The table below gives the concentration of SO2 Cl2(g) as a function of time for the reaction des

step 1 So before we actually answer this question, we have to recall that for a first order reaction, L

The table below gives the concentration of SO2 Cl2(g) as a...

The table below gives the concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g)$ as a function of time for the reaction described by the equation \begin{tabular}{lc} $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$ \\ \hline$\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right] / \mathrm{M}$ & $t / \mathrm{min}$ \\ \hline $0.0345$ & 0 \\ $0.0245$ & $3.8$ \\ $0.0212$ & $5.6$ \\ $0.0154$ & $9.8$ \\ $0.0103$ & $14.0$ \\ \hline \end{tabular} Verify that this reaction is a first-order reaction by plotting $\ln \left(\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]=\mathrm{M}\right)$ versus time and determine the value of the rate constant.

The table below gives the concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g)$ as a function of time for the reaction described by the equation
\begin{tabular}{lc}
$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$ \\
\hline$\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right] / \mathrm{M}$ & $t / \mathrm{min}$ \\
\hline $0.0345$ & 0 \\
$0.0245$ & $3.8$ \\
$0.0212$ & $5.6$ \\
$0.0154$ & $9.8$ \\
$0.0103$ & $14.0$ \\
\hline
\end{tabular}
Verify that this reaction is a first-order reaction by plotting $\ln \left(\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]=\mathrm{M}\right)$ versus time and determine the value of the rate constant.

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Key Concepts

Graphical Determination of Reaction Order

Plotting ln[Concentration] versus time is a standard method to determine whether a reaction follows first-order kinetics. If the resulting graph is a straight line, it confirms that the reaction is first order, and the slope of the line, which is equal to -k, allows for the determination of the rate constant. This graphical method is a crucial tool in kinetic analysis to verify the order of a reaction and extract kinetic parameters.

Integrated Rate Law for First-order Reactions

The integrated rate law for a first-order reaction is given by ln[A] = ln[A]0 - kt, where [A]0 is the initial concentration, [A] is the concentration at time t, and k is the rate constant. This equation shows that if a reaction is first order, the natural logarithm of the concentration decreases linearly with time.

First-order Kinetics

First-order kinetics refers to reactions in which the rate is directly proportional to the concentration of one reactant. This means that as the concentration decreases, the reaction slows down proportionally. A key characteristic of such reactions is that a plot of the natural logarithm of the reactant concentration versus time yields a straight line, indicating first-order behavior.

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