Gas State

(1)

Level 1

Q No: 1

Three flasks of equal volumes contain CH4, CO2 and Cl2 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 Correct Answer: 3 Status: unattempted

[X]

Avogadro's Law

Otherwise think in terms of n =

Avogadro's Law :→ "At same condition of temperature and pressure, equal volumes of different gases contains equal number of molecules."

Q No: 2

At 0ºC, 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

Correct Answer: 1 Status: unattempted

[X]

(2)

Q No: 3

8.2 L of an ideal gas weight 9.0 gm at 300 K and 1 atm pressure. The molecular mass of gas

is-(1) 9 (2) 27 (3) 54 (4) 81

[X]

Ideal gas equation

Q No: 4

A gas 'A' having molecular weight 4 diffuses thrice as fast as the gas B. The molecular weight of gas B

is-(1) 36 (2) 12 (3) 18 (4) 24

[X]

rA = 3 rB

Grahamís Law of effusion or diffusion

Q No: 5

Equal volumes of two gases A and B diffuse through a porous pot in 20 and 10 seconds respectively. If the molar mass of A be 80, find the molar mass of B.

(1) 80 g mol–1

(2) 20 g mol–1

(3) 40 g mol–1

(3)

[X]

t1 = t2 (same time interval)

Q No: 6

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 Correct Answer: 3 Status: unattempted

Kinetic Theory of Gases's postulates Elastic collisions.

According to K.T.G., collision of gaseous molecules is elastic collision. Q No: 7

The average speed of an ideal gas molecule at 27ºC is 0.3 m sec–1_{. Calculate average}

speed at 927ºC. (1) 0.15 m/sec (2) 1.2 m/sec (3) 2.4 m/sec (4) 0.6 m/sec

(4)

Q No: 8

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 L of volume

(4) At which one mole of it occupies volume of 22.4 L Correct Answer: 2 Status: unattempted

Definition of Critical temp.

Critical Temperature (TC) :→ The temperature above which liquification of gas cannot take

place however high pressure is applied on it. NA

Q No: 9

The compressibility factor for an ideal gas is :

(1) 1.5 (2) 1.0 (3) 2.0 (4) ∞

Correct Answer: 2 Status: unattempted For ideal gas PV = nRT

PV = nRT for ideal gas

(5)

One litre of an unknown gas weighs 1.25 gm at N.T.P. which of the following gas pertains to the above data

-(1) CO2

(2) NO2

(3) N2

(4) O2

[X]

N.T.P. (22.4 L 1 mole gas) M.W. (weight of 22.4 L) Decide from options.

Weight of 1 L gas at N.T.P. = 1.25 g.

∴ M.W. = weight of 22.4 L = 1.25 × 22.4 = 28 g.

from option N2 (M.W. = 28)

Q No: 11

V versus T curves at constant pressure P1 and P2 for an ideal gas are shown in fig. Which

is correct

-(1) P1 > P2

(2) P1 < P2

(3) P1 = P2

(4) All

Higher slope, lower pressure. Otherwise at same temperature

(6)

Q No: 12

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

Kinetic Energy is function of temperature only for ideal gas

K.E. of a gas is function of temperature only. Q No: 13

A box of 1L capacity is divided into two equal compartments by a thin partition which are filled with 2g H2 and 16gm CH4 respectively. The pressure in each compartment is

recorded as P atm. The total pressure when partition is removed will be

-(1) P (2) 2P (3) P/2 (4) P/4

Does by opening door between two rooms, pressure of each room becomes 2 atm? or remains 1 atm?

after removing partition pressure will be same in both sides. NA

(7)

Helium atom is twice times heavier than a hydrogen molecule. At 25ºC the average K.E. of helium atom is

-(1) Twice that of hydrogen (2) Same as that of hydrogen (3) Four times that of hydrogen (4) Half that of hydrogen

K.E. of gas does not depends upon M.W. K.E. of gas function of temperature only

Q No: 15

Which of the following molecule has the lowest average speed at 273 K ? (1) CO

(2) CH4

(3) CO2

(4) C2H6

(8)

Q No: 16

A real gas is expected to exhibit maximum deviations from ideal gas laws at -(1) Low T and High P

(2) Low T and Low P (3) High T and High P (4) High T and Low P

At high temperature force of attraction deceases i.e. 'a' becomes very small. At low pressure, molecular volumes becomes insignificant i.e.

b << v

Real gas at high temperature, low pressure

At high temperature and low pressure real gases behaves as ideal gas. Q No: 17

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

-(1) (2) (3) (4)

(9)

Volume of sphere

b = 4 NAV Volume of one molecule

= 4. NA

Q No: 18

The units of the van der Waal's constant 'b' are -(1) atmosphere

(2) joules (3) L mol–1

(4) mol L–1

Dimensional analysis

In addition or subtraction of two Quantity dimensions must be same. Dimension of V and nb are same

(V – nb)

∴ unit of b = (L mole–1₎

Q No: 19

At 100 ºC a gas has 1 atm. pressure and 10 L volume. Its volume at NTP would be -(1) 10 litres

(2) Less than 10 litres (3) More than 10 litres (4) None

Charle's Law Compare T1 and T2. At 100ºC (= 373 K) V = 10 L at cont P V œ T ∴ at 273 k V < 10 L. Level 2 [X]

(10)

Avogadro's Law

Otherwise think in terms of n =

Avogadro's Law :→ "At same condition of temperature and pressure, equal volumes of different gases contains equal number of molecules."

Level 2

Q No: 1

An open flask containing air is heated from 300 K to 500 K. What percentage of air will be escaped to the atmosphere, if pressure is kept constant ?

(1) 80 (2) 40 (3) 60 (4) 20

Correct Answer: 2 Status: unattempted Open vessel heating P,V const.

Apply n1T1 = n2T2

Q No: 2

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

(1) 251 K (2) 502 K (3) 250 K (4) 400 K

(11)

If P1 = P then P2 = 1.004 P

Q No: 3

A rigid container containing 5 mole H2 gas at same pressure and temperature. The gas

has been allowed to escape by simple process from the container due to which pressure of the gas becomes half of its initial pressure and temperature become (2/3)rd_{of its}

intitial. The mass of gas remaining is : (1) 7.5 g

(2) 1.5 g (3) 2.5 g (4) 3.5 g

[X]

Write initial and final n, T and P in appropriate terms.

(12)

No: 4

821 mL N2(g) was collected over liquid water at 300 K and 1 atm. If vapour pressure of

H2O is 30 torr then moles of N2(g) in moist gas mixture is :

(1) 0.39 (2) 0.032 (3) 0.96 (4) 0.0013

[X]

Use partial pressure of N2 only

Q No: 5

Equal masses of SO2, CH4 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

(13)

(2) 0.75 atm (3) 1.2 atm (4) 0.6 atm

cv

Q No: 6

At what temperature will average speed of the molecules of the second member of the series CnH2n be the same of Cl2 at 627ºC ?

(1) 259.4 K (2) 400 K (3) 532.4 K (4) None of these

(14)

Q No: 7

Compressibility factor(Z) for N2 at –50ºC and 800 atm pressure is 1.95 Calculate mole of

N2 gas required to fill a gas cylinder of 100 L capacity under the given conditions.

(1) 2.24 × 103

(2) 22.4 (3) 44.8 (4) 2296

[X]

Convert all terms in approperiate units Determine moles.

8. The behaviour of a real gas is usually depicted by plotting compressibility factor Z

versus P at a constant temperature. At high temperature and high pressure, Z is usually more than one This fact can be explained by van der Walls' equation when :

1

) The constant a is negligible and not b 2

) The constant b is negligible and not a 3 Both the constant a and b are negligible

(15)

) 4

) Both the constants a and b are not negligible Write vander wall's equations (for 1 mole)

at high pressure a/v2_{<< P}

Z =

Q No: 9

What will be the pressure exerted by a mixture of 3.2 g of methane and 4.4 g of carbon dioxide contained in a 9 dm3_{flask at 27ºC ?}

(1) 8.31 × 104_bar

(2) 8.31 × 104_Pa

(3) 8.31 × 106_Pa

(4) 4.15 × 104_Pa

Correct Answer: 2 Status: unattempted alton's Law of Partial Pressure

nT = nA + nB

(16)

Q No: 10

The root mean square velocity of hydrogen is times than that of nitrogen. If T is the temperature of the gas, then :

(1) (2) (3) (4)

[X]

Take ratio of Vr.m.s. of H2 to N2

(17)

Q No: 11

Calculate relative rate of effusion of O2 to CH4 through a container containing O2 and

CH4 in 3 : 2 mass ratio.

(1) (2) (3)

(4) none of these

Correct Answer: 2 Status: unattempted Convert mass ratio to mole ratio

Take mole ratio = Pressure ratio Use graham's Law of diffusion

(18)

No: 12

Calculate the number of moles of gas present in the container of volume 10 L at 300 K. If the manometer containing glycerin shows 5 m difference in level as shown diagram. (Given : dglycrin = 2.72 g/mL; dmercury = 13.6 g/mL)

(1) 0.94 mole (2) 0.49 mole (3) 0.64 mole (4) none of these

Determine Pressure in terms of Height of mercury column. haρag = hbρbg

Determine Pressure of gas and use ideal gas equation haρag = hbρbg

(5) (2.72) = (h) (13.6)

Q No: 13

At what temperature will most probable speed of the molecules of the second member of homologous series CnH2n–2 be the same as that of SO2 at 527ºC.

(1) 500ºC (2) 727ºC (3) 227ºC

(19)

Q No: 14

Two flask A and B of equal volumes maintained at temperature 300 K and 700 K contain equal mass of He(g) and N2(g) respectively. What is the ratio of total translational kinetic

energy of gas in flask A to that of flask B ? (1) 1 : 3

(2) 3 : 1 (3) 3 : 49

(4) None of these

(20)

Q No: 15

4 gm of sulphur dioxide gas diffuses from a container in 8 min. Mass of helium gas diffusing from the same container over the same time interval is :

(1) 0.5 gm (2) 1 gm (3) 2 gm

(4) None of these

[X]

(21)

Q No: 16

Two closed vessel A and B of equal volume of 8.21 L are connected by a narrow tube of negligible volume with open valve. The left hand side container is found to contain 3 mole CO2 and 2 mole of He at 400 K, what is the partial pressure of He in vessel B at

500 K ?

(1) 2.4 atm (2) 8 atm (3) 12 atm (4) none of these

[X]

(22)

Q No: 17

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

-(1) Same as that in Y (2) Half of that in Y (3) Twice of that in Y (4) 8 times of that in Y

(23)

Q No: 18

Temperature at which most probable speed of O2 becomes equal to root mean square

speed of N2 is [Given : N2 at 427°C]

(1) 732 K (2) 1200 K (3) 927 K (4) 800 K

[X]

(24)

Q No: 19

The density of gas A is twice that of B at the same temperature the molecular weight of gas B is thrice that of A. The ratio of pressure of gas A and gas B will be

(1) 1 : 6 (2) 7 : 8 (3) 6 : 1 (4) 1 : 4

Take ratio of dA and dB from hint (1).

Q No: 20

Compressibility factor (z) for real gas at very high pressure is (1)

(2) 1 (3)

(25)

(4) 1 –

Write vander waalís equation for 1 mole At high P P >>

Z =

Q No: 21

At 0ºC and 1 atm pressure, volume occupied by one mole of a gas is greater than 22.4L. Compressibility factor (z) for the gas is

(1) greater than 1 (2) less than 1 (3) equal to 1

(4) can be greater or less than on Correct Answer: 1 Status: unattempted

For ideal gas PVm = RT

Zreal < Zideal

Compare (Vm)real and (Vm)ideal.

For ideal at 0ºC and 1 atm Vm = 22.4 L

for real gas if Z > 1, Vm > 22.4 L. if Z < 1, Vm < 22.4 L

Level 3

(26)

A mixture of hydrogen and helium is prepared such that the number of wall collisions per unit time by molecules of each gas is the same. Which gas has the higher concentration?

(1) He (2) H2

(3) Both

(4) None of these

Number of molecuels colliding at wall/time =

NA Q No: 2

For a gaseous reaction, 2A(g) → 3B(g) + C(g)

Whose extent of dissociation depends on temperature is performed in a closed container, it is known that extent of dissociation of A is different in different temperature range. With in a temperature range it is constant. (Temperature range T0 – T1, T1 – T2, T2 – T∞).

A plot of P v/s T is drawn under the given condition. Given : tan55 = 1.42, tan50 = 1.19, tan60 = 1.73

If is the degree of dissociation of A then in the temperature range Ti → Ti + 1

(1) (2) (3) (4)

(27)

V = constant P Vs T is straight line and passes from origin. tanθ = n (Number of moles)

Q No: 3

For a gaseous reaction, 2A(g) → 3B(g) + C(g)

Whose extent of dissociation depends on temperature is performed in a closed container, it is known that extent of dissociation of A is different in different temperature range. With in a temperature range it is constant. (Temperature range T0 – T1, T1 – T2, T2 – T∞).

A plot of P v/s T is drawn under the given condition. Given : tan55 = 1.42, tan50 = 1.19, tan60 = 1.73

If initially 1 mole of A is taken in a 0.0821 l container then [R = 0.0821 atm lit/k] (1)

(2) (3) (4)

(28)

tan 50 = 1.19 = 1 + α α = 0.19 tan 55 = 1 + α 1.42 = 1 + α ; α = 0.42. NA Q No: 4

Select the correct option(s) for an ideal gas

(1) Most probable speed increases with increase in temperature

(2) Fraction of particles moving with most probable speed increases with increase in temperature

(3) Fraction of particles moving with most probable speed are more for Cl2 than H2

under similar condition of T, P & V.

(4) Most probable speed is more for Cl2 than H2 at same temperature

Correct Answer: 1,3 Status: unattempted

Q No: 5

For two gases A and B, P v/s V isotherms are drawn at T K as shown. TA & TB are

(29)

Which of following is true? (1) TA < T < TB

(2) TA > T > TB

(3) TA > TB > T

(4) none of above

[X]

Experiment Temp > TC then gas cannot be liquified.

TA > T < TB

NA Q No: 6

For two gases A and B, P v/s V isotherms are drawn at T K as shown. TA & TB are

critical temperatures of A & B respectively

The correct statement(s) is/are

(I) Pressure correction term will be more negligible for gas B at T K. (II) The curve for gas 'B' will be of same shape as for gas A if T > TB

(III) Gas 'A' will show same P v/s V curve as of gas 'B' if T > TA

(1) III only (2) II and III (3) II only (4) All

(30)

If a = 0 then attraction is zero so gas can not be liquified. T > (TC)B so gas show that graph.

TA is critical point of A and above TC gas can not be liquified.

Q No: 7

On the recently discovered 10th_{planet it has been found that the gases follow the}

relationship PeV/2_{= nCT where C is constant other notation are as usual (V in lit., P in}

atm and T in Kelvin). A curve is plotted between P and V at 500 K & 2 moles of gas as shown in figure

The value of constant C is (1) 0.01

(2) 0.001 (3) 0.005 (4) 0.002

Applying PeV/2 _{= nCT.}

NA Q No: 8

(31)

Find the slope of the curve plotted between P Vs T for closed container of volume 2 lit. having same moles of gas

(1)

(2) 2000 e (3) 500 e (4)

NA NA Q No: 9

If a closed container of volume 200 lit. of O2 gas (ideal gas) at 1 atm & 200 K is taken to

planet. Find the pressure of oxygen gas at the planet at 821 K in same container (1)

(2) (3) 1 atm (4) 2 atm

(32)

NA NA Q No: 10

The molar volume of He at 10.1325 MPa and 273 K is 0.011075 of its molar volume at 101.325 KPa at 273 K.Calculate the radius of helium atom. The gas is assumed to show real gas nature. Neglect the value of a for He.

(1) r = 1.33 × 10–8_cm

(2) r = 2.33 × 10–8_cm

(3) r = 1.33 × 10–6_cm

(4) r = 5.23 × 10–3_cm

For He a = 0

NA Q No: 11

Sign of initial slope of compressibility factor (z) versus P curves is ________ if a gas is below its Boyle's temperature and ________ if it is above its Boyle's temperature. (1) +ive, +ive

(2) –ive, +ive (3) –ive, –ive (4) +ive, –ive

For He a = 0

(33)

Q No: 12

A commercial cylinder contains 6.91 m3_{of O}

2 at 15 M Pa and 21°C. the critical

constants for O2 are TC = –126°C, PC = 50 bar. Determine the reduced pressure and

reduced temperature for O2 under these conditions.

(1) PR = 3, TR = 2

(2) PR = 2, TR = 3

(3) PR = 5, TR = 2

(4) PR = 3, TR = 5

[X]

Put in the same unit. NA

Q No: 13

Calculate the number of moles of gas present in the container of volume 10 lit at 300 K. If the manometer containing glycerin shows 5m difference in level as shown in diagram. Given : dglycerin = 2.72 gm/ml, dmercury = 13.6 gm/ml.

(1) 0.94 mole (2) 0.93 mole (3) 0.84 mole (4) 0.90 mole

Correct Answer: 1 Status: unattempted eight is determine for glycerin.

h1d1 = h2d2

(34)

Q No: 14

A manometer attached to a flask contains NH3 gas have no difference in mercury level

initially as shown in diagram. After the sparking into the flask, it have difference of 19 cm in mercury level in two columns. Calculate % dissociation of ammonia.

(1) 21% (2) 22% (3) 24% (4) 25%

P1M1 = P2M2

76 × 17 = 95 × M2

M2 = 13.6

(35)

1.0 × 10–2_{kg of hydrogen and 6.4 × 10}–2_{kg of oxygen are contained in a 10 × 10}–3_m3

flask at 473 K. Calculate the total pressure of the mixture. If a spark ignities the mixture. What will be the final pressure.

(1) Ptotal = 27.54 × 105 N/m2, Pfinal = 19.66 × 105 N/m2

NA

Q No: 16

Calculate relative rate of effusion of SO2 to CH4 under given condition

(i) Under similar condition of pressure & temperature

(ii) Through a container containing SO2 and CH4 in 3 : 2 mass ratio

(iii) If the mixture obtained by effusing out a mixture for

three effusing steps. (1)

(i) ; (ii) ; (iii) (2)

(i) ; (ii) ; (iii) (3)

(i) ; (ii) ; (iii) (4) None of these

(36)

Q No: 17

Find the number of diffusion steps required to separate the isotopic mixture initially containing some amount of H2 gas and 1 mol of D2 gas in a container of 3 lit capacity

maintained at 24.6 atm & 27 °C to the final mass ratio .

(1) 1 (2) 2 (3) 3 (4) 4

(37)

Q No: 18

Calculate the fraction of N2 molecules at 101.325 kPa and 300 K whose speeds are in the

range of ump – 0.005 ump to ump + 0.005 ump.

(1) 8.303 × 10–3

(2) 7.303 × 10–3

(3) 8.501 × 10–3

(4) 5.323 × 10–3

U2 – U1 = Ump + 0.005Ump – Ump + 0.005Ump = 0.01 Ump 0.01 Ump

f = 0.01 Q No: 19

One mole of an ideal gas is subjected to a process in which P (in atm) = V (in Litre). If the process is operating from a initial pressure 1 atm to final pressure 10 atm (no higher pressure achieved during the process) then what would be the maximum temperature obtained & at what instant will it occur in the process.

(1) 10,000 K (2) 20,000 K (3) 15,000 K (4) 19,000 K

Moles remains constant.

(38)