Question on Ideal gases and Kinetic theory?

• prg

  5 Jan 09, 11:46

  
  

  A sealed container holds a mixture of nitrogen molecules and helium molecules at a temperature of 290K. The total pressure exerted by the gas on the container is 120kPa.
  
  (M) molar mass of helium = 4 x 10^-3 kg / mol
  R= 8.31 J / K mol 
  Na= 6.02 x 10^23 /mol
  
  i) calculate root mean square speed of the helium molecules
  

  **Kindly check if this is ok**

  for v_rms

  Average kinetic energy per mole :   (1/2)* Na*m v^2 = 3/2 RT

  if M = Na*m= 4 x 10^-3 kg / mol

  then,  v^2 = ( (3* R T) / M = 3 * 8.31 * 290 / (4 x 10^-3) =1.81 x 10^6

          v_rms = √1.81 x 10^6 =  1346 m/s

  
  

  ii)calculate average kinetic theory of a nitrogen molecule 
  
  iii)If there are twice as many helium molecules as nitrogen molecules in the container, calculate pressure exerted on the container by helium molecules

• eagle

  5 Jan 09, 18:09

  Can some kind forumer pls help out here first? I only have time very late tonight to take a look...

• eagle

  7 Jan 09, 08:39

  Part (i) is correct

   

  Part (ii), I guess you are talking about average kinetic energy, not theory...

  The answer is 3/2  K T, where K is the boltzmann's constant

   

  Part (iii)

  pV = nRT, from here, u see that R is constant, T and V is same for both helium and nitrogen. Only difference is n.
  So, we can expect that helium molecules will exert twice the amount of pressure as the nitrogen molecules in this question
  Hence, ans is 80 kPa.

• Takchek

  9 Jan 09, 03:34

  For part iii, it is also known as Dalton's law.

  I would just like to add that deviations from a strictly linear/proportional relationship can occur even under low pressures and high temperatures (so-called approximations to ideal gas conditions) if there are interactions between the two species.