The rate of a first - order is `0.04 "mol l"^(-1) s^(-1)` at 10 seconds and `0.03 "mol l"^(-1) s^(-1)`. At 20 seconds after initiation of the reaction. The half - life period of the reaction is

Explanation

`24.14" min "r_(2) =k_(1) C_(1) and r_(2) =k_(2) C_(2)`
Since rate of first-order reaction is directly proportional to the concentration of its reactant,
`therefore (r_(1))/(r_(2))=(C_(1))/(C_(2))=(0.04)/(0.03)`
According to first-order reaction `k=(2.303)/(t_(20)-t_(10))" log "(C_(1))/(C_(2))`
On substituting the various values `j=0.0287" m in"^(-1)`
`t_(1//2) =(0.693)/(k) =(0.693)/(0.0287)=24.14` m in