\mathrm{P}_{3}$
(d) All of above

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 59

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) $3 \mathrm{P}$

Narayan Hari

Numerade Educator

Problem 60

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) $24: 1$

Narayan Hari

Numerade Educator

Problem 61

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

Narayan Hari

Numerade Educator

Problem 62

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) $\mathrm{Xe}$

Narayan Hari

Numerade Educator

Problem 63

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

Narayan Hari

Numerade Educator

Problem 64

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

Narayan Hari

Numerade Educator

Problem 65

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

Narayan Hari

Numerade Educator

Problem 66

The following graph illustrates
(a) Boyle's law
(b) Charles law
(c) Dalton's law
(d) Gay-Lussac's law

Narayan Hari

Numerade Educator

Problem 67

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

Narayan Hari

Numerade Educator

Problem 68

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) $20 \mathrm{~L} \mathrm{NH}_{3}, 10 \mathrm{~L} \mathrm{~N}_{2}, 30 \mathrm{~L} \mathrm{H}_{2}$

Narayan Hari

Numerade Educator

Problem 69

A general form of equation of state for gases is $\mathrm{PV}=$ $\mathrm{RT}\left[\mathrm{A}+\mathrm{B} / \mathrm{V}+\mathrm{C} / \mathrm{V}^{2}+\ldots\right]$, where $\mathrm{V}$ is the molar
volume of the gas and $\mathrm{A}, \mathrm{B}, \mathrm{C} \ldots .$ are constants for the gas. The values of $\mathrm{A}$ and $\mathrm{B}$, if the gas obeys van der Waals equation, are respectively
(a) $1, \frac{a}{27 b}$
(b) $1, \mathrm{~b}-\frac{\mathrm{a}}{\mathrm{RT}}$
(c) $\frac{a}{R T}$
(d) $\frac{2 \mathrm{a}}{\mathrm{RT}}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 70

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

Narayan Hari

Numerade Educator

Problem 71

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) $0.478$

Narayan Hari

Numerade Educator

Problem 72

Which curve does not represent Boyle's law?

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 73

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) $273 \mathrm{~K}$

Narayan Hari

Numerade Educator

Problem 74

$0.24 \mathrm{~g}$ 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) $59.73$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 75

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

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 76

$\mathrm{X} \mathrm{mL}$ 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 : $\mathrm{CO}_{2}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 77

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) $\frac{1}{4}$

Ajay Singhal

Numerade Educator

Problem 78

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) $\left[\frac{\left(\mathrm{n}_{1} \mathrm{C}_{1}+\mathrm{n}_{2} \mathrm{C}_{2}+\mathrm{n}_{3} \mathrm{C}_{3}+\ldots\right)^{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}+\mathrm{n}_{3}+\ldots}\right]^{1 / 2}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 79

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) $0.95 \times 10^{3} \mathrm{~m} / \mathrm{s}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 80

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) $3.0 \mathrm{~m} / \mathrm{sec}$

Narayan Hari

Numerade Educator

Problem 81

If the rate of effusion of helium gas at a pressure of 1000 torr is 10 torr $\min ^{-1}$. Find the rate of effusion of hydrogen gas at a pressure of 2000 torr at the same temperature.
(a) 20 torr $\min ^{-1}$
(b) 10 torr $\mathrm{min}^{-1}$
(c) $30-2$ torr $\min ^{-1}$
(d) $20 \sqrt{2}$ torr $\min ^{-1}$

Narayan Hari

Numerade Educator

Problem 82

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) $8.0$

Narayan Hari

Numerade Educator

Problem 83

An ideal gas obeying kinetic gas equation can be liquefied if
(a) it cannot be liquefi ed at any value of $\mathrm{P}$ and $\mathrm{T}$
(b) its temperature is more than Boyle's temperature
(c) its temperature is more than critical temperature
(d) its pressure is more than critical pressure

Narayan Hari

Numerade Educator

Problem 84

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) $16 / 17$

Narayan Hari

Numerade Educator

Problem 85

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

Narayan Hari

Numerade Educator

Problem 86

The correct representation of Charle's law is given in
(a)
(b)
(c)
(d)

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 87

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) $0.01$

Narayan Hari

Numerade Educator

Problem 88

Distribution of fraction of molecules with velocity is represented in the figure. The velocity corresponding to point $\mathrm{X}$ is
(a) $\sqrt{\frac{2 R T}{M}}$
(b) $\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$
(c) $\sqrt{\left(\frac{8 \mathrm{RT}}{\pi \mathrm{M}}\right)}$
(d) none of the above

Narayan Hari

Numerade Educator

Problem 89

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) $3482.9 \mathrm{~kg}$

Narayan Hari

Numerade Educator

Problem 90

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) $\mathrm{PV}=\mathrm{nRT}$

Narayan Hari

Numerade Educator

Problem 91

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

Narayan Hari

Numerade Educator

Problem 92

A gas has the van der Waals constants, $a=1.49 \mathrm{~L}^{2}$ $\operatorname{atm} \mathrm{mol}^{2}$ and $\mathrm{b}=0.04 \mathrm{~L} \mathrm{~mol}^{-1} .$ Its Boyle's temperature
is nearly
(a) $50^{\circ} \mathrm{C}$
(b) $354^{\circ} \mathrm{C}$
(c) $454 \mathrm{~K}$
(d) $408 \mathrm{~K}$

Narayan Hari

Numerade Educator

Problem 93

A monoatomic gas 'A' and a diatomic gas 'B', both initially at the same temperature and pressure are compressed adiabatically from a volume $\mathrm{V}$ to $\mathrm{V} / 2$. The gas which has higher temperature is
(a) $\mathrm{B}$
(b) $\mathrm{A}$
(c) both have same temperature
(d) can not be said

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 94

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) $6.25 \mathrm{~atm}$

Narayan Hari

Numerade Educator

Problem 95

Pressure vs density curve for an ideal gas at two different temperatures $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ is shown below. Which is the correct relation here?
Figure 3.11
(a) $\mathrm{T}_{1}>\mathrm{T}_{2}$
(b) $\mathrm{T}_{1}<\mathrm{T}_{2}$
(c) $\mathrm{T}_{1}=\mathrm{T}_{2}$
(d) cannot be said

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 96

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

Narayan Hari

Numerade Educator

Problem 97

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) $u_{\operatorname{me}}=\sqrt{(E / 3 M)}$

Narayan Hari

Numerade Educator

Problem 98

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 $\frac{\mathrm{PV}}{\mathrm{nRT}}<1$

Narayan Hari

Numerade Educator

Problem 99

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

Narayan Hari

Numerade Educator

Problem 100

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) $0.06 \mathrm{~cm}^{3}$

Narayan Hari

Numerade Educator

Problem 101

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) $\mathrm{V}_{\mathrm{a}}=44.8 \mathrm{~L}$

Narayan Hari

Numerade Educator

Problem 102

A closed vessel contains equal number of molecules of $\mathrm{O}_{2}$ and $\mathrm{H}_{2}$. Consider the following statements:
1. The average speed of hydrogen molecules will be greater.
2. Weight of hydrogen is $1 / 8$ th of the weight of oxygen.
3. Hydrogen molecules strike the walls more often.
4. The two gases have different average energies. The statements are wrong in
(a) 2 and 4
(b) 2 and 3
(c) 1 and 4
(d) 1 and 3

Narayan Hari

Numerade Educator

Problem 103

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) $\mathrm{T}\left(\mathrm{H}_{2}\right)=\sqrt{7} \mathrm{~T}\left(\mathrm{~N}_{2}\right)$

Narayan Hari

Numerade Educator

Problem 104

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

Narayan Hari

Numerade Educator

Problem 105

When the critical volume of gas is $0.072 \mathrm{~L} \mathrm{~mol}^{-1}$. The radius of the molecule will be, in $\mathrm{cm}$
(a) $\left(4 \pi / 3 \times 10^{-20}\right)^{1 / 3}$
(b) $\left(3 / 4 \pi \times 10^{-25}\right)^{1 / 3}$
(c) $\left(3 / 4 \pi \times 10^{-17}\right)$
(d) $\left(3 \pi / 4 \times 10^{-3 y}\right)^{13}$

Narayan Hari

Numerade Educator

Problem 106

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) $15: 16$

Narayan Hari

Numerade Educator

Problem 107

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) $1.086: 2$

Narayan Hari

Numerade Educator

Problem 108

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) $1 / 3$

Narayan Hari

Numerade Educator

Problem 109

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) $12 \mathrm{~kg}$

Narayan Hari

Numerade Educator

Problem 110

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

Narayan Hari

Numerade Educator

Problem 111

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)

Rajesh Singh

Numerade Educator

Problem 112

$10 \mathrm{~mL}$ of propane are mixed with $70 \mathrm{~mL}$ of oxygen and exploded. What would be the volume of residual gases after explosion and after exposure of the residual gases to alkali? All volume measurements are made at the same temperature and pressure.

Narayan Hari

Numerade Educator

Problem 113

The most probable speeds of the molecules of gas $\mathrm{A}$ at $\mathrm{T}_{1} \mathrm{~K}$ and gas $\mathrm{B}$ at $\mathrm{T}_{2} \mathrm{~K}$ are in the ratio $0.715: 1 .$ The
same ratio for $\mathrm{gas} \mathrm{A}$ at $\mathrm{T}_{2} \mathrm{~K}$ and gas $\mathrm{B} \mathrm{T}_{1} \mathrm{~K}$ is $0.954$.
Find the ratio of molar masses $\mathrm{M}_{\mathrm{A}}: \mathrm{M}_{\mathrm{a}^{-}}$
(a) $1.965$
(b) $1.0666$
(c) $1.987$
(d) $1.466$

Narayan Hari

Numerade Educator

Problem 114

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) $339 \mathrm{~g}$

Narayan Hari

Numerade Educator

Problem 115

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) $168 \mathrm{~mm}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 116

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.

Narayan Hari

Numerade Educator

Problem 117

A 2 mole mixture of $\mathrm{Ne}(\mathrm{g}), \mathrm{H}_{2}(\mathrm{~g})$ and $\mathrm{O}_{2}(\mathrm{~g})$ are placed in a closed container at a pressure equal to 50 atm. An electric spark is passed and pressure noted is $12.5 \mathrm{~atm}$ after cooling. Oxygen gas is introduced for pressure to become 25 atm. Again electrical spark is passed and pressure drops to 10 atm. (all measurements are at same $\mathrm{T}$ and $\mathrm{P}$ )
(a) Moles fraction of $\mathrm{O}_{2}$ in original mixture is $0.25$
(b) Moles of $\mathrm{O}_{2}$ added after first spark is $0.5$
(c) Mole fraction of $\mathrm{H}_{2}$ in original mixture is $0.7$
(d) Mole fraction of Ne in original mixture is $0.005$

Rajesh Singh

Numerade Educator

Problem 118

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

Narayan Hari

Numerade Educator

Problem 119

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 $\mathrm{He}$.

Narayan Hari

Numerade Educator

Problem 120

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.

Narayan Hari

Numerade Educator

Problem 121

According to Charle's Law
(a) $\left(\frac{\mathrm{dV}}{\mathrm{dT}}\right)_{\mathrm{P}}=\mathrm{k}$
(b) $\left(\frac{\mathrm{dT}}{\mathrm{dV}}\right)_{\mathrm{P}}=\mathrm{k}$
(c) $\left[\frac{1}{T}-\frac{\mathrm{V}}{\mathrm{T}^{2}}\right]=0$
(d) $\mathrm{V} \alpha \frac{1}{\mathrm{~T}}$

Narayan Hari

Numerade Educator

Problem 122

At low pressures, the Van der Waal's gas equation for 1 mole of a gas may be written as
(a) $\mathrm{PV}=\mathrm{RT}-\frac{\mathrm{a}}{\mathrm{V}}$
(b) $\mathrm{PV}=\mathrm{RT}$
(c) $\mathrm{PV}=\mathrm{RT}+\mathrm{Pb}$
(d) $\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^{2}}=\frac{\mathrm{RT}}{\mathrm{V}}$

Narayan Hari

Numerade Educator

Problem 123

Identify the correct statements.
(a) Unit of gas constant, $\mathrm{R}=0.082 \mathrm{kPa} \mathrm{dm}^{3} \mathrm{~K}^{-1} \mathrm{~mole}^{-1}$
(b) Inversion temperature, $T_{i}=\frac{2 a}{R b}$
(c) Boyle's temperature, $\mathrm{T}_{\mathrm{a}}=\frac{2 \mathrm{a}}{\mathrm{Rb}}$
(d) Critical temperature, $T_{c}=\frac{8 a}{27 R b}$

Narayan Hari

Numerade Educator

Problem 124

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 $-\frac{\mathrm{Mb}}{(\mathrm{RT})^{2}}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 125

The Maxwell-Boltzmann distribution for molecular speeds is shown in the following figure. In the figure, $\mathrm{H}$ is the height of the peak, $\mathrm{L}$ is the location of the maximum and $\mathrm{W}$ is the width at half height. As the temperature is increased.
(a) L increase
(d) H decreases
(c) H increases
(d) W increases

Rajesh Singh

Numerade Educator

Problem 126

The compressibility factor of a gas is less than unity at STP. Therefore
(a) $\mathrm{Vm}>22.4 \mathrm{lit}$
(b) $\mathrm{Vm}<22.4$ lit
(c) $\mathrm{Vm}=22.4 \mathrm{lit}$
(d) $\mathrm{Vm}=11.2$ lit

Narayan Hari

Numerade Educator

Problem 127

Identify the correct relationship
(a) $\mathrm{T}_{\mathrm{b}}: \mathrm{T}_{i}: \mathrm{T}_{c}=1: 2: \frac{27}{8}$
(b) $\mathrm{T}_{\mathrm{b}}: \mathrm{T}_{\mathrm{i}} ; \mathrm{T}_{\mathrm{c}}=2: 1: \frac{27}{8}$
(c) $\mathrm{T}_{\mathrm{b}}: \mathrm{T}_{i}: \mathrm{T}_{6}=1: 2: \frac{8}{27}$
(d) $\mathrm{T}_{\mathrm{b}}: \mathrm{T}_{\mathrm{i}}: \mathrm{T}_{6}=8: 27: 16$

Narayan Hari

Numerade Educator

Problem 128

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) $1: 2$

Narayan Hari

Numerade Educator

Problem 129

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) $1: 2: 3$

Narayan Hari

Numerade Educator

Problem 130

Oxygen has a density of $1.429 \mathrm{gm} / \mathrm{L}$ at $\mathrm{STP}$. 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) $6.41 \times 10_{3}$

Narayan Hari

Numerade Educator

Problem 131

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

Narayan Hari

Numerade Educator

Problem 132

Match the following
Column-I
(A) $\mathrm{U}_{\mathrm{zm}}$
(B) $\mathrm{U}_{\mathrm{m} p}^{\mathrm{im}}$
(C) $\mathrm{U}_{w v}$
(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) $\sqrt{\frac{2 R T}{M}}$

Rajesh Singh

Numerade Educator

Problem 133

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) $\mathrm{r}=\frac{\mathrm{K} . \mathrm{P}}{\sqrt{\mathrm{M}}}$
(r) $\mathrm{d}=\frac{\mathrm{PM}}{\mathrm{RT}}$
(s)
(t)

Rajesh Singh

Numerade Educator

Problem 134

Match the following Column-I
(a) Compressibility factor, $Z=1$
(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

Rajesh Singh

Numerade Educator

Problem 135

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.

Narayan Hari

Numerade Educator

Problem 136

When $10 \mathrm{ml}$ of a strong acid is added to $10 \mathrm{ml}$ of an alkali, the temperature rises by $5^{\circ} \mathrm{C}$. If $100 \mathrm{ml}$ of each liquid is mixed, the temperature rise would be

Rajesh Singh

Numerade Educator

Problem 137

$60 \mathrm{~g}$ of gaseous $\mathrm{C}_{2} \mathrm{H}_{6}$ are mixed with $28 \mathrm{~g}$ of gaseous CO. The pressure of the resulting gaseous mixture is 3 atm. The partial pressure of $\mathrm{C}_{2} \mathrm{H}_{6}$ in the mixture is atm.

Narayan Hari

Numerade Educator

Problem 138

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

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 139

At $27^{\circ} \mathrm{C}, 0.5 \mathrm{~L}$ of $\mathrm{H}_{2}$ at $0.8$ bar and $2.0 \mathrm{~L}$ of oxygen at $0.7$ bar are introduced in a $1 L$ vessel. The total pressure of the gas mixture is $1.8 \times 10^{\circ}$ bar where $n$ is

Narayan Hari

Numerade Educator

Problem 140

An LPG cylinder contains $20 \mathrm{~kg}$ of butane gas at $27^{\circ} \mathrm{C}$ and 10 atm pressure. It was leaking and the pressure came down to 8 atmosphere after 20 hours. The gas lost is $\mathrm{kg}$.

Narayan Hari

Numerade Educator

Problem 141

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 $88 \times 10^{-4}$. The value of $x$ is

Narayan Hari

Numerade Educator

Problem 142

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 $\mathrm{x}$ is

Narayan Hari

Numerade Educator

Problem 143

$4 \mathrm{gm}$ of oxygen diffuses through a very narrow hole in 30 sec. What mass of hydrogen in gm will diffuse in the same time under identical conditions?

Narayan Hari

Numerade Educator

Problem 144

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?

Narayan Hari

Numerade Educator

Problem 145

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

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 146

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

Rajesh Singh

Numerade Educator

Problem 147

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

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 148

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) $\sqrt{313 / 293}$
(d) $313 / 293$

Narayan Hari

Numerade Educator

Problem 149

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

Narayan Hari

Numerade Educator

Problem 150

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

Narayan Hari

Numerade Educator

Problem 151

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? [2005]
(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

Narayan Hari

Numerade Educator

Problem 152

An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If $T_{i}$ is the initial temperature and $T_{f}$ is the final temperature, which one of the following statements is correct? $[\mathbf{2 0 0 6}]$
(a) $\left(\mathrm{T}_{g}\right)_{\text {inev }}>\left(\mathrm{T}_{F}\right)_{\text {rer }}$
(b) $\mathrm{T}_{f}>\mathrm{T}_{i}$ for reversible process but $\mathrm{T}_{\mathrm{f}}=\mathrm{T}_{i}$ for irreversible process
(c) $\left(\mathrm{T}_{\mathrm{e}}\right)_{\text {ines }}=\left(\mathrm{T}_{\mathrm{F}}\right)_{\mathrm{ivv}}$
(d) $\mathrm{T}_{\mathrm{f}}=\mathrm{T}_{1}$ for both reversible and irreversible processes

Narayan Hari

Numerade Educator

Problem 153

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) $2 / 3$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 154

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

Narayan Hari

Numerade Educator

Problem 155

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) $1-\mathrm{Pb} / \mathrm{RT}$

Narayan Hari

Numerade Educator

Problem 156

For gaseous state if most probable speed is denoted 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:
$\mid 2013]$
(a) $\mathrm{C}^{*}: \overline{\mathrm{C}}: \mathrm{C}=1: 128: 1.225$
(b) $C^{*}: \overline{\mathrm{C}}=1: 1.225: 1.128$
(c) $\mathrm{C}^{*}: \overline{\mathrm{C}}: \mathrm{C}=1.225: 1.128: 1$
(d) $C^{*}: \overline{\mathrm{C}}: \mathrm{C}=1.128: 1.225: 1$

Narayan Hari

Numerade Educator

Problem 157

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) $Z=1+\frac{a}{V R T}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 158

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) $7: 32$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 159

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

Rajesh Singh

Numerade Educator

Problem 160

Two closed bulbs of equal volume ( $V$ ) containing an ideal gas initially at pressure $P_{1}$ 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 $[\mathbf{2 0 1 6}]$
(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) $p_{i}\left(\frac{T_{1} T_{2}}{T_{1}+T_{2}}\right)$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator