JEE MAIN - Chemistry (2008 - No. 22)
For a reaction $${1 \over 2}A \to 2B$$ rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the
expression
$$ - {{d[A]} \over {dt}}$$ = $${1 \over 2}{{d[B]} \over {dt}}$$
$$ - {{d[A]} \over {dt}}$$ = $${1 \over 4}{{d[B]} \over {dt}}$$
$$ - {{d[A]} \over {dt}}$$ = $${{d[B]} \over {dt}}$$
$$ - {{d[A]} \over {dt}}$$ = $$4{{d[B]} \over {dt}}$$
Explanation
The rates of reactions for the reaction
$${1 \over 2}A \to 2B$$
can be written either as
$$ - 2{d \over {dt}}\left[ A \right]\,\,$$ with respect to $$'A'$$
or $$\,\,\,\,\,$$ $${1 \over 2}{d \over {dt}}\left[ B \right]\,\,\,\,$$ with respect to $$'B'$$
From the above, we have
$$ - 2{d \over {dt}}\left[ A \right] = {1 \over 2}{d \over {dt}}\left[ B \right]$$
or $$\,\,\,\,\,$$ $$ - {d \over {dt}}\left[ A \right] = {1 \over 4}{d \over {dt}}\left[ B \right]$$
i.e., correct answer is (b)
$${1 \over 2}A \to 2B$$
can be written either as
$$ - 2{d \over {dt}}\left[ A \right]\,\,$$ with respect to $$'A'$$
or $$\,\,\,\,\,$$ $${1 \over 2}{d \over {dt}}\left[ B \right]\,\,\,\,$$ with respect to $$'B'$$
From the above, we have
$$ - 2{d \over {dt}}\left[ A \right] = {1 \over 2}{d \over {dt}}\left[ B \right]$$
or $$\,\,\,\,\,$$ $$ - {d \over {dt}}\left[ A \right] = {1 \over 4}{d \over {dt}}\left[ B \right]$$
i.e., correct answer is (b)
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