JEE MAIN - Chemistry (2021 - 31st August Morning Shift - No. 17)
For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is ____________. (Integer answer)
Answer
2
Explanation
$$k = {{2.303} \over t}\log {a \over {a - x}}$$
$${{2.303} \over {{t_{50\% }}}}\log {{100} \over {100 - 50}} = {{2.303} \over {{t_{75\% }}}}\log {{100} \over {100 - 75}}$$
$$ \Rightarrow $$ $${t_{75\% }} = 2{t_{50\% }}$$
$${{2.303} \over {{t_{50\% }}}}\log {{100} \over {100 - 50}} = {{2.303} \over {{t_{75\% }}}}\log {{100} \over {100 - 75}}$$
$$ \Rightarrow $$ $${t_{75\% }} = 2{t_{50\% }}$$
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