Question

a) Derive integrated rate equation for the first order reaction.
b) According to collision theory, what are the two factors that lead to effective collisions?

Answer 1

a) Integrated rate equation for the first order reaction:
The differential rate equation for the first order reaction is $-\frac{d\left[A\right]}{dt}=k\left[A\right]$
Rearrange and integrate between the limits
$\left[A\right]=[A{]}_0$ at $t=0$ and $\left[A\right]=[A{]}_t$ at $t=t$
reaction is ${\int }_{[A{]}_0}^{[A{]}_t}\frac{d\left[A\right]}{\left[A\right]}=-k{\int }_0^{t}dt$
$\left[ln\right[A]{]}_{[A{]}_0}^{[A{]}_t}=-k(t{)}_0^t$
$ln[A{]}_t-ln[A{]}_0=-kt$
$ln\frac{[A{]}_t}{[A{]}_0}=-kt$
$k=\frac{1}{t}ln\frac{[A{]}_0}{[A{]}_t}$
$k=\frac{2.303}{t}log\frac{[A{]}_0}{[A{]}_t}$
b) According to collision theory, the two factors that lead to effective collisions are
(i) Molecules must collide with a certain minimum kinetic energy which is required to arrange outer electrons in breaking and making of bonds.
(ii) Molecules must collide with a certain minimum kinetic energy called activation energy.