Properties of gases – problem sheet 1. Calculate the most probable speed, the mean speed, and the root-mean-square speed for carbon dioxide molecules at 298 K. 2. Calculate: (a) the mean free path of molecules in air at 1 bar pressure and 25 ° C (take the average collision cross section, σ , to be 0.43 nm 2 ); (b) the pressure at which the mean free path in air becomes equal to 10 cm; (c) the number of collisions per cm 3 in one second between oxygen and nitrogen molecules in air at 25 ° C and 1 bar pressure (take the radii to be equal to 178 and 185 pm, respectively). 3. Graham’s law of effusion states that the rate at which gas is lost from a vessel into a vacuum through a small hole is proportional to M 1/2 , where M is the molecular mass. (a) By considering the number of molecules, N , striking a hole of area A0 , show that the rate of effusion is given by d N d t = p A0 N A (2 π MRT ) 1/2 (b) Show that the rate of change of pressure in a vessel of volume V is given by dln p d
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This note was uploaded on 05/09/2010 for the course CHE 3051 taught by Professor Sitimachmud during the Spring '08 term at National Central University.