Units of the rate constant for reactions whose order is greater than 1 In many textbooks, it is written that:


  The value of rate constant depends on the nature of the reactants, temperature and catalyst. It is independent of the concentration of the reactants.


However, the unit of the rate constant is

$$\left(\frac{\mathrm{mol}}{\mathrm{l}}\right)^{1-n} \mathrm{s}^{-1}$$

where $n$ is the order of reaction.

Therefore, except for first order reactions, the unit of the rate constant will have a concentration term $\displaystyle\frac{\textrm{mol}}{\textrm{l}}$ for all other reactions. Does this contradict the statement given in books?
As an example if the reaction is $\ce{A + B -&gt; C}$ the rate expression for the appearance of $\ce{C}$ is

$$\frac{\mathrm d[\ce{C}]}{\mathrm dt} = +k[\ce{A}][\ce{B}].$$

The units have to be the same on both sides of this equation, these are concentration/time on the left and to be the same on the right the rate constant $k$ has to have units $(1/\text{concentration})(1/\text{time})$ usually expressed as $\mathrm{dm^3\,mol^{-1}\,s^{-1}}.$ 

It is true that the numerical value of the rate constant usually depends of several things such as temperature, but the units remain the same for each type of rate constant, 0th,  1st, 2nd, 3rd simply because the rate equation units have to balance.