Question

For a certain first-order reaction 32% of the reactant is left after $570s$. The rate constant of this reaction is ______$\times {10}^{-3}{s}^{-1}$. (Round off to the Nearest Integer).
[Given: ${\log }_{10}2=0.301,ln10=2.303$]

Answer 1

For first order reaction,
$k=\frac{1}{t}ln\frac{a}{[a-x]}$

$k=\frac{2.303}{570}log\frac{100}{32}$

$k=\frac{2.303}{570}[log{10}^2-log{2}^5]$

$k=\frac{2.303}{570}\times 0.5$

$k=2\times {10}^{-3}{s}^{-1}$