Answer to Question 3 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   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 ×     = 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.)