The decomposition of a compound is found to follow the first order rate law. If it takes 15 minutes for 20 per cent of the original material to react, calculate
i) the specific rate constant
ii) the time in which 10 percent of the original material remains unreacted.
iii) The time it takes for the next 20 percent of the reactant left to react.

Explanation

Step. I. Calculation of specific rate constant (k).
For the first order reaction, `k=2.303/t log a/(a-x)`
`a=100%,x=20%`, (a-x) = (100-20) = 80%, t=15 min
`k= 2.303/(15 min) log 100/80 = 2.303/(15 min) log 1.25 = 2.303/(15 min) xx 0.0969 = 0.015 min^(-1)`
Step ii) Calculation of time in which `10%` of original substance remains unreacted.
`a=100%, (a-x)=10%, k=0.015 min^(-1)`
`t=2.303/k log a/(a-x) = 2.303/(0.015 min^(-1))log100/10 = 153.5 min`
Step III. Calculation of time in which `20%` of the reactant left to reactant ater first 15 minutes.
`a=80%, x=80 xx 20//100 = 16%, (a-x) = (80-16) = 64%, k =0.015 min^(-1)`
`t=2.303/k log a/(a-x)= 2.303/(0.015 min^(-1)) log80/64`
`=2.303/(0.015min^(-1)) log 1.25 = 2.303/(0.015 min^(-1)) xx 0.969 = 15 min`