Question

A certain reaction obeys the rate equation (in the integrated form) $\left[ C ^{(1- n )}- C _{0}^{(1- n )}\right]=( n -1) kt$ where $n$ is the order of the reaction; $C _{0}$ the initial concentration and $C$, the concentration after time $t$. What is the unit of $k$ for $n =3$ :-

• A. $sec ^{-1}$
• B. litre $mol ^{-1} sec ^{-1}$
• C. mol litre $^{-1} \sec ^{-1}$
• D. litre $^{2} mol ^{-2} sec ^{-1}$

Answer 1

Answer: (D)

$ C ^{(1- n )}- C _{0}^{(1- n )}=( n -1) kt $
put $n =3 \,\,\,C ^{-2}- C _{0}^{-2}=2 kt$
concentration i.e. $=\frac{ mol }{\ell}$
$\left(\frac{ mol }{\ell}\right)^{-2}= K \times$ second
$k =\ell^{2} mol ^{-2} sec ^{-1}$