Two gases A and B having the same volume diffuse through a porous partition in 20 and 10 seconds respectively. The molecular mass of A is 49u. Molecular mass of B will be

12.25 u

6.50 u

25.00 u

50.00 u

Solution

12.25 u

fraction numerator Rate space of space diffusion space of space straight I space gas over denominator Rate space of space diffusion space II space gas end fraction space equals space square root of M subscript B over M subscript A end root fraction numerator begin display style bevelled v subscript 1 over t subscript 1 end style over denominator begin display style bevelled v subscript 2 over t subscript 2 end style end fraction space equals space space square root of M subscript B over 49 end root since space the space volumes space are space equal space straight V subscript 1 space equals space straight V subscript 2 fraction numerator begin display style 10 end style over denominator begin display style 20 end style end fraction space equals space space square root of M subscript B over 49 end root fraction numerator begin display style 10 end style over denominator begin display style 20 end style end fraction space equals space space fraction numerator square root of straight M subscript 2 end root over denominator 7 end fraction square root of straight M subscript 2 end root space equals fraction numerator 10 space straight x space 7 over denominator 20 end fraction space equals space 3.5 square root of straight M subscript 2 end root space equals space 3.5 Thus comma straight M subscript 2 space equals space 12.25 space straight u

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