Question

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

Time (s)	Reactant (mM)
0	5.4
1	4.6
2	3.9
3	3.2
4	2.7
5	2.3

Short answer

The second-order reaction and the rate constant is 0.185mM⁻¹s⁻¹.

Step-by-step solution

Unimolecular reactions

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 there are two molecules of reactant.

First order reaction

The given reaction is in the first order if the linear plot is generated when the t(s) is plotted on the X-axis and the reactant is plotted on the Y-axis.

Second order reaction

The given reaction is the second order reaction if the linear plot is generated when the t(s) is plotted on the X-axis and $\frac{\text{1}}{\text{Reactant}}$is plotted on the Y-axis.

Tabulation to plot the graph

Time (s)	$\text{ln}\left[\text{Reactant}\right]$(mM⁻¹)
0	1.68
1	1.52
2	1.36
3	1.16
4	0.99
5	0.83

Graphical representation

Rate constant

Therate constant is,

$$\begin{gathered} k=\frac{y_2-y_1}{x_2-x_1} \\ k=\frac{0.37}{2} \\ k=0.185m{M}^{-1}{s}^{-1} \end{gathered}$$

Thus, the rate constant for the first order reactionhas been verified by using the time and the reactant.