Answer to Question 3

Back

A cylinder of volume 0.25 m3 contains nitrogen gas at a temperature of 17 oC and a pressure of 1.0 105 Pa.  Molar mass of nitrogen = 0.028 kg mol-1.  Calculate:

a)      The number of moles of gas in the cylinder   

 

Use pV = nRT

 

Rearrange:

 

n = pV = 1.0 105 Pa 0.25 m3 = 10.4 mol

      RT     8.3 J mol-1 K-1 290 K  

 

                                

 

b)      The rms speed of the gas molecules at 17 oC  

 

Use p = 1/3 r<c2>

 

Work out density 

r = mass volume = 10.4 mol 0.028 kg mol-1 = 0.291 kg = 1.16 kg m-3

                                              0.25 m3                      0.25 m3

 

 

 

1.0 105 Pa = 1/3 1.16 kg m-3 <c2>

 

 

<c2> = 3 1.0 105 Pa =  2.59 105 m2 s-2

                1.16 kg m-3

 

RMS speed =  509 m s-1

 

 

      

c)      The average translational KE of a nitrogen molecule;   

 

Average Kinetic energy per molecule = 3/2 kT 

 

= 3/2 1.38 10-23 J K-1 290 K = 6.0 10-21 J

                                     

 

 

d)   The total kinetic energy of the gas in the  cylinder.

 

Total number of molecules = 10.4 mol 6.02 10-23 mol-1 = 6.26 1024

 

 

Total kinetic energy = 6.26 1024 6.0 10-21 = 37 600 J = 38 000 J (2 s.f.)