Question

# A certain gas takes three times as long to effuse out as helium. Its molecular mass will be:

A
36u
B
64u
C
9u
D
27u

Solution

## The correct option is B $$36u$$A certain gas takes three times as long to effuse out as helium. The rate of effusion is inversely proportional to the molecular mass.$$\cfrac { { r }_{ 1 } }{ { r }_{ 2 } } =\sqrt { \cfrac { { M }_{ { w }_{ 2 } } }{ { M }_{ { w }_{ 1 } } } }$$The rate of effusion is the ratio of the volume effused to the time taken$$\cfrac { { V }_{ 1 } }{ { t }_{ 1 } } \times \cfrac { { t }_{ 2 } }{ { V }_{ 2 } } =\sqrt { \cfrac { { M }_{ { w }_{ 2 } } }{ { M }_{ { w }_{ 1 } } } }$$Volume is same, so  $$\cfrac { 3 }{ 1 } =\sqrt { \cfrac { { M }_{ { w }_{ 2 } } }{ 4 } }$$                                  $$9=\cfrac { { M }_{ { w }_{ 2 } } }{ 4 }$$$$\therefore { M }_{ { w }_{ 2 } }=36$$The molecular mass of the gas is $$36 u$$. So, the correct option is $$A$$Chemistry

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