Question

The $t\frac{1}{2}$ of first order reaction is 60 min. What will be $\%$ of substance left after 240 min?

Answer 1

Amount of the substance left after one half life $=\frac{A_0}{2}$
Amount of the substance left after two half-lives $=\frac{A_0}{2^2}$
Amount of the substance left after two half lives $=\frac{A_0}{2^3}$
In general,
Amount of the substance left after n half life $=\frac{A_0}{2^n}$
The half life period of a first ordered reaction is 60 minutes
Number of half lives $=\frac{240}{60}=4i.e.n=4$
Amount of the substance left after 4 half lives $=\frac{A_0}{2^4}=\frac{A_0}{16}$
$=0.0625of{A}_0=6.25\%$