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Gases

 

Kelvin  temperature

T = t + 273

T  Kelvin temperature  in K

t   temperature in ^oC                                                                       

 

Ideal Gas Law

 

pV = n R T

 

p  pressure in  Pa   

V  volume in m³

n  number of moles

R  gas constant   R = 8.3145 Jmol^-1K^-1

T  Kelvin temperature  in K

 

Example

In a tank of 200 ℓ is helium. The pressure in the tank is 30 bar and the temperature  is 20 ^oC.

Calculate the mass of helium.

 

p V = n R T

 

(30 x 10⁵ )(200 x 10^-3 ) = n (8.31)(293) 

 

n = (30 x10⁵   * 200 x 10^-3) / (8.31 x 293) = 246 mol

 

mass per mol of helium is 4.0 g mol^-1

 

mass of helium : 246 x 4 = 985.7 g = 9.9 x 10² g 

 

For a fixed mass of gas is:

( p₁V₁) /T₁ = (p₂V₂)/T₂            (fixed number of moles)

 

Example

The pressure in a tank of 20 ℓ is 3.0 bar at a temperature of 17 ^oC.

The temperature is raised. The volume increases to 21 ℓ and the pressure to 3.5 bar.

Calculate the new temperature.

 

( p₁V₁) /T₁ = (p₂V₂)/T₂                                     T in Kelvin !

 

(3.0 x 20) /290 = (3.5 x 21) /T₂

 

60/290 = 73.5/T₂

 

60 T₂ = 73.5 x 290

 

60 T₂ = 21315

 

T₂ = 355 K = 82 ^oC

 

Special cases of the Gas Law:

Boyle’s law           pV = constant

                               p₁V₁ = p₂V₂         (number of moles and temperature constant)

 

 Gay-Lussac’s law

                                p/T = constant   ( number of moles and the volume constant)

p₁/T₁ = p₂/T₂             Remark  : T in K

    

Charles’s law         V/T = constant    ( number of moles and pressure constant)     

                                               V₁/T₁=V₂/T₂              Remark : T in K