If half life period for a first order reaction in A is 2 minutes, how long will it take [A] to reach (i) `25%` of its initial concentration ii) `10%` of its initial concentration?

Explanation

Step. 1) Calculation of rate constant
`k=0.693/t_(1//2) = 0.693/(2min) = 0.3465 "min"^-1`
Step. 2) 1st case, `a=100%`, (a-x) = `25%`
`t=(2.303)/klog(a/(a-x))`
`=(2.303)/(0.3465 "min"^-1) log (100/25)`
`= 2.303 /(0.3465 "min"^-1) log 4`
`=(2.303xx0.602)/(0.3465 "min"^-1)=4.0 min`

2nd case, `a=100%`, (a-x) = `10%`
`t=(2.303)/klog(a/(a-x))`
`=(2.303)/(0.3465 "min"^-1) log (100/10)`
`= 2.303 /(0.3465 "min"^-1) log 10`
`=(2.303xx1)/(0.3465 "min"^-1)=6.65 min`