Question

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

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

Hint:

A quick way to remember the units of the rate constant is to use the formula: (Concentration)$^{1-n}$ (Time)$^{-1}$. For example, for a zero-order reaction (n=0), units are (mol/L)$^1$ s$^{-1}$. For a second-order reaction (n=2), units are (mol/L)$^{-1}$ s$^{-1}$ or L mol$^{-1}$ s$^{-1}$.

Answer 1

The Correct Option is D

Let's consider a general rate law for an nth-order reaction:
Rate = $k[C]^n$
where 'k' is the rate constant and [C] is the concentration.
We can determine the units of 'k' by substituting the units for the other terms.
Units of Rate = $\frac{\text{Concentration}}{\text{Time}} = \frac{\text{mol L}^{-1}}{\text{s}} = \text{mol L}^{-1} \text{s}^{-1}$.
Units of Concentration [C] = mol L$^{-1}$.
Substituting these into the rate law:
$(\text{mol L}^{-1} \text{s}^{-1}) = (\text{Units of k}) \times (\text{mol L}^{-1})^n$
$(\text{mol L}^{-1} \text{s}^{-1}) = (\text{Units of k}) \times (\text{mol}^n \text{L}^{-n})$
Now, solve for the units of k:
Units of k = $\frac{\text{mol}^1 \text{L}^{-1} \text{s}^{-1}}{\text{mol}^n \text{L}^{-n}}$
Units of k = $(\text{mol}^{1-n}) (\text{L}^{-1 - (-n)}) (\text{s}^{-1})$
Units of k = mol$^{1-n}$ L$^{n-1}$ s$^{-1}$.
This matches option (D).