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Question

The time required to decompose half of the substance for $$n$$th order reaction is inversely proportional to: ($$a$$ is initial concentration)


A
an+1
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B
an1
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C
an2
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D
an
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Solution

The correct option is B $${ a }^{ n-1 }$$
For $$ { n }^{ th }$$ order reaction
$$ -\cfrac { da }{ dt } =k{ a }^{ n }\\ -\cfrac { da }{ { a }^{ n } } =kdt\\ -\int _{ { a }_{ o } }^{ { a }_{ f } }{ \cfrac { da }{ { a }^{ n } }  } =k\int _{ 0 }^{ { t }_{ f } }{ dt } \\ \cfrac { 1 }{ { a }^{ n-1 } } =\cfrac { 1 }{ { { { a }_{ o } }^{ n-1 } } } +(n-1)kt\\ { t }_{ f }\propto \cfrac { 1 }{ { { { a }_{ o } }^{ n-1 } } } $$

Chemistry

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