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Answer 1 · 2017-02-12T10:17:45

We know that the equation of rate constant for 1st oder reaction is as follows

#color(blue)(k=1/tln(C_0/C_t)......[1])#

where

#k->"rate constant"#
#t->"the time for which change being observed"#
#C_0->"concentration of the reactant at t=0"#

#C_t->"concentration of the reactant at t th instant"#

For 50% completion of the reaction time is 30 min

so for #t=30min" "C_0/C_t=100/50=2#

So inserting these in [1] we get

#k=1/30ln2......[2]#

Let the reaction becomes 90% complete in #Tmin#.This means 10% reactant remains.
So #C_0/C_T=100/10=10#

The equation [1] then becomes

#k=1/Tln(10).........[3]#

Comparing [2] and [3] we get

#1/30ln2=1/Tln(10)#

#=>T=(30ln10)/ln2~~99.65 min#