Question

Give the unit of Rate Constant of a Reaction.

Answer 1

Step 1: Unit of Rate Constant:

The rate of a chemical reaction may be defined as the change in concentration of any reactant or product of the reaction in a particular time interval.

Consider a general equation, $\mathrm{aA}+\mathrm{bB}\to \mathrm{cC}+\mathrm{dD}$

Rate, $r=k{\left[A\right]}^x{\left[B\right]}^y$

Where, $x+y$ is the order of the reaction

Let $n$ is the order of the reaction

So, generally $r=k{\left[Concentration\right]}^n$

That is, $k=\frac{r}{{\left[Concentration\right]}^n}......\left(1\right)$

Here rate is $r=\frac{Concentration}{time}....\left(2\right)$

Therefore, by substituting equation (2) in (1) we get,

$$\begin{gathered} k=\frac{Concentration}{time}\times \frac{1}{{\left[Concentration\right]}^n} \\ k={\left[Concentration\right]}^{1-n}tim{e}^{-1} \end{gathered}$$

The unit of concentration is $mol{L}^{-1}$

The unit of time is $s^{-1}$

Therefore, the unit of the rate constant is;

$$\begin{gathered} k={\left[mol{L}^{-1}\right]}^{1-n}{s}^{-1} \\ k=mo{l}^{1-n}{L}^{-1+n}{s}^{-1} \\ k=mo{l}^{1-n}{L}^{n-1}{s}^{-1} \end{gathered}$$

Step 2: For the Zero-order reaction:

The order of the reaction, $n=0$

Therefore, the unit of the rate constant for the zero-order reaction is

$$\begin{gathered} k=mo{l}^{1-n}{L}^{n-1}{s}^{-1} \\ k=mo{l}^{1-0}{L}^{0-1}{s}^{-1} \\ k=mo{l}^1{L}^{-1}{s}^{-1} \end{gathered}$$

Step 3: For the First-order reaction:

The order of the reaction, $n=1$

Therefore, the unit of the rate constant for the First-order reaction is

$$\begin{gathered} k=mo{l}^{1-1}{L}^{1-1}{s}^{-1} \\ k=mo{l}^0{L}^0{s}^{-1} \\ k=s^{-1} \end{gathered}$$

Step 4: For the Second-order reaction:

The order of the reaction, $n=2$

Therefore, the unit of the rate constant for the second-order reaction is

$$\begin{gathered} k=mo{l}^{1-n}{L}^{n-1}{s}^{-1} \\ k=mo{l}^{1-2}{L}^{2-1}{s}^{-1} \\ k=mo{l}^{-1}{L}^1{s}^{-1} \end{gathered}$$

Step 5: For the Third-order reaction:

The order of the reaction, $n=3$

Therefore, the unit of the rate constant for the third-order reaction is

$$\begin{gathered} k=mo{l}^{1-n}{L}^{n-1}{s}^{-1} \\ k=mo{l}^{1-3}{L}^{3-1}{s}^{-1} \\ k=mo{l}^{-2}{L}^2{s}^{-1} \end{gathered}$$