Establish the integrated rate equation for a first order reaction and reaction and with its help prove that for 99.9% completion of the reaction, the time required is 10 times of the half-life of the reaction.

Explanation

Second part : To calculate t, we use the relation
`t=(2.303)/(k)log.(a)/(a-x)`
When 99.9% of the reaction is completed,
`a-x=a-0.999a=axx10^(-3)`
Substituting the value of (a-x) into the above
equation , we get, `t=(2.303)/(k)log.(a)/(axx10^(-3))=(6.909)/(k)`
For a first order reaction, `t_(1//2)=(0.693)/(k)`
Comparing the values of `t and t_(1//2) " gives "t ~~10t_(1//2)`