3. 1.000 mole of ar(g) (molecular diameter = 3.76 x 10-10 m and mass = 39.948 g/mol) occupies 22.414 liters at 1.000 atm of pressure and at 273.15 k. (a) calculate the mean speed ((c)) of the gas in the container. (b) calculate the number of collisions a single molecule makes in one second. (c) calculate the amount of time (in seconds) that occurs in between each collision. (d) calculate the average mean free path of the gas (in units of angstrom). (e) calculate the distance that a molecule will travel along a zigzag path during a random walk in 1 second (hint: the total number of steps during a random walk in 1 second is equal to the collision frequency calculated in part b). (1) calculate how far a molecule will be displaced from its starting point in 1 second and after 1 minute (hint: root mean squared displacement is (d? ) = vc)at). (g) calculate the binary collision frequency in units of molar per second (ms) and comment on how the binary collision frequency can be used to calculate an upper limit for the rate of a gas phase reaction at this temperature and pressure.