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Question

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


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