Assignment Gaseous State JH Sir-2621

Contents Topic

Page No.

Theory

01 - 07

Exercise - 1

08 - 26

Exercise - 2

27 - 35

Exercise - 3

36 - 38

Exercise - 4

39 - 40

Answer Key

41 - 44

Syllabus Gaseous Gaseous State State Gaseous state : Absolute : Absolute scale of temperature, ideal gas equation; Deviation from ideality, van der Waals Wa als equation; Kinetic theory of gases, average, root mean square and most probable velocities and their relation relatio n with temperature; Law of partial pressures; Vapour Vapour pressure; Diffusion of gases.

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PART - I : OBJECTIVE QUESTIONS Section A : Gas Laws A-1.

At constant temperature, in a given mass of an ideal gas (A) The ratio of pressure and volume always remains constant (B) Volume always remains constant (C) Pressure always remains constant (D) The product of pressure and volume always remains constant

A-2.

Three flasks of equal volumes contain CH4, CO 2 and Cl2 gases respectively. They will contain equal number of molecules if (A) the mass of all the gases is same (B) the moles of all the gas is same but temperature is different (C) temperature and pressure of all the flasks are same (D) temperature, pressure and masses same in the flasks

A-3.

A certain mass of a gas occupies a volume of 2 litres at STP. Keeping the pressure constant at what temperature would the gas occupy a volume of 4 litres (A) 546ºC (B) 273ºC (C) 100ºC (D) 50ºC

A-4.

At 100 ºC a gas has 1 atm. pressure and 10 L volume. Its volume at NTP would be (A) 10 litres (B) Less than 10 litres (C) More than 10 litres (D) None

A-5.

If 500 ml of a gas 'A' at 1000 torr and 1000 ml of gas B at 800 torr are placed in a 2L container, the final pressure will be(A) 1 00 to rr (B) 6 50 to rr (C ) 1 800 to r r (D ) 2 400 to rr

A-6.

Two flasks A and B of 500 ml each are respectively filled with O2 and SO2 at 300 K and 1 atm. pressure. The flasks will contain(A) The same number of atoms (B) The same number of molecules (C) More number of moles in flask A as compared to flask B (D) The same amount of gases

A-7.

In the gas equation PV = nRT, the value of universal gas constant would depend only on (A) T he nat u re of th e g as (B) T he pre ssu re of th e g a s (C ) T he tem per at ure of th e g as (D ) T he uni t s of m ea sur em e nt

A-8.

8.2 L of an ideal gas weight 9.0 gm at 300 K and 1 atm pressure. The molecular mass of gas is(A) 9 (B) 2 7 (C ) 54 (D ) 81

A-9.

Energy in an ideal gas is (A) C om p let ely k i net ic ( C ) K E + PE

(B) C om p let el y p ote nti al (D ) All th e a bove.















A-12.

If the density of a gas A is 1.5 times that of B then the molecular mass of A is M. The molecular mass of B will be(A) 1.5 M (B) M/1.5 (C ) 3M (D ) M /3

A-13.

When the pressure of 5L of N2 is doubled and its temperature is raised from 300K to 600K, the final volume of the gas would be(A) 10 L (B) 5 L (C ) 15 L (D ) 20 L

A-14.

The value of gas constant per mole is approximately(A) 1 cal (B) 2 cal (C) 3 c al

(D) 4 c al

A-15.

A gas is found to have a formula [CO] x. If its vapour density is 70 the value of x is(A) 2 .5 (B) 3 .0 (C* ) 5 .0 (D ) 6 .0

A-16.

If the pressure of a gas contained in a closed vessel is increased by 0.4 % when heated by 1ºC its initial temperature must be : (A) 250 K (B) 250ºC (C) 25ºC (D) 25 K

A-17.

A thin balloon filled with air at 47ºC has a volume of 3 litre. If on placing it in a cooled room its volume becomes 2.7 litre , the temperature of room is : (A) 42ºC (B) 100ºC (C) 15ºC (D) 200ºC

A-18.

If a mixture containing 3 moles of hydrogen and 1 mole of nitrogen is converted completely into ammonia, amm onia, the ratio of initial and final volume under the same temperature and pressure would be : (A) 3 : 1 (B) 1 : 3 (C) 2 : 1 (D) 1 : 2

A-19.

Two flasks of equal volume are connected by a narrow tube (of negligible volume) volume) all at 27ºC and contain 0.35 mole of H2 each at 0.5 atm. One of the flask is then immersed into a bath kept at 127º C, while the other remains at 27º C. The final pressure in each flask f lask is : (A) Final pressure = 0.5714 atm (B) Final pressure = 1.5714 atm (C) Final pressure = 0.5824 atm (D) None of these

A-20.

Two flasks of equal volume are connected by a narrow tube (of negligible volume) all at 27º C and contain 0.70 moles of H2 at 0.5 atm. One of the flask is then immersed into a bath kept at 127º C , while the other remains at 27º C. The number of moles of H2 in flask 1 and flask 2 are : (A) Moles Moles in flask 1 = 0.4, 0.4, Moles in flask flask 2 = 0.3 (B) Moles Moles in flask 1 = 0.2, 0.2, Moles in flask flask 2 = 0.3 (C) Moles Moles in flask 1 = 0.3, Moles Moles in flask 2 = 0.2 (D) Moles Moles in flask 1 = 0.4, Moles Moles in flask 2 = 0.2

A-21.

A gas is heated from 0°C to 100°C at 1.0 atm pressure. If the initial volume of the gas is 10.0 ! , its final volume would be : (A) 7.32 !

(B) 10.00 !

(C) 13.66 !

(D) 20.00 !

A-22.

Under what conditions will a pure sample of an ideal gas not only exhibit a pressure of 1 atm but also a concentration of 1 mol litre !1. [ R = 0.082 litre atm mol !1 K !1 ] (A) at S.T.P. (B) when V = 22.42 L (C) when T = 12 K (D) impossible under any condition

A-23.

A and B are two identical vessels. A contains 15 g ethane at 1atm and 298 K. The vessel B contains 75 g of















A-25.

A 0.5 dm3 flask contains gas A and 1 dm3 flask contains gas B at the same temperature. If density of A = 3 g/dm3 and that of B = 1.5 g/dm3 and the molar mass of A = 1/2 of B, the ratio of pressure exerted by gases is : PA

PA

(A) P = 2 B A-26.

PA

(B) P = 1 B

(C) P = 4 B

Which expression among the following represents Boyle's law ? (A) (dP/dV) T = K/V (B) (dP/dV) T = –K/V 2 (C) (dP/dV) T = –K/V

PA

(D) P = 3 B

(D) (dP/dV) T = K

A-27.

For a fixed mass of a gas at constant pressure, which of the following is correct (A) Plot of volume versus Celsius temperature is linear with intercept zero (B) Plot of volume versus kelvin temperature is linear with a nonzero intercept (C) Plot of V/T versus T is linear with a positive slope (D) Plot of V/T versus T is linear with a zero slope

A-28.

The density of carbon monoxide at STP is (A) 0. 0.625 g L 1 (B) 1. 1 .25 g L 1 –

–

(C) 2. 2.5 g L 1 –

(D) 1. 1.875 g L 1 –

A-29.

At a given temperature "(X) = 2"(Y) and M(Y) = 3 M(X), where " and M stand respectively for density and molar mass of the gases X and Y, then the ratio of their pressures will be (A) p(X) / p(Y) = 1/4 (B) p(X) / p(Y) = 4 (C) p(X) / p(Y) = 6 (D) p(X) / p(Y) = 1/6

A-30.

Which of the following expression gives the variation of density of ideal gas with changes in temperature? (A)

d2 P2 T1 # d1 P1T2

(B) d 2 #

d1T1 T2

(C)

d2 T2 # d1 T1

(D) d 2 #

d2P2 T2 P1T1

A-31.

The volume of ammonia obtained by the combination of 10ml of N2 and 30ml H2 is (A) 20 m l (B) 40 m l (C ) 30 m l (D ) 10 m l

A-32.

Hydrogen and Argon are kept in two separate but identical vessels at constant temperature and pressure (A) Both contain same number of atoms. (B) The number of atoms of argon is half that of hydrogen. (C) The number of atoms of argon is double that of hydrogen (D) None of these

A-33.

Which of the following represents the avogadro number (A) Number of molecules present in 1 L of gas at N.T.P. (B) Number of molecules present in 22.4 ml of gas at N.T.P. (C) Number of molecules present in 22.4 L of gas at 298K and 1 atm. pressure (D) Number of molecules present in one mole of gas at any temp. and pressure.

A-34.

26 c.c. of CO 2 are passed over red hot coke. The volume of CO evolved is (A) 1 5 c .c (B) 1 0 c. c. (C ) 32 c. c. (D ) 52 c. c.

A-35.

10 gm of a gas at NTP occupies 5 litres. The temp. at which the volume becomes double for the same















A-37.

V versus T curves at constant pressure P 1 and P2 for an ideal gas are shown in fig. Which is correct -

(A) P1 > P2 A-38.

A-41.

(D) All

(B) 250 ºC

(C) 250 0K

(D) 25ºC

At a constant pressure, what should be the percentage increase in the temperature in kelvin for a 10% increase in volume (A) 1 0%

A-40.

(C) P1 = P2

If pressure of a gas contained in a closed vessel is increased by 0.4% when heated by 1ºC its initial temperature must be (A) 25 0K

A-39.

(B) P 1 < P2

(B) 2 0%

(C ) 5%

(D ) 5 0%

There is 10 litre of a gas at STP. Which of the following changes keeps the volume constant (A) 2 73 K a n d 2 a tm

(B) 273ºC and 2 atm

(C) 546ºC and 0.5 atm

(D) 0ºC and 0 atm

The density of oxygen gas at 25ºC is 1.458 mg/litre at one atmosphere. At what pressure will oxygen have the density twice the value(A) 0.5 atm/25ºC

(B) 2 atm/25ºC

(C) 4 atm/25 ºC

(D) None

A-42.

A flask of methane (CH4) was weighed. Methane was then pushed out and the flask again weighed when filled with oxygen at the same temperature and pressure. The mass of oxygen would be (A) T he sam e a s the m e tha ne (B) H alf of t he m e tha ne (C ) D oub le o f th at of m e tha ne (D ) N egl igi b le in co m par iso n t o t hat of m e t ha ne

A-43.

A balloon filled with methane (CH4) is pricked with a sharp point and quickly plunged into a tank of hydrogen at the same pressure. After sometime, the balloon will have (A) Enlarged (B) Shrinked (C) Rem ain unchanged in size (D) Ethylene (C2H4) inside it

A-43.

Containers X, Y and Z of equal volume contain oxygen, neon and methane respectively at the same temperature and pressure. The correct incereasing order of their masses is (A) X < Y < Z (B) Y < Z < X (C ) Z < X < Y (D ) Z < Y < X

A-44.

Two flasks X and Y have capacity 1L and 2L respectively and each of them contains 1 mole of a gas. The temperature of the flask are so adjusted that average speed of molecules in X is twice as those in Y. The pressure in flask X would be ( A ) Sa m e a s t h a t i n Y (B) Ha lf of that in Y (C) Twice of that in Y (D ) 8 ti m es o f t hat in Y

A-45.

A gas can be liquefied by -















Section B: Daltons Law of Partial Pressures B-1.

A cylinder is filled with a gaseous mixture containing equal masses of CO and N2. The ratio of their partial pressure is(A) PN = P CO 2

(B) P CO = 0.875 PN2

(C) PCO = 2 PN

2

(D) PCO =

1 P 2 N2

B-2.

The total pressure of a mixture of two gases is (A) The sum of partial pressures of each gas (B) The difference in partial pressures (C) The product of partial pressures (D) The ratio of partial pressures.

B-3.

Equal masses of SO 2, CH 4 and O2 are mixed in empty container at 298 K, when total pressure is 2.1 atm. The partial pressures of CH4 in the mixture is (A) 0. 5 a tm (B) 0 .7 5 a tm (C ) 1. 2 a tm (D ) 0. 6 a tm

B-4.

Air contains 79% N 2 and 21% O2 by volume. If the pressure is 750 mm of Hg, the partial pressure of O2 is (A) 157.5 mm of Hg Hg (B) 175.5 mm of Hg Hg (C) 315.0 mm of Hg (D) 257.5 mm of Hg

B-5.

Equal weights of ethane & hydrogen are mixed in an empty container at 25º C, the fraction of the total pressure exerted by hydrogen is: (A) 1: 2 (B) 1: 1 (C) 1: 16 (D) 15: 16

B-6.

A mixture of hydrogen and oxygen at one bar pressure contains conta ins 20% by weight of hydrogen. Partial pressure of hydrogen will be (A) 0.2 bar (B) 0.4 bar (C) 0.6 bar (D) 0.8 bar

B-7.

A compound exists in the gaseous phase both as monomer (A) and dimer (A2). The atomic atom ic mass of A is 48 and molecular mass m ass of A2 is 96. In an experiment 96 g of the compound was confined in a vessel of volume 33.6 litre and heated to 273ºC. The pressure developed if the compound exists as dimer to the extent of 50 % by weight under these conditions will be : (A) 1 atm (B) 2 atm (C) 1.5 atm (D) 4 atm

B-8.

In the below experiment, the value of P is 1mol gas A

2 mol gas B

250 mm

250 mm

(A) 250 m m

Partition $ $ $ $ % removed at same tem ! perature( T )

(B) 500 m m

Pr essure

#P ( C ) 30 0 m m

( D ) 40 0 m m

B-9.

A closed vessel contains equal number of oxygen and hydrogen molecules at a total pressure of 740 mm. If oxygen is removed from the system, the pressure (A) Beco m es ha lf of 74 0 m m . (B) Re m ai ns unch ang ed (C ) Beco m es 1/ 9th of 74 0 m m . (D ) Beco m e s d oub le of 74 0 m m .

B-10.

At constant temperature 200 cm3 of N2 at 720 mm and 400 cm3 of O2 at 750 mm pressure are put together in a one litre flask. The final pressure of mixture is -

















B-12.

The partial pressure of hydrogen in a flask containing 2gm of H2 & 32gm of SO2 is (A)

1 of o f total pressure 16

( B)

1 of total pressure 2

(C)

2 of o f tot al pressure 3

(D)

1 of total pressure. 8

B-13.

The mass of CO2 that must be mixed with 20 g of oxygen such that 27 ml of a sample of the resulting mixture contains equal number of m olecules of each gas – ( A) 1 3 . 7 5 g ( B) 2 7 . 5 g (C ) 41 .2 5 g ( D) 5 5 g

B-14.

A mixture of hydrogen and oxygen (45 ml) is sparked to form liquid water. The component compon ent not in excess reacts completely and 15 ml is left over. (All measurements are made at the same temperature and pressure). The composition by volume in the original mixture of H2 : O2 is ( A) 4 : 5 ( B) 7 : 2 (C) eit her 4 : 5 no r 7 : 2 (D) 2 : 1

B-15.

In a gaseous mixture at 20°C the partial pressure of the components are, : H2 : 150 Torr, CO2 : 200 Torr, rr, CH4 : 300 Torr, C2H4 : 100 100 Tor Torrr, Volume olume pe perc rcen entt of of H2 is : ( A) 2 6 . 6 7 ( B) 7 3 . 3 3 (C) 80.00 (D) 20

B-16.

At STP, a container has 1 mole of Ar, 2 moles of CO 2, 3 moles of O 2 and 4 moles of N 2. Without changing the total pressure if one mole of O2 is removed, the partial pressure of O2 : (A) is is c h a n g e d b y a b o u t 2 6 % ( B) i s h a l ve d (C) is uncha nged (D) chang e d by 33 %

B-17.

Which of the f ollowing gases will have the same rate of diffusion under identical conditions? (i) CO, ( i i ) C O 2, (iii) N2O, (iv) N2, (v) C2H4 (vi) C3H8 (A) CO,CO 2,C2H4 (B) CO 2,C2H4,N2O (C) C3H8,N2O,CO2 (D) CO, N2,C2H4,C3H8

Section C : Grahams Law of Diffusion. C-1.

The rates of diffusion of SO3, CO2, PCl3 and SO2 are in the following order (A) PCl3 > SO3 > SO2 > CO2 (B) CO2 > SO2 > PCl3 > SO3 (C) SO2 > SO3 > PCl3 > CO2 (D) CO2 > SO2 > SO3 > PCl3

C-2.

20 ! of SO SO2 diffuses through a porous partition in 60 seconds. Volume Volume of O2 diffuse under similar conditions in 30 seconds will be : (A) 12.14 ! (B) 14.14 ! (C) 18.14 ! (D) 28.14 !

C-3.

See the figure-1 :

















C-5.*

‘ ’ and ‘B’ are in the ratio 16: 3. If the ratio of their masses present in the The rate of diffusion of 2 gases A mixture is 2 : 3. Then (A) The ratio of their molar masses is 16 : 1 (B) The ratio of their molar masses is 1 : 4 (C) The ratio of their moles present inside the container is 1 : 24 (D) The ratio of their moles present inside the container is 8 : 3

C-6.

A gas 'A' having molecular weight 4 diffuses thrice as fast as the gas B. The molecular weight of gas B is(A) 36 (B) 1 2 (C ) 18 (D ) 24

C-7.

The increasing order of effusion among the gases, H2, O2, NH 3 and CO2 is(A) H2, CO 2, NH 3, O2 (B) H2, NH 3, O2, CO 2 (C) H2, O2, NH 3, CO 2 (D) CO2, O2, NH 3, H2

C-8.

The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight of X is (A) 64 (B) 3 2 (C ) 4 (D ) 8

C-9.

A gas X diffuses three times faster than another gas Y the ratio of their densities i.e., D x : Dy is(A)

C-10.

1 3

(B)

1 9

(C)

1 6

(D)

1 12

In which of the following pairs the gaseous species diffuse through a porous plug with the same rate of diffusion (A) N O, CO

(B) N O , C O 2

(C) NH3, PH 3

(D) NO, C 2H6

C-11.

A balloon filled with ethylene is pricked with a sharp pointed needle and quic kly placed in a tank full of hydrogen at the same pressure. After a while the balloon would have : (A) shrunk (B) enlarged ( C ) c o m p le t e l y c o l l a ps e d ( D ) r e m a i n u n ch a n g e d i n s i ze .

C-12.

A certain gas is diffused from two different vessels A and B. The vessel A has a circular orifice while vessel B has square orifice of length equal to the radius of the orifice of vessel A. The ratio of the rates of diffusion of the gas form vessel A to that of in vessel B assuming same T & P is : (A) ' (B) 1/ ' (C) 1 : 1 (D) 2 : 1

C-13.

The vapour densities of CH4 and O2 are in the ratio 1 : 2 . The ratio of rates of diffusions of O 2 and a nd CH4 at same P and T is -

















D-3.

Which of the following expression does not give root mean square velocity-

( 3RT + ) M ,-

(A) *

D-4.

1 2

( 3P + ) DM ,-

(B) *

(B) C arb on di oxi de

(B) 1 7 2.6 K

(D) Carbon monoxide. –

(C) 596 K

(D) 1192 K

The RMS velocity at NTP of the species can be calculated from the expression -

( 3P + * ) d ,

(B)

( 3PV + * ) M ,

(C)

( 3RT + * ) M ,

(D) All are correct.

Among the following gases which one has the lowest root mean square velocity at 25 ºC(A) SO 2

D-9.

(C) Sulphur dioxide –

(A)

D-8.

( 3PV + ) M ,-

(D) *

1 2

If the r.m.s. velocity of nitrogen molecules is 5.15 ms 1 at 298 K, then a velocity of 10.30 ms 1 will be possessed at a temp(A) 149 K

D-7.

( 3P + ) D ,

(C) *

1 2

Which one of the following gases would have the highest R.M.S. velocity at 25ºC (A) Oxygen

D-6.

1 2

(B) N 2

(C) O2

(D) Cl2

By how many folds the temp of a gas would increase when the r.m.s. velocity of gas molecules in a closed container of fixed volume is increased from 5 x 104 cm s 1 to 10 x 10 4 cm s 1 –

(A) 0 .5 tim e s D-10.

D-11.

(B) 2 tim es

(C ) 4 tim es

–

(D ) 1 6 t im e s.

At S.T.P. the order of mean square velocity of molecules H2, N2, O2 and HBr is (A) H2 > N2 > O2 > HBr

(B) HBr > O 2 > N2 > H2

(C) HBr > H 2 > O2 > N2

(D) N2 > O2 > H2 > HBr

Most probable speed, average speed and RMS speed are related as (A) (A) 1 : 1.1 1.128 28 : 1.2 1.224 24 (B) (B) 1 : 1.1 1.128 28 : 1.4 1.424 24 (C) (C) 1 : 2.1 2.128 28 : 1.2 1.224 24 (D) (D) 1 : 1.4 1.428 28 : 1.4 1.442 42

D-12.

The root mean square velocity of an ideal gas in a closed container of fixed volume is increased from 5 x 104 cm. s 1 to 10 x 10 4 cm. s 1. Which of the following statements might correctly explain how the change accomplished (A) By heating the gas, the temperature is doubled –

–

(B) By heating the gas, the pressure is made four times

















D-16.

The average kinetic energy (in joules of) molecules in 8.0 g of methane at 27º C is : (A) 6.21 × 10-20 J/ J/molecule (B) 6.21 × 10-21 J/molecule (C) 6.21 × 10-22 J/molecule (D) 3.1 × 10-22 J/molecule

D-17.

According to kinetic theory of gases, for a diatomic molecule m olecule : (A) The pressure exerted by the gas is proportional to the mean velocity of the molecule. (B) The pressure exerted by the gas is proportional proport ional to the r.m.s. velocity of the molecule. (C) The r.m.s. velocity of the molecule is inversely proportional to the temperature. tem perature. (D) The mean translational K.E. of the molecule molecul e is proportional to the absolute temperature.

D-18.

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root-mean-square velocity of the gas molecules is v, at 480 K it becomes : (A) 4v (B) 2v (C) v/2 (D) v/4

D-19.

The ratio between the r.m.s. velocity of H2 at 50 K and that of O2 at 800 K is: (A) 4 (B) 2 (C) 1 (D) 1/4

D-20.* If a gas is allowed to expand at constant tem peature then which of the following does not hold true : (A) the kinetic energy of the gas molecules decreases (B) the kinetic energy of the gas molecules increases (C) the kinetic energy of the gas molecules remains the sam e (D) Can not be predicted D-21.

The total kinetic energy of 0.6 mol of an ideal gas at 27° C is (A) 1122 J (B) 1681 J (C) 2245 J

(D) 2806 J

D-22.

Which of the following molecule has the lowest average speed at 273 K ? (A) CO (B) CH 4 (C) CO2 (D) C2H6

D-23.

Which of the following is true -

(A) urms > / > 0. D-24.

(C) urms > / < 0.

(D) urms < / > 0.

At what temperature will be total kinetic energy (KE) of 0.30 mole of He be the same as the total KE of 0.40 mole of Ar at 400K(A) 40 0K

D-25.

(B) u rms < / < 0.

(B) 373 K

(C ) 53 3K

(D) 300 K

Four particles have speed 2,3,4 and 5 cm/s respectively. Their rms speed is (A) 3. 5cm /s

(B) ( 27/ 2) cm /s

(C )

54 cm /s

(D) ( 54 /2) cm/s] cm/ s]

















D-30.

Helium atom is twice times heavier than a hydrogen molecule. At 25ºC the average K.E. of helium atom is (A) Twice that of hydrogen (B) Sam e as that of hydrog en (C) Four tim es that of hydrogen (D) Half that of hydrogen

D-31.

If a gas is expanded at constant temperature(A) Number of molecules of the gas decreases (B) The kinetic energy of the molecule decreases (C) The kinetic energy of the molecules remains the same (D) The kinetic energy of the molecules increases

D-32.

Three gases of densities A(0.82), A(0.82), B(0.25), C(0.51) are enclosed in a vessel of 4L capacity. capacity. Pick up the correct statement : I. Gas A will tend to lie at the bottom II. The number of atom s of various gases A, B, C are same III. The gases will diffuse to form homogeneous mixture. IV. IV. The average kinetic energy of each gas is same. ( A) I , I V ( B) o n l y I I I (C) II I , IV ( D) II , II I

D-33.

Which of the following statem ents is not true ? (A) The ratio of the mean speed to to the rms speed is independent independent of the temperature. temperature. (B) The square of the mean speed of the molecules molecules is equal to the mean squared squared speed at a certain certain temperature. (C) (C) Mean kinetic energy energy of the gas molecules at any given given temperature temperature is independent independent of the mean speed. (D) None None of of these these

D-34.

The temperature of an ideal gas is increased from 140 K to 560 K. If at 140 K the root-mean square velocity of the gas molecule s is V, V, at 560 K it becom es : ( A) 5 V ( B) 2 V ( C ) V/ 2 ( D ) V/ 4

D-35.

If for two gases of molecular weights weights MA and MB at temperature TA and TB, T AMB = T BMA, then which property has the same magnitude for both the gases : ( A) d e n s i t y (B) p ressure ( C ) K. E. p e r m o l e (D) r.m . s. speed

D-36.

At what temperature temperatu re will the total K. E. of 0.30 mol of He be the same as the total t otal K.E. of 0.40 mol of Ar at 400 K ? ( A) 5 3 3 K ( B) 4 0 0 K (C) 3 46 K (D) 3 00 K

D-37.

A mixture of methane and ethene in the mole mo le ratio X : Y has a mean molecular molecula r weight = 20. What would be the mean m olecular weight if the same gas es are mixed in the ratio Y : X



















E-3.

The term that accounts for intermolecular force in vander Waal's equation for non ideal gas is (A) RT

E-4.

( C ) ( P + a / V 2)

(B) V - b

(D) [RT ]-1

The critical temperature of a substance is (A)The temperature above which the substance undergoes decomposition (B)The temperature above which a substance can exist only as a gas (C) Boiling point of the substance (D) All are wrong

E-5.

E-6.

Critical temperature of the gas is the temperature(A) Be Below whi which it can ann not be liq liquifi uifie ed

(B) Above wh which it can ann not be liq liquifi uifie ed

(C) At which which it occupies occupies 22.4 L of volume volume

(D) At which which one one mole mole of of it occu occupi pies es volume volume of 22.4 L

The units of the Van der Waal ’s constant ‘ a’ are (A) atm L2 mo moll 2 –

E-7.

–

–

(C) atm L mol 1 –

(D) atm mol L 2 –

The units of the van der Waal ’s constant ‘ b’ are (A) atm osphere

E-8.

(B) atm L 2 mol 2

(B) j oul es

(C ) L m o l 1 –

(D) mol L 1 –

The Van der Waal’s parameters for gases W, X, Y and Z are Gas a(atm L2 mol !2 ) b(Lmol!1 ) W 4.0 0.027 X

8.0

0.030

Y

6.0

0.032

Z

12 .0

0.027

Which one of these gases has the highest critical temperature ? (A) W (B) X (C ) Y

(D) Z

















E-13.

At low pressures (For 1 mole), the Vander Waal’s equation is written as a 5 8 p 2 6 3 V = RT V2 4 7

The compressibility factor is then equal to :

( )

(A) * 1 !

a + RTV ,

( )

(B) * 1 !

RTV + a ,

( )

(C) * 1 2

a + RTV ,

( )

(D) * 1 2

RTV + a ,

E-14.

Calculate the radius of He atoms if its Vander Waal's constant ‘b’ is 24 ml mol !1. (Note ml = cubic centimeter) (A) 1.355 Å (B) 1.314 Å (C) 1.255 Å (D) 0.355 Å

E-15.

In vander Waal's equation of state for a non ideal gas the term that accounts for intermolecular forces is : (A) nb (B) nRT (C) n2a/V2 (D) (nRT)-1

E-16.

The values of Vander Waal's constant "a" for the gases O2, N2, NH3 & CH4 are 1.36, 1.39, 4.17, 2.253 L2 atm mole-2 respectively. respectively. The gas which can most easily e asily be liquified is: (A) O2 (B) N2 (C) NH3 (D) CH4

E-17.

The correct order of normal boiling points of O2, N2, NH3 and CH4, for whom the values of vander Waal's constant ‘a’ are 1.360, 1.390, 4.170 and 2.253 L2. atm. mol!2 respectively, is : (A) O2< N2 < NH3 < CH4 (B) O2< N2 < CH4 < NH3 (C) NH3 < CH4 < N2 < O2 (D) NH3 < CH4 < O2 < N2

E-18.

NH3 gas is liquefied more easily than N2. Hence: (A) Vander Waal’s constants 'a' and 'b' of NH 3 > that of N2 (B) Vander Waal’s constants 'a' and 'b' of NH 3 < that of N2 (C) a (NH3) > a (N2) but b (NH3) < b (N2) (D) a (NH3) < a (N2) but b (NH3) > b (N2)

















E-23.

Let the most probable velocity of hydrogen molecules at a temperature 1oC is Vo. Vo. Suppose all the molecules molec ules o dissociate into atoms when temperature is raised to (2t + 273) C then the new rms velocity is : (A)

2 3

V0

(B)

3( 2 2 273) 1 / Vo

(C) 2 /

3Vo

(D)

6Vo

E-24.

The P of real gases is less than the P of an ideal gas because of (A) Increase in num be ber of collisions (B) Finite size of m olecule (C ) I ncr eas e i n KE o f m ole c ul es (D) Interm olecular forces

E-25.

Average K.E. of CO 2 at 27ºC is E. The average kinetic energy of N2 at the same temperature will bebe(A) E

E-26.

(B) 2 2E

The rate of diffusion of hydrogen is about (A) O ne half th at of He (C) Twice th at of He

( C ) E/ 2 2

(D) E/ 2

(B) 1 .4 tim e s th at of He (D ) F our ti m es th at of He

E-27.

A gas is said to behave like an ideal gas when the reaction PV/T = constant, holds. When do you expect a real gas to behave like an ideal gas (A) When temperature and pressure are low (B) When temperature and pressure are high (C) When temperature is low and pressure is high (D) When temperature is high and pressure is very low.

E-28.

If temperature and volume are same, the pressure of a gas obeying Vander Waals equation is (A) Sma Smalller th than th that of an an id ideal ga gas (B) Larger than that of an an ide ideal gas (C ) Sam e a s t hat of an i de a l g as (D ) N on e o f t he se

E-29.

In case of hydrogen and helium the Vander Waals forces are (A) Strong (B) Very strong (C ) W e ak

(D) Very weak

















E-35.

Which of the following expressions between between the van der Waals constant b and the radius r of spherical molecules is correct -

( 4 3 + ' r - NA ) 3 ,

(A) b # *

( 4 3 + 'r ) 3 ,

(B) b # *

( 4 3 + ' r - NA ) 3 ,

(C) b # 2 *

( 4 3 + ' r - NA ) 3 ,

(D) b # 4 *

E-36.

The value of compression factor at the critical state of a van der Waals gas is (A) 3/8 (B) 8/3 (C) 1 (D) 5/8

E-37.

A gas with formula CnH2n+2 diffuses through the porous plug at a rate one sixth of the rate of diffusion of hydrogen gas under similar conditions. The formula of gas is – (A) C2H6 (B) C10H22 (C) C5H12 (D) C6H14

E-38.

The values of critical temperature (TC) and critical pressure (PC) for some gases are given below. Which of the gases can not be liquefied at 100 K and 50 atm? Gases (i) (ii) (i ii ) (iv) PC (atm ) 2.2 14 35 45 TC (K) 5.1 33 127 140 (A) (iv) only (B) (i) only (C) (i) and ( ii) (D) (iii) and (iv)

E-39.

Let f1 and f2 be the fractions of molecules in the range c and c + dc for SO2 at 2T and O 2 and T, respectively which of the following expressions is correct (A) f 1 > f2 (B) f 1 < f2 (C) f 1 = f2 (D) f 1 and and f2 cannot be correlated

PART - II : MISCELLANEOUS QUESTIONS

COMPREHENSION

















2.

f or ‘G’ : For a real gas ‘G’ Z > 1 at STP Then for Which of the following is true : (A) 1 mole of the gas occupies occupie s 22.4 L at NTP (B) 1 mole of the gas occupies 22.4 L at pressure higher than that at STP (keeping temperature tem perature constant) (C) 1 mole of the gas occupies 22.4 L at pressure press ure lower than that at STP (keeping temperature constant) (D) None of the above

3.

Following graph represents represents a pressure (P) volume (V) relationship at a fixed temperature (T) for n moles of a real gas. The graph has two regions marked (I) and (II). W hich of the following options is true.

(A) Z < 1 in the region (II) (C) Z = 1 for the curve

(B) Z = 1 in the region (II) (D) Z approaches 1 as we move from region (II) to region (I)

Comprehension 2. Real gases deviates from ideal behaviour because of the following two faulty assumptions of kinetic theory: (i) The actual volume occupied by molecules is negligible as compared to the total volume of the gas. (ii) The forces of attraction and repulsion between molecules of the gas are negligible. The extent of deviation of a real gas from ideal behaviour is expressed in terms of compressibility factor(z) Hence suitable corrections were applied to the ideal gas equation. So that it can also explain the behavior of real gases. The equation obtained by applying the two corrections to the usual gas equation is known as Vander Waal equation.



















6.

At low pressure, the Vander Wall ’s equation for 1 mole gas is (A) PV = RT +

7.

a V

(B) PV = RT

–

a V

(C) PV = RT +

a V

2

Identify the wrong statement related to the above graph : (A) (A) Between Between 50 K and 150 150 K temperature temperature and pressure pressure ranging ranging from 10 atm to 20 atm matter m atter may have liquid state. (B) (B) Zero is is the maximum value value of the the slope slope of P-V Curve (C) (C) If vander wall wall equation equation of state is applicable applicable above above critical temperature temperature then cubic equation of Vm will have one real and two imaginary imagin ary roots. (D) At 100 K and pressure pressure below below 20 atm it has liquid state state only

MATCH THE COLUMN 8.

M atch the fo llow ing List I

List II

( A)

Urms /Uav

(i)

1 .2 2

( B)

Uav /Ump

( ii )

1 .1 3

(C)

Urms /Ump

( ii i )

1 .0 8

(D) PV = RT

–

a V2

















11.

M atch th e c olumn Colu mn I

Colum n II P

T1 T2

(i)

T 1 > T 2 > T 3

T3

(A)

1/V

Temperature-constant Pressure-constant

V

(ii)

Charle’s Law

(B) n (no. of moles)

(iii)

Boyle ’s law

(C)

V

Temperature-constant Mass-constant

















13.

For a fixed amount of the gas match the two column : Column-I

Column-II

(A)

(p) T 1 > T2 > T3

(B)

(q) P1 > P2 > P3

(C)

(r) V1 > V2 > V3

















17.

Statement-1 : Gas with lower molar mass will effuse or diffuse faster. Statement-2 : Total Kinetic Energy of any gas depends upon its molar mass. m ass.

18.

Statement-1 : Pressure exerted by a mixture of gases is equal to the sum of their partial pressures. Statement-2 : Reacting gases react to form a new gas having pressure equal to the sum of both. both .

19.

Statement-1 : CH4,CO2 has value of Z (compressibility (com pressibility factor) less than one, generally. Statement-2 : Z < 1 is due to repulsive forces among the molecules.

20.

Statement-1 : Critical temperature of the gas is the temperature at which it occupies 22.4 L of volume. Statement-2 : Molar volume of every gas at NTP is 22.4 L.

21.

Statement-1 : Excluded volume or co-volume equals to (v –nb) for n moles gas. Statement-2 : Co-volume depends on the effective size of gas molecules.

22.

Statement-1 : Gases like N2, O2 behave as ideal gases at high temperature and low pressure. Statement-2 : Molecular interaction diminishes at high temperature and low pressure .

23.

Statement-1 : Most probable velocity is the velocity possessed by maximum fraction of molecules at the same temperature. temperature. Statement-2 : On collision, more and more molecules acquire higher speed at the same sam e temperature.

24

Statement-1 : Noble gases can be liquefied.

















PART - I : MIXED OBJECTIVE Single choice type 1.

I, II, III are three isotherms isotherm s respectively at T1, T2 and T3 as shown in graph. Temperature Temperature will be in order.

(A) T1 = T2 = T3 2.

(B) T 1 < T2 < T3

(C) T1 > T2 > T3

(D) T 1 > T2 = T3

Oxygen and cyclopropane at partial pressures of 570 torr and 170 torr respectively are mixed in a gas cylinder. cylinder. What is the ratio of the number of moles of cyclopropane to the number numbe r of moles of oxygen? (A)

170 = 0.23 740

(B)

170 8 170 :70 5 2 / 6 = 0.19 32 34 42 7 42



















9.

A sample of a gas was heated from 300C to 600C at constant pressure. Which of the following statement(s) is/are true. (A) Kinetic energy of the gas is doubled (B) Boyle’s law will apply (C) Volume of the gas will be doubled (D) None of the above

10.

An amount of 1.00 g of a gaseous compound com pound of boron and hydrogen occupies 0.820 liter at 1.00 atm and at 30C. The compound is (R = 0.0820 liter atm mole!1 0K!1; at. wt: H = 1.0, B = 10.8) (A) BH3 (B) B4H10 (C) B2H6 (D) B3H12

11.

A certain volume of argon gas (Mol. (Mol . Wt. = 40) requires 45 s to effuse effus e through a hole at a certain pressure and temperature. The same sam e volume of another gas of unknown molecular m olecular weight requires 60 s to pass through the same hole under the same conditions of temperature and pressure. The molecular weight of the gas is : (A) 53 (B) 35 (C) 71 (D) 120

















19.

Consider the following statements: The coefficient B in the virial equation of state (i) is independent of temperature

( B + C * 1 .......... 2 2 2 PVm = RT * V 2 Vm m ) ,

(ii) is equal to zero at boyle tem perature (iii) has the dimension of molar volume Which of the above statements statement s are correct. (A) i and ii 20.

(B) i and iii

(C) ii and iii

(D) i, ii and iii

Consider the following statements: If the van der Waal’s parameters of two gases are given as a (atm lit2 mol 2)b (lit mol 1) G X 65 0 05 6 –

–

















25.

For a real gas the P-V curve was experimentally plotted and it had the following appearance. With respect to liquifaction. Choose the correct statement. statement.

(A) at T = 500 K, P = 40 atm, the state will be liquid. (B) at T = 300 K, P = 50 atm, the state will be gas (C) at T < 300 K, P > 20 atm, the state will be gas (D) at 300 K < T < 500 K, P > 50 atm, the state will be liquid.

















More than one choice type 36.

37.

A gas cylinder containing cooking gas can withstand a pressure of 14.9 atmosphere. atm osphere. The pressure guaze of cylinder indicates 12 atmosphere at 27 ºC. Due to sudden fire in the building temperature starts rising. The temperature at which cylinder will explode is : (A) 372.5 K (B) 99.5 ºC (C) 199 ºC (D) 472.5 k

















44.

For a gaseous system, the pressure can be increased by (A) increasing the volume of container but keeping the am ount and temperature constant (B) increasing the amount of gas at constant tem perature and volume (C) decreasing the volume of container but keeping the amount and temperature constant (D) decreasing temperature but keeping amount and volume constant

45.

Boyle’s law is represented by -

(A)

(B)

(C)

(D)



















PART - II : SUBJECTIVE QUESTIONS 1.

A gas is present at a pressure of 2 atm. What should be the increase in pressure so that the volume of

















7.

The temperature of a certain m ass of a gas is doubled. If the initially the gas is at 1 atm pressure. Find the % increase in pressure ?

8.

Pressure of gas contained in a closed vessel is increased by 0.4%, when heated by 1ºC. Calculate its final temperature. Assume ideal nature.

















23.

The vander waals constant for HCI are a = 371.843 KPa.dm6 mol 2 and b = 40.8 cm c m3 mol 1 find the critical constant of this substance.

24.

The vander waals constant for fo r gases A, B and C are as follows : 2 1 6 3 G

–

–

















PART - I : IIT-JEE PROBLEMS (PREVIOUS YEARS)

















11.*

Figure displays the plot of the compression factor Z verses p for a few gases IV I I II

[JEE-2006, 5/184]

























































































Assignment Gaseous State JH Sir-2621

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