Solved Example: Gaseous State | Chemistry for JEE Main & Advanced PDF Download

 Page 1


JEE Solved Example on Gaseous State 
JEE Mains 
Q1:  Gas ?? ( ?? ?????? ) dissociates in a closed rigid container of volume 0.16 lit. as per following 
reaction ?? ?? ( ?? )? ?? ?? ( ?? )+ ???? ( ?? ) 
If degree of dissociation of ?? is 0.4 and remains constant in entire range of temperature, then the 
correct ?? vs ?? graph is [Given ?? = ?? . ???? lit-atm mol /?? ] 
 
Ans:  ?? = 0.16l 
AIM ? to find slope of P -T curve 
???? = ?????? ?? ?? =
????
??   
2Ag( g)? 3 B( g)+ 2C ( g)
1 - 0.4
3
2
( 0.4)
2
2
× 0.4
0.6 0.6 0.4
 Total moles ? 0.6 + 0.6 + 0.4
 ? 1.6
 
 Slope tan ?? =
?? ?? =
????
?? =
1.6 × 0.08
0.16
tan ?? = 0.8
?? = tan
-1
 0.8
 
 
 
 
 
 
Page 2


JEE Solved Example on Gaseous State 
JEE Mains 
Q1:  Gas ?? ( ?? ?????? ) dissociates in a closed rigid container of volume 0.16 lit. as per following 
reaction ?? ?? ( ?? )? ?? ?? ( ?? )+ ???? ( ?? ) 
If degree of dissociation of ?? is 0.4 and remains constant in entire range of temperature, then the 
correct ?? vs ?? graph is [Given ?? = ?? . ???? lit-atm mol /?? ] 
 
Ans:  ?? = 0.16l 
AIM ? to find slope of P -T curve 
???? = ?????? ?? ?? =
????
??   
2Ag( g)? 3 B( g)+ 2C ( g)
1 - 0.4
3
2
( 0.4)
2
2
× 0.4
0.6 0.6 0.4
 Total moles ? 0.6 + 0.6 + 0.4
 ? 1.6
 
 Slope tan ?? =
?? ?? =
????
?? =
1.6 × 0.08
0.16
tan ?? = 0.8
?? = tan
-1
 0.8
 
 
 
 
 
 
Q2:  Calculate the ratio of rate of effusion of ?? ?? and ?? ?? from a container containing ???????? ?? ?? and 
?????? ?? ?? : 
(A) ?? : ?? 
(B) ?? : ?? 
(C) ?? : ?? 
(D) 4: 1 
 Ans: (A) ?? O
2
?
?? O
2
v
M
O
2
?
?? O
2
v
?? O
2
?? H
2
?
?? H
2
v
?? H
2
?
?? H
2
v
?? H
2
 
?? O
2
?? H
2
= v
?? H
2
?? O
2
?? O
2
?? H
2
=
v
2
32
(
 
16
/32
 
2
/3
) =
1
8
 
 
 
Q3:  Kinetic energy of one mole of ????
?? at ' ?? ' ?? is: 
(A) 3 RT 
(B) ?? /?? RT 
(C) ?? /?? RT 
(D) None of these 
Ans: (C) Kinetic energy of CO
2
 at T K 
Total K.E. of energy ?
3
2
 RT 
 
 
Q4:  The mean kinetic energy of 1 mole of ????
?? at ?????? ?? is ?? . The average kinetic energy at 
???????? ?? will be: 
(A) ?? /?? 
(B) ???? 
(C) ?? /???? 
(D) ?? 
Ans:  (B) K.E. =
3
2
???? 
So at T = 300 
K.E. = ?? =
3
2
?? ( 300 ) 
At ?? = 1500 
?? . ?? . =
3
2
?? ( 1500 )= (
3
2
?? ( 300 ) )( 5)= ?? 5 = 5?? 
Answer = B 
Page 3


JEE Solved Example on Gaseous State 
JEE Mains 
Q1:  Gas ?? ( ?? ?????? ) dissociates in a closed rigid container of volume 0.16 lit. as per following 
reaction ?? ?? ( ?? )? ?? ?? ( ?? )+ ???? ( ?? ) 
If degree of dissociation of ?? is 0.4 and remains constant in entire range of temperature, then the 
correct ?? vs ?? graph is [Given ?? = ?? . ???? lit-atm mol /?? ] 
 
Ans:  ?? = 0.16l 
AIM ? to find slope of P -T curve 
???? = ?????? ?? ?? =
????
??   
2Ag( g)? 3 B( g)+ 2C ( g)
1 - 0.4
3
2
( 0.4)
2
2
× 0.4
0.6 0.6 0.4
 Total moles ? 0.6 + 0.6 + 0.4
 ? 1.6
 
 Slope tan ?? =
?? ?? =
????
?? =
1.6 × 0.08
0.16
tan ?? = 0.8
?? = tan
-1
 0.8
 
 
 
 
 
 
Q2:  Calculate the ratio of rate of effusion of ?? ?? and ?? ?? from a container containing ???????? ?? ?? and 
?????? ?? ?? : 
(A) ?? : ?? 
(B) ?? : ?? 
(C) ?? : ?? 
(D) 4: 1 
 Ans: (A) ?? O
2
?
?? O
2
v
M
O
2
?
?? O
2
v
?? O
2
?? H
2
?
?? H
2
v
?? H
2
?
?? H
2
v
?? H
2
 
?? O
2
?? H
2
= v
?? H
2
?? O
2
?? O
2
?? H
2
=
v
2
32
(
 
16
/32
 
2
/3
) =
1
8
 
 
 
Q3:  Kinetic energy of one mole of ????
?? at ' ?? ' ?? is: 
(A) 3 RT 
(B) ?? /?? RT 
(C) ?? /?? RT 
(D) None of these 
Ans: (C) Kinetic energy of CO
2
 at T K 
Total K.E. of energy ?
3
2
 RT 
 
 
Q4:  The mean kinetic energy of 1 mole of ????
?? at ?????? ?? is ?? . The average kinetic energy at 
???????? ?? will be: 
(A) ?? /?? 
(B) ???? 
(C) ?? /???? 
(D) ?? 
Ans:  (B) K.E. =
3
2
???? 
So at T = 300 
K.E. = ?? =
3
2
?? ( 300 ) 
At ?? = 1500 
?? . ?? . =
3
2
?? ( 1500 )= (
3
2
?? ( 300 ) )( 5)= ?? 5 = 5?? 
Answer = B 
 
Q5:  At what temperature the RMS velocity of oxygen molecules is equal to that of ????
?? at ?????? ?? ? 
(A) +??????
°
?? 
(B) -??????
°
?? 
(C) ????
°
?? 
(D) ?????? ?? 
Ans: (B) RMS velocity = v
3????
?? 
Let temperature be to 
RMS
O
2
= RMS
SO
2
 ? v
3RT
MO
2
= v
3RT( 300 )
M
SO
2
 ? T
0
=
300× 32
64
= 150 K = -123
°
C
 
 
 
Q6:  Temperature at which most probable speed of ?? ?? becomes equal to root mean square speed 
of ?? ?? is [Given: ?? ?? at ??????
°
?? ]: 
(A) ?????? ?? 
(B) ???????? ?? 
(C) ?????? ?? 
(D) ?????? ?? 
Ans: (B) 
v
2?? ?? 0
?? O
2
=
v
3????
?? N
2
=
2×?? 0
32
=
3×700 K
28
 
? T
0
= 1200 K 
 
 
Q7:  A rigid container containing ???????? gas at some pressure and temperature. The gas has been 
allowed to escape (do not consider any effusion or diffusion) from the container due to which 
pressure of the gas becomes half of its initial pressure and temperature become ( ?? /?? rd 
 of its 
initial. The mass of gas (in gms) escaped is: 
(A) 7.5 
(B) 1.5 
(C) 2.5 
(D) 3.5 
Ans: (C) Final pressure, temperature = ?? ?? , ?? ?? 
Initial pressure, temperature = P
0
'T
i
 
Page 4


JEE Solved Example on Gaseous State 
JEE Mains 
Q1:  Gas ?? ( ?? ?????? ) dissociates in a closed rigid container of volume 0.16 lit. as per following 
reaction ?? ?? ( ?? )? ?? ?? ( ?? )+ ???? ( ?? ) 
If degree of dissociation of ?? is 0.4 and remains constant in entire range of temperature, then the 
correct ?? vs ?? graph is [Given ?? = ?? . ???? lit-atm mol /?? ] 
 
Ans:  ?? = 0.16l 
AIM ? to find slope of P -T curve 
???? = ?????? ?? ?? =
????
??   
2Ag( g)? 3 B( g)+ 2C ( g)
1 - 0.4
3
2
( 0.4)
2
2
× 0.4
0.6 0.6 0.4
 Total moles ? 0.6 + 0.6 + 0.4
 ? 1.6
 
 Slope tan ?? =
?? ?? =
????
?? =
1.6 × 0.08
0.16
tan ?? = 0.8
?? = tan
-1
 0.8
 
 
 
 
 
 
Q2:  Calculate the ratio of rate of effusion of ?? ?? and ?? ?? from a container containing ???????? ?? ?? and 
?????? ?? ?? : 
(A) ?? : ?? 
(B) ?? : ?? 
(C) ?? : ?? 
(D) 4: 1 
 Ans: (A) ?? O
2
?
?? O
2
v
M
O
2
?
?? O
2
v
?? O
2
?? H
2
?
?? H
2
v
?? H
2
?
?? H
2
v
?? H
2
 
?? O
2
?? H
2
= v
?? H
2
?? O
2
?? O
2
?? H
2
=
v
2
32
(
 
16
/32
 
2
/3
) =
1
8
 
 
 
Q3:  Kinetic energy of one mole of ????
?? at ' ?? ' ?? is: 
(A) 3 RT 
(B) ?? /?? RT 
(C) ?? /?? RT 
(D) None of these 
Ans: (C) Kinetic energy of CO
2
 at T K 
Total K.E. of energy ?
3
2
 RT 
 
 
Q4:  The mean kinetic energy of 1 mole of ????
?? at ?????? ?? is ?? . The average kinetic energy at 
???????? ?? will be: 
(A) ?? /?? 
(B) ???? 
(C) ?? /???? 
(D) ?? 
Ans:  (B) K.E. =
3
2
???? 
So at T = 300 
K.E. = ?? =
3
2
?? ( 300 ) 
At ?? = 1500 
?? . ?? . =
3
2
?? ( 1500 )= (
3
2
?? ( 300 ) )( 5)= ?? 5 = 5?? 
Answer = B 
 
Q5:  At what temperature the RMS velocity of oxygen molecules is equal to that of ????
?? at ?????? ?? ? 
(A) +??????
°
?? 
(B) -??????
°
?? 
(C) ????
°
?? 
(D) ?????? ?? 
Ans: (B) RMS velocity = v
3????
?? 
Let temperature be to 
RMS
O
2
= RMS
SO
2
 ? v
3RT
MO
2
= v
3RT( 300 )
M
SO
2
 ? T
0
=
300× 32
64
= 150 K = -123
°
C
 
 
 
Q6:  Temperature at which most probable speed of ?? ?? becomes equal to root mean square speed 
of ?? ?? is [Given: ?? ?? at ??????
°
?? ]: 
(A) ?????? ?? 
(B) ???????? ?? 
(C) ?????? ?? 
(D) ?????? ?? 
Ans: (B) 
v
2?? ?? 0
?? O
2
=
v
3????
?? N
2
=
2×?? 0
32
=
3×700 K
28
 
? T
0
= 1200 K 
 
 
Q7:  A rigid container containing ???????? gas at some pressure and temperature. The gas has been 
allowed to escape (do not consider any effusion or diffusion) from the container due to which 
pressure of the gas becomes half of its initial pressure and temperature become ( ?? /?? rd 
 of its 
initial. The mass of gas (in gms) escaped is: 
(A) 7.5 
(B) 1.5 
(C) 2.5 
(D) 3.5 
Ans: (C) Final pressure, temperature = ?? ?? , ?? ?? 
Initial pressure, temperature = P
0
'T
i
 
Mole ratio = Mass ratio 
? Escaped gas = 10 - 10 ×
3
4
= 2.5gms 
 
 
 
Q8 : if the absolute temperature and pressure of a gas are doubled, its volume would become: 
(A) Doubled 
(B) Halve 
(C) Increases four times 
(D) Remains the same 
Ans: (D) P
0
 V
0
= ???? T
0
 
When pressure and temperature doubled 
?? ?? ?? ?? = ???? ?? ?? 2?? 0
?? ?? = ???? ( 2?? 0
)
?? ?? =
???? ?? 0
?? 0
= ?? 0
 from (i) 
 
? Volume remains same 
 
 
Q9:  Two gases contained separately in flasks of equal pressures of 1 atmosphere each. What will 
be the resultant pressure if the flasks are connected? 
(A) 2 atmosphere 
(B) 1/2 atmosphere 
(C) 1 atmosphere 
(D) None of these 
 Ans: (C) ?? 0
?? 0
= ???? ?? 0
?? ?? ?? ?? = ?? ?? ?? ?? ?? Now ?? ?? = ?? 0
, ?? ?? = 2?? 0
, ?? ?? = 2?? 0
 ? ?? ?? =
?? 0
?? ?? 0
?? 0
= ?? 0
?? ?? = ?? 0
= 1 atm
 
 
 
 
 
 
Page 5


JEE Solved Example on Gaseous State 
JEE Mains 
Q1:  Gas ?? ( ?? ?????? ) dissociates in a closed rigid container of volume 0.16 lit. as per following 
reaction ?? ?? ( ?? )? ?? ?? ( ?? )+ ???? ( ?? ) 
If degree of dissociation of ?? is 0.4 and remains constant in entire range of temperature, then the 
correct ?? vs ?? graph is [Given ?? = ?? . ???? lit-atm mol /?? ] 
 
Ans:  ?? = 0.16l 
AIM ? to find slope of P -T curve 
???? = ?????? ?? ?? =
????
??   
2Ag( g)? 3 B( g)+ 2C ( g)
1 - 0.4
3
2
( 0.4)
2
2
× 0.4
0.6 0.6 0.4
 Total moles ? 0.6 + 0.6 + 0.4
 ? 1.6
 
 Slope tan ?? =
?? ?? =
????
?? =
1.6 × 0.08
0.16
tan ?? = 0.8
?? = tan
-1
 0.8
 
 
 
 
 
 
Q2:  Calculate the ratio of rate of effusion of ?? ?? and ?? ?? from a container containing ???????? ?? ?? and 
?????? ?? ?? : 
(A) ?? : ?? 
(B) ?? : ?? 
(C) ?? : ?? 
(D) 4: 1 
 Ans: (A) ?? O
2
?
?? O
2
v
M
O
2
?
?? O
2
v
?? O
2
?? H
2
?
?? H
2
v
?? H
2
?
?? H
2
v
?? H
2
 
?? O
2
?? H
2
= v
?? H
2
?? O
2
?? O
2
?? H
2
=
v
2
32
(
 
16
/32
 
2
/3
) =
1
8
 
 
 
Q3:  Kinetic energy of one mole of ????
?? at ' ?? ' ?? is: 
(A) 3 RT 
(B) ?? /?? RT 
(C) ?? /?? RT 
(D) None of these 
Ans: (C) Kinetic energy of CO
2
 at T K 
Total K.E. of energy ?
3
2
 RT 
 
 
Q4:  The mean kinetic energy of 1 mole of ????
?? at ?????? ?? is ?? . The average kinetic energy at 
???????? ?? will be: 
(A) ?? /?? 
(B) ???? 
(C) ?? /???? 
(D) ?? 
Ans:  (B) K.E. =
3
2
???? 
So at T = 300 
K.E. = ?? =
3
2
?? ( 300 ) 
At ?? = 1500 
?? . ?? . =
3
2
?? ( 1500 )= (
3
2
?? ( 300 ) )( 5)= ?? 5 = 5?? 
Answer = B 
 
Q5:  At what temperature the RMS velocity of oxygen molecules is equal to that of ????
?? at ?????? ?? ? 
(A) +??????
°
?? 
(B) -??????
°
?? 
(C) ????
°
?? 
(D) ?????? ?? 
Ans: (B) RMS velocity = v
3????
?? 
Let temperature be to 
RMS
O
2
= RMS
SO
2
 ? v
3RT
MO
2
= v
3RT( 300 )
M
SO
2
 ? T
0
=
300× 32
64
= 150 K = -123
°
C
 
 
 
Q6:  Temperature at which most probable speed of ?? ?? becomes equal to root mean square speed 
of ?? ?? is [Given: ?? ?? at ??????
°
?? ]: 
(A) ?????? ?? 
(B) ???????? ?? 
(C) ?????? ?? 
(D) ?????? ?? 
Ans: (B) 
v
2?? ?? 0
?? O
2
=
v
3????
?? N
2
=
2×?? 0
32
=
3×700 K
28
 
? T
0
= 1200 K 
 
 
Q7:  A rigid container containing ???????? gas at some pressure and temperature. The gas has been 
allowed to escape (do not consider any effusion or diffusion) from the container due to which 
pressure of the gas becomes half of its initial pressure and temperature become ( ?? /?? rd 
 of its 
initial. The mass of gas (in gms) escaped is: 
(A) 7.5 
(B) 1.5 
(C) 2.5 
(D) 3.5 
Ans: (C) Final pressure, temperature = ?? ?? , ?? ?? 
Initial pressure, temperature = P
0
'T
i
 
Mole ratio = Mass ratio 
? Escaped gas = 10 - 10 ×
3
4
= 2.5gms 
 
 
 
Q8 : if the absolute temperature and pressure of a gas are doubled, its volume would become: 
(A) Doubled 
(B) Halve 
(C) Increases four times 
(D) Remains the same 
Ans: (D) P
0
 V
0
= ???? T
0
 
When pressure and temperature doubled 
?? ?? ?? ?? = ???? ?? ?? 2?? 0
?? ?? = ???? ( 2?? 0
)
?? ?? =
???? ?? 0
?? 0
= ?? 0
 from (i) 
 
? Volume remains same 
 
 
Q9:  Two gases contained separately in flasks of equal pressures of 1 atmosphere each. What will 
be the resultant pressure if the flasks are connected? 
(A) 2 atmosphere 
(B) 1/2 atmosphere 
(C) 1 atmosphere 
(D) None of these 
 Ans: (C) ?? 0
?? 0
= ???? ?? 0
?? ?? ?? ?? = ?? ?? ?? ?? ?? Now ?? ?? = ?? 0
, ?? ?? = 2?? 0
, ?? ?? = 2?? 0
 ? ?? ?? =
?? 0
?? ?? 0
?? 0
= ?? 0
?? ?? = ?? 0
= 1 atm
 
 
 
 
 
 
Q10:  At very low pressure, the Vander Waal's equation for one mole is written is: 
(A) ???? - ???? = ???? 
(B) ???? + ?? = ???? 
(C) ???? = ???? 
(D) ( ?? + ?? /?? ?? ) ( ?? )= ???? 
Ans: (D) At very low pressure, attractive forces are low, volume occupied is higher compared to 
volume occupied by molecule 
 ? V >> b
 ? Real gas equation 
( P +
a
V
2
)V = RT
 
 
 
 
 
Q11:  A gas cylinder contains 0.3 mol of ?? ?? , ?? . ?? mol of ?? ?? and 0.5 mol of helium. If the total 
pressure is ?? atmospheres, what will be the partial pressure of nitrogen? 
(A) ?? /?? ?????? 
(B) ?? . ?? × ?? × ?????? ???? 
(C) 
?? ?? .?? × ?????? ???? 
(D) 
?? ?? .?? × ?????? 
Ans:  (B) ?? 1
 mole fraction of N
2
=
0.3
0.3+0.2+0.5
= 0.3 ? Partial pressure = ?? P
P 
= 0.3Patm 
= 0.3P× 760 mm of Hg 
 
 
Q12: ???? ?? each of sulphur dioxide, phosphine and hydrogen are kept in three flasks. Decreasing 
order of number of atoms is: 
(A) Phosphine, sulphur dioxide, hydrogen 
(B) Hydrogen, phosphine, sulphur dioxide 
(C) Sulphur dioxide, phosphine, hydrogen 
(D) Hydrogen, sulphur dioxide, phosphine 
Ans: (B) 10 g each of SO
2
, PH
3
 and H
2
 are kept in 3 flasks 
We know, 
Number of atom ? Number of molecule 
And, for a given mass of gas 
Number of mole =
 Mass 
 Molecule weight 
 
Which implies