Question

What will be the unit of rate constant $\left(k\right)$ for a third order reaction?

• A. $s^{-1}$
• B. $mo{l}^2{L}^{-2}{s}^{}$
• C. $mo{l}^{-2}{L}^2{s}^{-1}$
• D. $mo{l}^{-1}{L}^{-2}s$

Answer 1

The correct option is C $mo{l}^{-2}{L}^2{s}^{-1}$

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 $\frac{mol}{L.s}$

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

$\text{Units of}k={\left(\frac{mol}{L}\right)}^{(1-n)}\times s^{-1}$

For a third order reaction, $n=3$:
$\text{Units of}k={\left(\frac{mol}{L}\right)}^{-2}\times s^{-1}=mo{l}^{-2}{L}^2{s}^{-1}$