Question

Question #f875f

Answer 1

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#