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The rate of a first - order is 0.04 "mol...

The rate of a first - order is `0.04 "mol l"^(-1) s^(-1)` at 10 seconds and `0.03 "mol l"^(-1) s^(-1)`. At 20 seconds after initiation of the reaction. The half - life period of the reaction is

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Rate `=k[A]`
`0.04=k[A]_(10)` and `0.03=k[A]_(20)`
`([A]_(10))/([A]_(20))=(0.04)/(0.03)=(4)/(3)`
`t=(2.303)/(k)log.([A]_(10))/([A]_(20))` when `t=10^(1)`min.
`10=(2.303)/(k)log.(4)/(3)`
`k=(2.303)/(10)log.(4)/(3)=0.0288min^(-1)`
`t_((1)/(2))=(0.693)/(k)=(0.693)/(0.0288)=24.06min`.
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