Half-life of a first order reaction at a given temperature is a 3 min. Calculate the time required for the completion of 3/4 th of the reaction.

Explanation

For a first order reaction , `t_(1//2)=(0.693)/(k)`
Hence, `k=(0.693)/(t_(1//2))=(0.693)/(3)"min"^(-1)=0.231"min"^(-1)`
For a first order reaction , `t=(2.303)/(k)log.(a)/(a-x)`
When 3/4 th of the reaction completes,
`x=axx(3)/(4)=(3a)/(4)and(a-x)=a-(3a)/(4)=(a)/(4)`
`therefore t = (2.303)/(0.231)log.(a)/(a/4)=6min`
So , the time required for the completion of 3/4 th of the reaction is 6min.