Question

A substance reacts according to $I$ order kinetics and rate constant for the reaction is $1\times {10}^{-2}{\sec }^{-1}$. If its initial concentration is $1M$.
(a) What is initial rate?
(b) What is rate after $1$ minute?

Answer 1

(a) Initial rate of a first order reaction $=kC$
$=1\times {10}^{-2}\times 1.0=1\times {10}^{-2}$ $mol$ $L^{-1}$ $s^{-1}$
(b) Concentration after $60$ seconds is calculated by applying first order kinetic equation,
$k=\frac{2.303}{60}{\log }_{10}\frac{1}{(1-x)}$
or $1\times {10}^{-2}=\frac{2.303}{60}[-\log (1-x)]$
or $\frac{60\times {10}^{-2}}{2.303}=-\log (1-x)=0.2605$
$\log (1-x)=-0.2605=\overline{1}.7395$
$(1-x)=$ antilog of $\left(\overline{1}.7395\right)=0.5489$ $mol$ $L^{-1}$
Rate of reaction after $1$ minute $=k\times C$
$=1\times {10}^{-2}\times 0.5489$
$=5.489\times {10}^{-3}$ $mol$ $L^{-1}$ $s^{-1}$