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In a first order reaction A products 60%...

In a first order reaction A products 60% of the given sample of a decomposes in 40 min. What is the half of the reaction ?

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For a first order reaction
`k=(2.303)/(k)"log"([R]_(0))/([R])`
`rArr k = (2.303)/("40 min")"log"(100)/(100-60)`
`=(2.303)/("40 min")"log"(10)/(4)`
`k = 8.924xx10^(-3)"min"^(-1)`
Therefore, `t_((1)/(2))` of the decomposition reaction is
`t_((1)/(2))=(0.693)/(k)`
`=(0.693)/(8.9xx10^(-3))` min.
= 77.7 min (approximately)
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