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).
$[Givenlo{g}_{10}2=0.301,ln10=2.303]$

• A. 2.0
• B. 2
• C. 2.00

Answer 1

Answer: (A), (B), (C)

$A\stackrel{}{\to }\text{Products}$
Rate constant of a first order is given as

$k=\frac{2.303}{t}log\frac{\left[A_0\right]}{\left[A_t\right]}$
$\left[A_0\right]$ is initial concentration of reactant A
$\left[A_t\right]$ is concentration of reactant A at time 't'

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

$k=\frac{2.303}{570}(log100-log32)$
$k=\frac{2.303}{570}(2-5\times 0.301)$
$k=\frac{2.303}{570}\times 0.5$
$k=2\times {10}^{-3}{s}^{-1}$