Question

The unit of rate constant for a reaction is $litr{{e}^{2}}mo{{l}^{-2}}{{t}^{-1}}$ . The order of the reaction is………………..

Answer 1

Hint: The units for the rate constant for nth order reaction are as follows.
\[lite{{r}^{n-1}}mo{{l}^{1-n}}{{t}^{-1}}\]
Here n = order of the reaction. By substituting the respective order of the reaction in place in the above formula we will get the units of rate constant for the respective order of the reaction.

Complete step by step solution:
- In the question it is given that to write the order of the reaction for the given units of rate constant.
- The units for the rate constant for nth order reaction are as follows.
\[lite{{r}^{n-1}}mo{{l}^{1-n}}{{t}^{-1}}\]
- By trial and error method we can find the given rate constant units which belong to which order of the reaction.
- First we will start from the first order reaction, for the first order reaction the value of n = 1.
- Substitute the n = 1 in the below units
\[\begin{align}
& lite{{r}^{n-1}}mo{{l}^{1-n}}{{t}^{-1}} \\
& lite{{r}^{1-1}}mo{{l}^{1-1}}{{t}^{-1}} \\
& lite{{r}^{0}}mo{{l}^{0}}{{t}^{-1}} \\
\end{align}\]
- The above obtained units are not going to match with the given units then the order of the reaction is not ‘1’.
- Next we will go with the second order reaction, for the second order reaction the value of n = 2.
- Substitute the n = 1 in the below units
\[\begin{align}
& lite{{r}^{n-1}}mo{{l}^{1-n}}{{t}^{-1}} \\
& lite{{r}^{2-1}}mo{{l}^{1-2}}{{t}^{-1}} \\
& lite{{r}^{1}}mo{{l}^{-1}}{{t}^{-1}} \\
\end{align}\]
- The above obtained units are not going to match with the given units then the order of the reaction is not ‘2’.
- Next we will go with the third order reaction, for the third order reaction the value of n = 3.
- Substitute the n = 3 in the below units
\[\begin{align}
& lite{{r}^{n-1}}mo{{l}^{1-n}}{{t}^{-1}} \\
& lite{{r}^{3-1}}mo{{l}^{1-3}}{{t}^{-1}} \\
& lite{{r}^{2}}mo{{l}^{-2}}{{t}^{-1}} \\
\end{align}\]
- The above obtained units are going to match with the given units then the order of the reaction is ‘3’.

- So, the order of the reaction is three with rate constant units $litr{{e}^{2}}mo{{l}^{-2}}{{t}^{-1}}$

Note: As the order of the reaction changes the rate constant units are also changed. Order of the reaction is going to depend on the number of chemicals involved in the reaction. The concentration of the reactants is going to decide the order of the reaction.