# A first-order reaction has a hall-life of 21.3s. How long does it take for the concentration of the reactant in the reaction to fall to one-eighth of its initial value?

Nov 23, 2017

It would take approximately $64.0 s$ given those data.

#### Explanation:

$21.3 s = \frac{0.693}{k}$
$\therefore k \approx 3.25 \cdot {10}^{-} 2 {s}^{-} 1$

$\ln \left(\frac{1}{8}\right) = - 3.25 \cdot {10}^{-} 2 {s}^{-} 1 \cdot t$
$\therefore t \approx 64.0 s$

Each equation I used is assuming this reaction's kinetics are of the first order, which is cited. The first equation is a simplified version for the half life of a first order reactant, and the second equation is the general equation for first order reactions in chemical kinetics.