The decomposition of a compound is found to follow a first order rate law. If it takes 15 minutes for 20 percent of original material to react, calculate (i) specific rate constant (ii) the time at 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 after the first 15 minutes.

The decomposition of a compound is found to follow a first order rate

1.	The decomposition of a compound is found to follow a first order rate law. If it takes 15 minutes for 20 percent of original material to react, calculate (i) specific rate constant (ii) the time at 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 after the first 15 minutes.
Answer» SOLUTION :(i) `k=(2.303)/(t)LOG""(a)/(a-x)=(2.303)/(15" min")log""(a)/(a-0.20a)=0.01488" min"^(-1)` (ii) `t=(2.303)/(k)log""(a)/(0.10a)=(2.303)/(0.01488)log10=154.77" min".` (iii) In first 15 minutes, `20%` has reacted. `:.` AMOUNT LEFT unreacted `=80%` of `a=0.80` a This is now initial CONCENTRATION. For next `20%` of this amount to react means `x=20%` of `0.80a=0.16a` `:.""t=(2.303)/(k)log""(0.80a)/(0.80a-0.16a)=(2.303)/(0.01488" min"^(-1))log""(0.80)/(0.64)` `=154.77" min "xxlog1.25=154.77xx0.0969" min "=15 "minutes"`