From the reaction data below, determine whether the reaction...

From the reaction data below, determine whether the reaction is first order or second order and calculate the rate constant. $$\begin{array}{cc} \hline \text { Time (s) } & \text { Reactant (mM) } \\ \hline 0 & 6.2 \\ \hline 1 & 3.1 \\ \hline 2 & 2.1 \\ \hline 3 & 1.6 \\ \hline 4 & 1.3 \\ \hline 5 & 1.1 \\ \hline \end{array}$$

From the reaction data below, determine whether the reaction is first order or second order and calculate the rate constant.
$$\begin{array}{cc}
\hline \text { Time (s) } & \text { Reactant (mM) } \\
\hline 0 & 6.2 \\
\hline 1 & 3.1 \\
\hline 2 & 2.1 \\
\hline 3 & 1.6 \\
\hline 4 & 1.3 \\
\hline 5 & 1.1 \\
\hline
\end{array}$$

Key Concepts

Graphical Analysis

Graphical analysis involves plotting the transformed experimental data according to the integrated rate laws to ascertain the reaction order. For example, plotting ln[A] versus time should yield a straight line for a first order reaction, and plotting 1/[A] versus time should yield a straight line for a second order reaction. The linearity of these plots helps confirm the reaction order.

Rate Constant

The rate constant (k) is a fundamental parameter in chemical kinetics that quantifies the speed of a reaction. It can be determined from the slope of the linear plot derived from the appropriate integrated rate law. In a first order reaction, k is the negative of the slope from the ln[A] versus time plot, whereas in a second order reaction, k corresponds to the slope from the 1/[A] versus time plot.

Integrated Rate Laws

Integrated rate laws provide mathematical relationships between reactant concentration and time for reactions of different orders. For a first order reaction, the integrated rate law is given by ln[A] = -kt + ln[A]?, whereas for a second order reaction, it is 1/[A] = kt + 1/[A]?. These equations are essential for analyzing experimental data to determine the reaction order and calculating the rate constant.

Reaction Order

Reaction order describes how the rate of a chemical reaction depends on the concentration of its reactants. Determining whether a reaction is first or second order involves analyzing the rate dependency; in a first order reaction, the rate is proportional to the first power of the reactant concentration, while in a second order reaction, the rate is proportional to the square of the reactant concentration.

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