A first order reaction takes 20 minutes for 25% decomposition. Calculate the time when 75% of the reaction will be completed.
Given : log 2 = 0.3010, log 3=0.4771, log 4 = 0.6021

Explanation

For a first order reaction, `K=(2.303)/(t)"log"(a)/(a-x)`
where, k=Rate constant
a=Initial concentration
(a-x) = concentration after time.t..
When a first order reaction is 25% complete in 20 min.
`a = 100, a - x=100-25=75, t = 20` min.
`:.k=(2.303)/(20)"log"(100)/(75)`
`=(2.303)/(20) [log 4-log 3] =0.0143"min"^(-1)`
For 75% completion of reaction,
`a=100, a-x=100-75 = 25, k=0.0143"min"^(-1)`
`t=(2.303)/(k)"log"(a)/(a-x)=(2.303)/(0.0143)"log"(100)/(25)`
`=(2.303)/(0.0143)log 4=96.961` min.