Physical Chemistry FDSC233 Problem Set #3 Kinetic Theory of Gases 1. Calculate the rms speed of helium atoms at 1 atm and 273 K, assuming ideal behavior. 2. Calculate the average kinetic energy of 1 mol of He at 0? and using the result from problem 1. 3. Derive an expression that states the mean-square speed of an ideal gas as a function of the density of the gas. 4. Calculate the rms speed of N2 at STP using the expression derived from problem 3.
5. A mixture of 0.50 mol of neon and 0.25 mol of krypton is contained in a 20-L flask. The effective atomic radii are 1.6 × 10-10 m for Ne and 2.0 × 10-10 m for Kr; the average velocities are 535 m s-1 and 263 m s-1, respectively. (a) Calculate the number of collisions per second per cubic meter. (b) Calculate the mean free path of neon if the same amount of that gas occupied the flask by itself. (c) What would be the mean free path of the neon if the pressure were increased by 10 times. (Hint : derive an expression for the mfp of an ideal gas that includes pressure).
6. Calculate the collision frequency of one molecule of oxygen when 1/2 mol of oxygen is confined in a 5.00-L container at 298 K. Take the effective diameter of an oxygen molecule to be 3.57 × 10-10 m.