Question

For a reaction of order (n), the unit of the rate constant is :

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• A. ${\text{mol}}^{1-n}{L}^{2n}{s}^{-1}$
• B. ${\text{mol}}^{1-n}{L}^{1-n}s$
• C. ${\text{mol}}^{1-n}{L}^{n-1}{s}^{-1}$
• D. ${\text{mol}}^{1-n}{L}^{1-n}{s}^{-1}$

Answer 1

The correct option is C ${\text{mol}}^{1-n}{L}^{n-1}{s}^{-1}$

Generalized formula for the unit of rate constant $\left(k\right)$ for a $n^{th}$ order reaction.
Let ,
$A\to \text{Products}$
is a $n^{th}$ order reaction.
$\text{Rate}\left(R\right)=k[A{]}^n$

$\text{Units of}k=\frac{\text{Units of rate}}{\text{Units of}[A{]}^n}$

Since, rate is change of concentration w.r.t time
So, units of rate are $\frac{mol}{L.s}$

$\text{Units of}k=\frac{\frac{mol}{L.s}}{{\left(\frac{mol}{L}\right)}^n}$

$\text{Units of}k={\left(\frac{mol}{L}\right)}^{(1-n)}\times s^{-1}=mo{l}^{1-n}{L}^{n-1}{s}^{-1}$
Option (c) is correct