From the reaction data below, determine whether the reaction is first order or second order and calculate the rate constant.

Time$\left(s\right)$	Reactant $\left(\mathrm{mM}\right)$
0	6.2
1	3.1
2	2.1
3	1.1
4	1.3
5	1.1

First-order reactions, also known as unimolecular reactions, occur when there is only one molecule of reactant present. Second-order reactions, also known as bimolecular reactions, are reactions in which two molecules of reactant are present.

In first-order reactions, a linear plot is generated when the $\mathrm{t}\left(\mathrm{s}\right)$is plotted on the $\mathrm{X}$-axis and the reactant is plotted on the $\mathrm{Y}$-axis. On the other hand, in second-order reactions, a linear plot is generated when the $\mathrm{t}\left(\mathrm{s}\right)$ is plotted on the $\mathrm{X}$ -axis and$\frac{1}{\mathrm{Reactant}}$ is plotted on the $\mathrm{Y}$ -axis.

The graph obtained from the tabulation is as follows:

A linear graph is obtained; thus, the reaction is of second-order.

The rate constant is obtained by calculating the slope of the graph. The slope of the graph is

$\mathrm{k}=\frac{{\mathrm{y}}_2‐{\mathrm{y}}_1}{{\mathrm{x}}_2‐{\mathrm{x}}_1}$

Where

$\mathrm{k}=$Rate constant

$\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)=$Coordinates of the first point in the line.

$\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)=$Coordinates of the second point in the line.

On substituting,

$$\begin{gathered} \mathrm{k}=\frac{0.29}{2} \\ \mathrm{k}=0.145{\mathrm{mM}}^{‐1}{\mathrm{s}}^{‐1} \end{gathered}$$