Gaseous state IIT JAM Notes | EduRev

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IIT JAM : Gaseous state IIT JAM Notes | EduRev

 Page 1


 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
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Physical 
Chemistry      
TOPIC: GASEOUS STATE CHEMISTRY 
IIT-JAM/DU M.Sc./CSIR-NET/GATE 
 
 
ALL FACULTY FROM IIT 
 
2637, Hudson Lane, Behind Khalsa College, Near 
G.T.B. Nagar Metro Station Gate No. 3 & 4, New 
Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: 
info@asfinstitute.com, www.asfinstitute.com 
Page 2


 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
 
 
Physical 
Chemistry      
TOPIC: GASEOUS STATE CHEMISTRY 
IIT-JAM/DU M.Sc./CSIR-NET/GATE 
 
 
ALL FACULTY FROM IIT 
 
2637, Hudson Lane, Behind Khalsa College, Near 
G.T.B. Nagar Metro Station Gate No. 3 & 4, New 
Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: 
info@asfinstitute.com, www.asfinstitute.com 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
GASEOUS STATE 
The state of matter in which the molecular forces of attraction between the particles of matter are 
minimum, is known as gaseous state. It is the simplest state and shows great uniformity in behaviour. 
 Characteristics of gases. 
(A) Gases or their mixtures are homogeneous in composition. 
(B) Gases have very low density due to negligible intermolecular forces. 
(C) Gases have infinite expansibility and high compressibility. 
(D) Gases exert pressure. 
(E) Gases possess high diffusibility. 
(F) Gases do not have definite shape and volume like liquids. 
(G) Gaseous molecules move very rapidly in all directions in a random manner i.e., gases have highest kinetic 
energy. 
(H) Gaseous molecules are loosely packed having large empty spaces between them. 
(I) Gaseous molecules collide with one another and also with the walls of container with perfectly elastic 
collisions. 
(J) Gases can be liquified, if subjected to low temperatures (below critical) or high pressures. 
(K) Thermal energy of gases >> molecular attraction. 
(L) Gases undergo similar change with the change of temperature and pressure. In other words, gases obey 
certain laws known as gas laws. 
 Measurable properties of gases. 
(A) The characteristics of gases are described fully in terms of four parameters or measurable properties : 
 (i) The volume, V, of the gas. 
 (ii) Its pressure, P 
 (iii)Its temperature, T 
 (iv) The amount of the gas (i.e., mass or number of moles). 
(B) Volume : (a)Since gases occupy the entire space available to them, the measurement of volume of a 
gas only requires a measurement of the container confining the gas. 
 (b) Volume is expressed in litres (L), millilitres (mL) or cubic centimetres ) (
3
cm or cubic metres ) (
3
m . 
 (c) mL L 1000 1 ? ; L mL
3
10 1
?
? 
  
3 3 3
10 1 1 cm dm L ? ? 
  L mL cm dm m
3 6 3 6 3 3 3
10 10 10 10 1 ? ? ? ? 
 (C) Mass : (a) The mass of a gas can be determined by weighing the container in which the gas is enclosed 
and again weighing the container after removing the gas. The difference between the two weights gives the 
mass of the gas. 
 (b) The mass of the gas is related to the number of moles of the gas i.e. 
Page 3


 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
 
 
Physical 
Chemistry      
TOPIC: GASEOUS STATE CHEMISTRY 
IIT-JAM/DU M.Sc./CSIR-NET/GATE 
 
 
ALL FACULTY FROM IIT 
 
2637, Hudson Lane, Behind Khalsa College, Near 
G.T.B. Nagar Metro Station Gate No. 3 & 4, New 
Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: 
info@asfinstitute.com, www.asfinstitute.com 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
GASEOUS STATE 
The state of matter in which the molecular forces of attraction between the particles of matter are 
minimum, is known as gaseous state. It is the simplest state and shows great uniformity in behaviour. 
 Characteristics of gases. 
(A) Gases or their mixtures are homogeneous in composition. 
(B) Gases have very low density due to negligible intermolecular forces. 
(C) Gases have infinite expansibility and high compressibility. 
(D) Gases exert pressure. 
(E) Gases possess high diffusibility. 
(F) Gases do not have definite shape and volume like liquids. 
(G) Gaseous molecules move very rapidly in all directions in a random manner i.e., gases have highest kinetic 
energy. 
(H) Gaseous molecules are loosely packed having large empty spaces between them. 
(I) Gaseous molecules collide with one another and also with the walls of container with perfectly elastic 
collisions. 
(J) Gases can be liquified, if subjected to low temperatures (below critical) or high pressures. 
(K) Thermal energy of gases >> molecular attraction. 
(L) Gases undergo similar change with the change of temperature and pressure. In other words, gases obey 
certain laws known as gas laws. 
 Measurable properties of gases. 
(A) The characteristics of gases are described fully in terms of four parameters or measurable properties : 
 (i) The volume, V, of the gas. 
 (ii) Its pressure, P 
 (iii)Its temperature, T 
 (iv) The amount of the gas (i.e., mass or number of moles). 
(B) Volume : (a)Since gases occupy the entire space available to them, the measurement of volume of a 
gas only requires a measurement of the container confining the gas. 
 (b) Volume is expressed in litres (L), millilitres (mL) or cubic centimetres ) (
3
cm or cubic metres ) (
3
m . 
 (c) mL L 1000 1 ? ; L mL
3
10 1
?
? 
  
3 3 3
10 1 1 cm dm L ? ? 
  L mL cm dm m
3 6 3 6 3 3 3
10 10 10 10 1 ? ? ? ? 
 (C) Mass : (a) The mass of a gas can be determined by weighing the container in which the gas is enclosed 
and again weighing the container after removing the gas. The difference between the two weights gives the 
mass of the gas. 
 (b) The mass of the gas is related to the number of moles of the gas i.e. 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
    moles of gas (n)
M
m
? ?
mass Molar 
grams in Mass
 
 (iii)Mass is expressed in grams or kilograms,  g Kg
3
10 1 ? 
(D) Temperature :  (a) Gases expand on increasing the temperature. If temperature is increased twice, the 
square of the velocity ) (
2
v also increases two times. 
 (b) Temperature is measured in centigrade degree ) ( C
o
 or celsius degree with the help of 
thermometers. Temperature  is also measured in Fahrenheit (F
o
). 
 (c) S.I. unit of temperature is kelvin (K) or absolute degree. 
     273 ? ? C K
o
 
 (iv) Relation between F and C
o
 is 
9
32
5
?
?
o o
F C
 
(E) Pressure :  (a) Pressure of the gas is the force exerted by the gas per unit area of the walls of the 
container in all directions. Thus, Pressure (P)
) ( Area
) ( on Accelerati ) ( Mass
) Area(
) Force(
a
a m
A
F ?
? ? 
 (b) Pressure exerted by a gas is due to kinetic energy )
2
1
(
2
mv KE ? of the molecules. Kinetic energy of 
the gas molecules increases, as the temperature is increased. Thus, Pressure of a gas ? Temperature (T). 
 (c) Pressure of a pure gas is measured by manometer while that of a mixture of gases by barometer. 
 (d) Commonly two types of manometers are used, 
  (a) Open end manometer;  (b) Closed end manometer 
 (e) The S.I. unit of pressure, the pascal (Pa), is defined as 1 newton per metre square. It is very small 
unit. 
  
2 1 2
1 1 1
? ? ?
? ? s m kg Nm Pa 
 (f)  C.G.S. unit of pressure is dynes 
2 ?
cm . 
 (g) M.K.S. unit of pressure is 
2
/ m kgf . The unit 
2
/ cm kgf sometime called ata (atmosphere technical 
absolute). 
 (h) Higher unit of pressure is bar, KPa or MPa. 
  KPa KNm Nm Pa bar 100 100 10 10 1
2 2 5 5
? ? ? ?
? ?
 
 (i) Several other units used for pressure are, 
Name  Symbol Value 
bar bar Pa bar
5
10 1 ? 
atmosphere atm Pa atm
5
10 01325 . 1 1 ? ? 
Torr Torr 
Pa Pa Torr 322 . 133
760
101325
1 ? ? 
millimetre of mercury mm Hg 
Pa Hg mm 322 . 133 1 ? 
 
 (j) The pressure relative to the atmosphere is called gauge pressure. The pressure relative to the 
perfect vacuum is called absolute pressure. 
Page 4


 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
 
 
Physical 
Chemistry      
TOPIC: GASEOUS STATE CHEMISTRY 
IIT-JAM/DU M.Sc./CSIR-NET/GATE 
 
 
ALL FACULTY FROM IIT 
 
2637, Hudson Lane, Behind Khalsa College, Near 
G.T.B. Nagar Metro Station Gate No. 3 & 4, New 
Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: 
info@asfinstitute.com, www.asfinstitute.com 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
GASEOUS STATE 
The state of matter in which the molecular forces of attraction between the particles of matter are 
minimum, is known as gaseous state. It is the simplest state and shows great uniformity in behaviour. 
 Characteristics of gases. 
(A) Gases or their mixtures are homogeneous in composition. 
(B) Gases have very low density due to negligible intermolecular forces. 
(C) Gases have infinite expansibility and high compressibility. 
(D) Gases exert pressure. 
(E) Gases possess high diffusibility. 
(F) Gases do not have definite shape and volume like liquids. 
(G) Gaseous molecules move very rapidly in all directions in a random manner i.e., gases have highest kinetic 
energy. 
(H) Gaseous molecules are loosely packed having large empty spaces between them. 
(I) Gaseous molecules collide with one another and also with the walls of container with perfectly elastic 
collisions. 
(J) Gases can be liquified, if subjected to low temperatures (below critical) or high pressures. 
(K) Thermal energy of gases >> molecular attraction. 
(L) Gases undergo similar change with the change of temperature and pressure. In other words, gases obey 
certain laws known as gas laws. 
 Measurable properties of gases. 
(A) The characteristics of gases are described fully in terms of four parameters or measurable properties : 
 (i) The volume, V, of the gas. 
 (ii) Its pressure, P 
 (iii)Its temperature, T 
 (iv) The amount of the gas (i.e., mass or number of moles). 
(B) Volume : (a)Since gases occupy the entire space available to them, the measurement of volume of a 
gas only requires a measurement of the container confining the gas. 
 (b) Volume is expressed in litres (L), millilitres (mL) or cubic centimetres ) (
3
cm or cubic metres ) (
3
m . 
 (c) mL L 1000 1 ? ; L mL
3
10 1
?
? 
  
3 3 3
10 1 1 cm dm L ? ? 
  L mL cm dm m
3 6 3 6 3 3 3
10 10 10 10 1 ? ? ? ? 
 (C) Mass : (a) The mass of a gas can be determined by weighing the container in which the gas is enclosed 
and again weighing the container after removing the gas. The difference between the two weights gives the 
mass of the gas. 
 (b) The mass of the gas is related to the number of moles of the gas i.e. 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
    moles of gas (n)
M
m
? ?
mass Molar 
grams in Mass
 
 (iii)Mass is expressed in grams or kilograms,  g Kg
3
10 1 ? 
(D) Temperature :  (a) Gases expand on increasing the temperature. If temperature is increased twice, the 
square of the velocity ) (
2
v also increases two times. 
 (b) Temperature is measured in centigrade degree ) ( C
o
 or celsius degree with the help of 
thermometers. Temperature  is also measured in Fahrenheit (F
o
). 
 (c) S.I. unit of temperature is kelvin (K) or absolute degree. 
     273 ? ? C K
o
 
 (iv) Relation between F and C
o
 is 
9
32
5
?
?
o o
F C
 
(E) Pressure :  (a) Pressure of the gas is the force exerted by the gas per unit area of the walls of the 
container in all directions. Thus, Pressure (P)
) ( Area
) ( on Accelerati ) ( Mass
) Area(
) Force(
a
a m
A
F ?
? ? 
 (b) Pressure exerted by a gas is due to kinetic energy )
2
1
(
2
mv KE ? of the molecules. Kinetic energy of 
the gas molecules increases, as the temperature is increased. Thus, Pressure of a gas ? Temperature (T). 
 (c) Pressure of a pure gas is measured by manometer while that of a mixture of gases by barometer. 
 (d) Commonly two types of manometers are used, 
  (a) Open end manometer;  (b) Closed end manometer 
 (e) The S.I. unit of pressure, the pascal (Pa), is defined as 1 newton per metre square. It is very small 
unit. 
  
2 1 2
1 1 1
? ? ?
? ? s m kg Nm Pa 
 (f)  C.G.S. unit of pressure is dynes 
2 ?
cm . 
 (g) M.K.S. unit of pressure is 
2
/ m kgf . The unit 
2
/ cm kgf sometime called ata (atmosphere technical 
absolute). 
 (h) Higher unit of pressure is bar, KPa or MPa. 
  KPa KNm Nm Pa bar 100 100 10 10 1
2 2 5 5
? ? ? ?
? ?
 
 (i) Several other units used for pressure are, 
Name  Symbol Value 
bar bar Pa bar
5
10 1 ? 
atmosphere atm Pa atm
5
10 01325 . 1 1 ? ? 
Torr Torr 
Pa Pa Torr 322 . 133
760
101325
1 ? ? 
millimetre of mercury mm Hg 
Pa Hg mm 322 . 133 1 ? 
 
 (j) The pressure relative to the atmosphere is called gauge pressure. The pressure relative to the 
perfect vacuum is called absolute pressure. 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
  Absolute pressure = Gauge pressure + Atmosphere pressure. 
 (k) When the pressure in a system is less than atmospheric pressure, the gauge pressure becomes 
negative, but is frequently designated and called vacuum. For example, 16 cm vacuum will be 
      bar 80 . 0 013 . 1
76
16 76
? ?
?
. 
 (l) If ‘h’ is the height of the fluid in a column or the difference in the heights of the fluid columns in 
the two limbs of the manometer d the density of the fluid ) / 6 . 13 / 10 6 . 13 (
3 3 3
cm g m Kg Hg ? ? ? and g is the 
gravity, then pressure is given by, dg h P P ? ?
atm gas
 
 
 
 
 
 
 
 
 
 
 
 
 (m) Two sets of conditions are widely used as 'standard' values for reporting data. 
Condition T P V
m
 (Molar volume) 
S.T.P./N.T.P. 273.15 K 1 atm 22.414 L 
S.A.T.P
*
.  298.15 K 1 bar 24.800 L 
* Standard Ambient temperature and pressure. 
  Boyle's law. 
 (A) In 1662, Robert Boyle discovered the first of several relationships among gas variables (P, T, V). 
 (B) It states that, “For a fixed amount of a gas at constant temperature, the gas volume is inversely 
proportional to the gas pressure.” 
    Thus, 
V
P
1
? at constant temperature and mass 
    or 
V
K
P ? (where K is constant) 
    or K PV ?                                                                 
  For two or more gases at constant temperature and mass. 
    K V P V P ? ? ? .......
2 2 1 1
 
  Boyle's law can also be given as, 
2
v
K
dV
dP
T
? ? ?
?
?
?
?
?
 
Height (h) of 
mercury column 
Atmospheric 
pressure 
Vacuum 
Mercury Barometer 
h 
?gas 
?gas 
?gas= ?gashdg 
Hg 
An open arm 
manometer 
Gas 
Page 5


 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
 
 
Physical 
Chemistry      
TOPIC: GASEOUS STATE CHEMISTRY 
IIT-JAM/DU M.Sc./CSIR-NET/GATE 
 
 
ALL FACULTY FROM IIT 
 
2637, Hudson Lane, Behind Khalsa College, Near 
G.T.B. Nagar Metro Station Gate No. 3 & 4, New 
Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: 
info@asfinstitute.com, www.asfinstitute.com 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
GASEOUS STATE 
The state of matter in which the molecular forces of attraction between the particles of matter are 
minimum, is known as gaseous state. It is the simplest state and shows great uniformity in behaviour. 
 Characteristics of gases. 
(A) Gases or their mixtures are homogeneous in composition. 
(B) Gases have very low density due to negligible intermolecular forces. 
(C) Gases have infinite expansibility and high compressibility. 
(D) Gases exert pressure. 
(E) Gases possess high diffusibility. 
(F) Gases do not have definite shape and volume like liquids. 
(G) Gaseous molecules move very rapidly in all directions in a random manner i.e., gases have highest kinetic 
energy. 
(H) Gaseous molecules are loosely packed having large empty spaces between them. 
(I) Gaseous molecules collide with one another and also with the walls of container with perfectly elastic 
collisions. 
(J) Gases can be liquified, if subjected to low temperatures (below critical) or high pressures. 
(K) Thermal energy of gases >> molecular attraction. 
(L) Gases undergo similar change with the change of temperature and pressure. In other words, gases obey 
certain laws known as gas laws. 
 Measurable properties of gases. 
(A) The characteristics of gases are described fully in terms of four parameters or measurable properties : 
 (i) The volume, V, of the gas. 
 (ii) Its pressure, P 
 (iii)Its temperature, T 
 (iv) The amount of the gas (i.e., mass or number of moles). 
(B) Volume : (a)Since gases occupy the entire space available to them, the measurement of volume of a 
gas only requires a measurement of the container confining the gas. 
 (b) Volume is expressed in litres (L), millilitres (mL) or cubic centimetres ) (
3
cm or cubic metres ) (
3
m . 
 (c) mL L 1000 1 ? ; L mL
3
10 1
?
? 
  
3 3 3
10 1 1 cm dm L ? ? 
  L mL cm dm m
3 6 3 6 3 3 3
10 10 10 10 1 ? ? ? ? 
 (C) Mass : (a) The mass of a gas can be determined by weighing the container in which the gas is enclosed 
and again weighing the container after removing the gas. The difference between the two weights gives the 
mass of the gas. 
 (b) The mass of the gas is related to the number of moles of the gas i.e. 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
    moles of gas (n)
M
m
? ?
mass Molar 
grams in Mass
 
 (iii)Mass is expressed in grams or kilograms,  g Kg
3
10 1 ? 
(D) Temperature :  (a) Gases expand on increasing the temperature. If temperature is increased twice, the 
square of the velocity ) (
2
v also increases two times. 
 (b) Temperature is measured in centigrade degree ) ( C
o
 or celsius degree with the help of 
thermometers. Temperature  is also measured in Fahrenheit (F
o
). 
 (c) S.I. unit of temperature is kelvin (K) or absolute degree. 
     273 ? ? C K
o
 
 (iv) Relation between F and C
o
 is 
9
32
5
?
?
o o
F C
 
(E) Pressure :  (a) Pressure of the gas is the force exerted by the gas per unit area of the walls of the 
container in all directions. Thus, Pressure (P)
) ( Area
) ( on Accelerati ) ( Mass
) Area(
) Force(
a
a m
A
F ?
? ? 
 (b) Pressure exerted by a gas is due to kinetic energy )
2
1
(
2
mv KE ? of the molecules. Kinetic energy of 
the gas molecules increases, as the temperature is increased. Thus, Pressure of a gas ? Temperature (T). 
 (c) Pressure of a pure gas is measured by manometer while that of a mixture of gases by barometer. 
 (d) Commonly two types of manometers are used, 
  (a) Open end manometer;  (b) Closed end manometer 
 (e) The S.I. unit of pressure, the pascal (Pa), is defined as 1 newton per metre square. It is very small 
unit. 
  
2 1 2
1 1 1
? ? ?
? ? s m kg Nm Pa 
 (f)  C.G.S. unit of pressure is dynes 
2 ?
cm . 
 (g) M.K.S. unit of pressure is 
2
/ m kgf . The unit 
2
/ cm kgf sometime called ata (atmosphere technical 
absolute). 
 (h) Higher unit of pressure is bar, KPa or MPa. 
  KPa KNm Nm Pa bar 100 100 10 10 1
2 2 5 5
? ? ? ?
? ?
 
 (i) Several other units used for pressure are, 
Name  Symbol Value 
bar bar Pa bar
5
10 1 ? 
atmosphere atm Pa atm
5
10 01325 . 1 1 ? ? 
Torr Torr 
Pa Pa Torr 322 . 133
760
101325
1 ? ? 
millimetre of mercury mm Hg 
Pa Hg mm 322 . 133 1 ? 
 
 (j) The pressure relative to the atmosphere is called gauge pressure. The pressure relative to the 
perfect vacuum is called absolute pressure. 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
  Absolute pressure = Gauge pressure + Atmosphere pressure. 
 (k) When the pressure in a system is less than atmospheric pressure, the gauge pressure becomes 
negative, but is frequently designated and called vacuum. For example, 16 cm vacuum will be 
      bar 80 . 0 013 . 1
76
16 76
? ?
?
. 
 (l) If ‘h’ is the height of the fluid in a column or the difference in the heights of the fluid columns in 
the two limbs of the manometer d the density of the fluid ) / 6 . 13 / 10 6 . 13 (
3 3 3
cm g m Kg Hg ? ? ? and g is the 
gravity, then pressure is given by, dg h P P ? ?
atm gas
 
 
 
 
 
 
 
 
 
 
 
 
 (m) Two sets of conditions are widely used as 'standard' values for reporting data. 
Condition T P V
m
 (Molar volume) 
S.T.P./N.T.P. 273.15 K 1 atm 22.414 L 
S.A.T.P
*
.  298.15 K 1 bar 24.800 L 
* Standard Ambient temperature and pressure. 
  Boyle's law. 
 (A) In 1662, Robert Boyle discovered the first of several relationships among gas variables (P, T, V). 
 (B) It states that, “For a fixed amount of a gas at constant temperature, the gas volume is inversely 
proportional to the gas pressure.” 
    Thus, 
V
P
1
? at constant temperature and mass 
    or 
V
K
P ? (where K is constant) 
    or K PV ?                                                                 
  For two or more gases at constant temperature and mass. 
    K V P V P ? ? ? .......
2 2 1 1
 
  Boyle's law can also be given as, 
2
v
K
dV
dP
T
? ? ?
?
?
?
?
?
 
Height (h) of 
mercury column 
Atmospheric 
pressure 
Vacuum 
Mercury Barometer 
h 
?gas 
?gas 
?gas= ?gashdg 
Hg 
An open arm 
manometer 
Gas 
 
2637, Hudson Lane, Behind Khalsa College, Near G.T.B. Nagar Metro Station Gate No. 3 & 4, New Delhi – 110009 
Mob. 09555785548, 08860929430, e-mail: info@asfinstitute.com, www.asfinstitute.com    
 (C) Graphical representation of Boyle's law : Graph between P and V at constant temperature is called 
isotherm and is an equilateral (or rectangular) hyperbola. By plotting P versus 
V
1
, this hyperbola can be 
converted to a straight line. Other types of isotherms are also shown below, 
  
 
 
 
 
 
 (D) At constant mass and temperature density of a gas is directly proportional to its pressure and inversely 
proportional to its volume. 
  Thus, 
V
P d
1
? ?  
?
?
?
?
?
?
?
d
V
mass
? 
  or K
V
V
P
P
d
d
? ? ? ? .......
1
2
2
1
2
1
 
 (E) At altitudes, as P is low d of air is less. That is why mountaineers carry oxygen cylinders. 
 (F) Air at the sea level is dense because it is compressed by the mass of air above it. However the density 
and pressure decreases with increase in altitude. The atmospheric pressure at Mount Everest is only 0.5 atm. 
 
Example :  At constant temperature, if pressure increases by 1%, the percentage decrease of volume is 
   (a) 1% (b) 100/101% (c) 1/101% (d) 1/100% 
Solution: (b) 
2 2 1 1
V P V P ? 
  If mm P 100
1
? , 
2
P will be 101 mm 
   Hence 
2
101 100 V V ? ? ? , 
   V V ? ?
101
100
2
, 
   Decrease in volume
101
1
101
100
? ? ?
V
V of V i.e. %
101
100
 
  Charle's law. 
 (A) French chemist, Jacques Charles first studied variation of volume with temperature, in 1787. 
 (B) It states that, “The volume of a given mass of a gas is directly proportional to the absolute temperature 
) 273 ( ? ? C
o
 at constant pressure”. 
  Thus, T V ? at constant pressure and mass 
  or ) 15 . 273 ) ( ( ? ? ? C t K KT V
o
 ,   (where k is constant),  
T1< T2< T3 
 T3 
 T2 
 T1 
 V or 1/d 
 P 
 O 
T1< T2< T3 
 T3 
 T2 
 T1 
 1/V or d 
 P 
 O 
T1< T2< T3 
 T3 
 T2 
 T1  
 P 
 PV 
 O 
 log P 
 O 
 log 1/V 
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