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A first order reaction takes 40 min for 30% decomposition. Calculate t_(1//2).

Answer»

Solution :At `30%` DECOMPOSITION, `x=30%` of a i.e., 0.30 a.
Using FIRST order equation,
`k=(2.303)/(t) "log"(a)/(a-x)=(2.303)/(40" MIN")"log"(a)/(a-0.30a)=(2.303)/(40)XX"log"(10)/(7) "min"^(-1)`
`=(2.303)/(40)xx0.1549"min"^(-1) = 8.918xx10^(-3)"min"^(-1)`
For a 1ST order reaction, `t_(1//2)=(0.693)/(k)=(0.693)/(8.918xx10^(-3)"min"^(-1))=77.7` min.


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