A first order reaction is 15% complete in 20 minutes. How long will it take to complete 60%?

Explanation

Step 1: To Calculate k.
`[R]_0=100 (say),[R]=100-15=85`
t=20 min, k=?
`k=(2.303)/(t)log([R]_0)/([R])`
`k=(2.303)/("20 min")log(100)/(85)`
`=(2.303)/("20 min")[log 100-log85]`
`=(2.303)/("20 min")[2-1.9294]`
`=(2.303xx0.0706)/("20 min")`
`=8.13xx10^(-3)" min"^(-1)`
Step II : To calculate t.
`[R]_0=100[R]=100-60=40`
`k=8.3xx10^(-3)"min"^(-1),t=?`
`t=2 (2.303)/(k)log([R_]_0)/([R])`
`=(2.303)/(8.13xx10^(-3)min^(-1))log(100)/(40)`
`=(2.303[log10-log4])/(8.13xx10^(-3)min^(-1))`
`=(2.303xx[1-0.6021])/(8.13xx10^(-3))` min
`=(2.303xx0.3979xx10^(3))/(8.13)` min
`=(2.303xx397.9)/(8.13)` min
=112.71 min