Important Gaseous State Formulas for JEE and NEET

 Page 1


  
   
 
 
 
        
 
 
       
     
  
 
  
   
      
          
           
         
GASEOUS STATE
Temperature Scale :
32 212
32 F
273 373
273 K
0 100
O C
?
?
?
?
?
?
?
?
 = 
) O ( R ) 100 ( R
) O ( R R
?
?
where R = Temp. on unknown scale.
Boyle?s law and measurement of pressure :
At constant temperature, V ??
P
1
P
1
V
1
 = P
2
V
2
Charles law :
At constant pressure, V ? T or
2
2
1
1
T
V
T
V
?
Gay-lussac?s law :
At constant volume, P ? T   
2
2
1
1
T
P
T
P
?
 ? temp on absolute scale
Ideal gas Equation :
PV = nRT
PV = 
m
w
RT or P = 
m
d
 RT or Pm = dRT
Page 2


  
   
 
 
 
        
 
 
       
     
  
 
  
   
      
          
           
         
GASEOUS STATE
Temperature Scale :
32 212
32 F
273 373
273 K
0 100
O C
?
?
?
?
?
?
?
?
 = 
) O ( R ) 100 ( R
) O ( R R
?
?
where R = Temp. on unknown scale.
Boyle?s law and measurement of pressure :
At constant temperature, V ??
P
1
P
1
V
1
 = P
2
V
2
Charles law :
At constant pressure, V ? T or
2
2
1
1
T
V
T
V
?
Gay-lussac?s law :
At constant volume, P ? T   
2
2
1
1
T
P
T
P
?
 ? temp on absolute scale
Ideal gas Equation :
PV = nRT
PV = 
m
w
RT or P = 
m
d
 RT or Pm = dRT
  
Daltons law of partial pressure :
v
RT n
P
1
1
? ,
v
RT n
P
2
2
? ,
v
RT n
P
3
3
? and so on.
Total pressure = P
1
 + P
2
 + P
3
 + ...........
Partial pressure = mole fraction X Total pressure.
Amagat?s law of partial volume :
V = V
1
 + V
2
 + V
3
 + .......
Average molecular mass of gaseous mixture :
M
mix
 = 
mixture in moles of . no Total
mixture of mass Total
 = 
3 2 1
3 3 2 2 1 1
n n n
M n M n M n
? ?
? ?
Graham?s Law :
Rate of diffusion r ? 
d
1
 ; d = density of gas
2
1
r
r
 = 
1
2
d
d
 = 
1
2
M
M
 = 
1
2
D . V
D . V
Kinetic Theory of Gases :
PV = 
3
1
 mN 
2
U   Kinetic equation of gases
Average K.E. for one mole =  N
A
 
?
?
?
?
?
?
2
U m
2
1
  = 
2
3
  K N
A
 T  = 
2
3
 RT
? Root mean suqare speed
U
rms
 = 
M
T R 3
molar mass must be in kg/mole.
? Average speed
U
av
 = U
1
 + U
2
 + U
3
 + ............ U
N
U
avg.
 = 
M
RT 8
?
 = 
m
KT 8
?
K  is Boltzmman constant
? Most probable speed
U
MPS
 = 
M
RT 2
 = 
m
KT 2
Page 3


  
   
 
 
 
        
 
 
       
     
  
 
  
   
      
          
           
         
GASEOUS STATE
Temperature Scale :
32 212
32 F
273 373
273 K
0 100
O C
?
?
?
?
?
?
?
?
 = 
) O ( R ) 100 ( R
) O ( R R
?
?
where R = Temp. on unknown scale.
Boyle?s law and measurement of pressure :
At constant temperature, V ??
P
1
P
1
V
1
 = P
2
V
2
Charles law :
At constant pressure, V ? T or
2
2
1
1
T
V
T
V
?
Gay-lussac?s law :
At constant volume, P ? T   
2
2
1
1
T
P
T
P
?
 ? temp on absolute scale
Ideal gas Equation :
PV = nRT
PV = 
m
w
RT or P = 
m
d
 RT or Pm = dRT
  
Daltons law of partial pressure :
v
RT n
P
1
1
? ,
v
RT n
P
2
2
? ,
v
RT n
P
3
3
? and so on.
Total pressure = P
1
 + P
2
 + P
3
 + ...........
Partial pressure = mole fraction X Total pressure.
Amagat?s law of partial volume :
V = V
1
 + V
2
 + V
3
 + .......
Average molecular mass of gaseous mixture :
M
mix
 = 
mixture in moles of . no Total
mixture of mass Total
 = 
3 2 1
3 3 2 2 1 1
n n n
M n M n M n
? ?
? ?
Graham?s Law :
Rate of diffusion r ? 
d
1
 ; d = density of gas
2
1
r
r
 = 
1
2
d
d
 = 
1
2
M
M
 = 
1
2
D . V
D . V
Kinetic Theory of Gases :
PV = 
3
1
 mN 
2
U   Kinetic equation of gases
Average K.E. for one mole =  N
A
 
?
?
?
?
?
?
2
U m
2
1
  = 
2
3
  K N
A
 T  = 
2
3
 RT
? Root mean suqare speed
U
rms
 = 
M
T R 3
molar mass must be in kg/mole.
? Average speed
U
av
 = U
1
 + U
2
 + U
3
 + ............ U
N
U
avg.
 = 
M
RT 8
?
 = 
m
KT 8
?
K  is Boltzmman constant
? Most probable speed
U
MPS
 = 
M
RT 2
 = 
m
KT 2
  
Van der Waal?s equation :
?
?
?
?
?
?
?
?
?
2
2
v
an
P
 (v ? nb) = nRT
? Critical constants :
V
c
 = 3b, P
C
 =  
2
b 27
a
, T
C
 = 
Rb 27
a 8