How would you rank the following gases, NO, Ar, #N_2#, #N_2O_5#, in order of increasing speed of effusion through a tiny opening and increasing time of effusion?
1 Answer
#Z_("eff",N_2) > Z_("eff",NO) > Z_("eff",Ar) > Z_("eff",N_2O_5)#
Clearly, the rate is the reciprocal of the time it takes, since the rate is in
#t_("eff",N_2) < t_("eff",NO) < t_("eff",Ar) < t_("eff",N_2O_5)#
The rate of effusion, which I will denote as
#Z_("eff",1)/(Z_("eff",2)) = sqrt(M_(m,2)/(M_(m,1))# where
#M_(m,i)# is the molar mass of compound#i# and#Z_("eff",i)# is the rate of effusion of compound#i# .
Since
#M_(m,NO) = 14.007 + 15.999 = "30.006 g/mol"#
#M_(m,Ar) = "39.948 g/mol"#
#M_(m,N_2) = 2xx14.007 = "28.014 g/mol"#
#M_(m,N_2O_5) = 2xx14.007 + 5xx15.999 = "108.009 g/mol"#
So, the ranking of molar masses goes as:
#M_(m,N_2) < M_(m,NO) < M_(m,Ar) < M_(m,N_2O_5)#
which means that:
#color(blue)(Z_("eff",N_2) > Z_("eff",NO) > Z_("eff",Ar) > Z_("eff",N_2O_5))#