Chemistry - Chemical Kinetics Question with Solution | TestHub

For a first order reaction, the rate constant $k$ is related to the half-life $t_{1/2}$ by the equation:

$k=\frac{0.693}{t_{1/2}}$

Substituting the given value of $t_{1/2}=69.3$ s:

$k=\frac{0.693}{69.3}=0.01$ s${}^{-1}=1.0\times 10^{-2}$ s${}^{-1}$

The rate of a first order reaction is given by:

Rate $=k[A]$

Given the concentration of the reactant $[A]=0.1$ M (or mol dm${}^{-3}$):

Rate $=(1.0\times 10^{-2}{\text{ s}}^{-1})\times (0.1{\text{ mol dm}}^{-3})$

Rate $=1.0\times 10^{-3}$ mol dm${}^{-3}$ s${}^{-1}$

Answer: $1.0\times 10^{-3}$ mol dm${}^{-3}$ s${}^{-1}$