Two equal volume flasks cotaining equal masses of `H_(2)` and `CH_(4)` are at `100 K` and `200 K`, repectively. The molecular diameter of `CH_(4)` is twice that of `H_(2)`.
(`i`) Which of the following statement about `Z_(1)` (number of collisions per molecule per `cm^(3)` per second) is true? (`a`) `Z_(11)` of `H_(2)=2Z_(1)` of `CH_(4)`
(`b`) `Z_(11)` of `H_(2)=4Z_(1)` of `CH_(4)`
(`c`) `Z_(11)` of `H_(2)=Z_(1)` of `CH_(4)`
(`d`) `Z_(11)` of `H_(2)=8Z_(1)` of `CH_(4)`
(`ii`) Which of the following statement about `Z_(11)` (number of bimolecular collisions per `cm^(3)` per second) is true?
(`a`) `Z_(1)` of `H_(2)=4Z_(11)` of `CH_(4)`
(`b`) `Z_(11)` of `H_(2)=8Z_(11)` of `CH_(4)`
(`c`) `Z_(1)` of `H_(2)=16Z_(11)` of `CH_(4)`
(`d`) `Z_(1)` of `H_(2)=32Z_(11)` of `CH_(4)`

Explanation

(`b`) `Z_(1)=(overline(c ))/(A)` (`overline(c )=` average velocity, `lambda=` mean free path)
`(Z_(1)A)/(Z_(1)B)=((overline(c )_(A))/(overline(c )_(B)))((lambda_(B))/(lambda_(A)))=2xx2=4`
`overline(c )_(A)=sqrt((8RT)/(pi M))`
`:. (overline(c )_(A))/(overline(c )_(B))=sqrt((T_(A))/(T_(B))xx(M_(B))/(M_(A)))=sqrt((100)/(200)xx(16)/(2))=2`
(`d`) `Z_(11)=(N^(*))/(2)Z_(1)` or `Z_(11) prop N^(*)Z_(1)`
`(Z_(11)A)/(Z_(11)B)=((N^(*)A)/(N^(*)B)xx(Z_(1)A)/(Z_(1)B))=8xx4=32`
`( :. (n_(A))/(n_(B))=(N^(*)A)/(N^(*)B)=8)`