CATAGORY: Other
QUESTION: What is the pressure inside a 50.0 L container holding 105.0 kg
of argon gas at 20C?

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The ideal gas law states

(1) PV = NkT

where P is the pressure V is the volume N is the number of particles,
k is boltzmans constant = 1.380 J/k and T is the temperature in
kelvin.

V = 50.0L or 50.0L x 1000 cm^3 x (1m/100cm)^3 = 5.0 x 10^-2 m^3

N = total mass/mass per argon atom

  = total mass/(atomic weight of argon x 1 atomic mass unit) 

  = 105.0kg/(39.962 x 1.66 x 10^-27kg)
  
  = 1.58 x 10^27
  
T = 20 + 273.15 = 293.15 K

Solving (1) for P gives

(2) P = NkT/V 

   = 1.58 x 10^27 x 1.380 x 10^-23 J/K x 293.15 K / 5.0 x 10^-2 m^3
      
   = 1.27 x 10^8 N/m^2 
   
   since 1atm = 1.013 x 10^5 Pa
   
   the pressure in atmospheres is about 1250 atm
   
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   * P = 1.27 x 10^8 N/m^2 *
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