The reaction SO2 Cl2(g) ⟶SO2(g)+Cl2(g) is first order in SO2 Cl2. Using the following kinetic da

step 1 In this problem, we're given the following reaction. We're told that this is a first order in ou

The reaction SO2 Cl2(g) ⟶SO2(g)+Cl2(g) is first order in SO2...

The reaction $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$ is first order in $\mathrm{SO}_{2} \mathrm{Cl}_{2}$. Using the following kinetic data, determine the magnitude and units of the first-order rate constant: $$ \begin{array}{cc} \hline \text { Time (s) } & \text { Pressure } \mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{kPa}) \\ \hline 0 & 101.3 \mathrm{kPa} \\ 2500 & 95.95 \mathrm{kPa} \\ 5000 & 90.69 \mathrm{kPa} \\ 7500 & 85.92 \mathrm{kPa} \\ 10,000 & 81.36 \mathrm{kPa} \\ \hline \end{array} $$

The reaction $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$ is first order in $\mathrm{SO}_{2} \mathrm{Cl}_{2}$. Using the following kinetic data, determine the magnitude and units of the first-order rate constant:
$$
\begin{array}{cc}
\hline \text { Time (s) } & \text { Pressure } \mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{kPa}) \\
\hline 0 & 101.3 \mathrm{kPa} \\
2500 & 95.95 \mathrm{kPa} \\
5000 & 90.69 \mathrm{kPa} \\
7500 & 85.92 \mathrm{kPa} \\
10,000 & 81.36 \mathrm{kPa} \\
\hline
\end{array}
$$

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Key Concepts

Integrated Rate Law for First-Order Reactions

The integrated rate law for a first-order reaction expresses the relationship between the concentration of the reactant and time in the form ln([A]?) = ln([A]?) - kt. This equation allows one to obtain a straight-line relationship when plotting the natural logarithm of the concentration (or any proportional measure like pressure for a gas) versus time, where the slope of the line is -k.

Rate Constant and Its Units

The rate constant (k) in first-order reactions quantifies the speed of the reaction and has units of inverse time (e.g., s?¹). Its magnitude can be determined from the slope of the linear plot obtained using the integrated rate law, reflecting how quickly the concentration decreases with time.

First-Order Reaction Kinetics

First-order kinetics describes reactions where the rate is directly proportional to the concentration of a single reactant. This means that as the concentration of the reactant decreases, the rate of the reaction decreases proportionally, and the decay of the reactant follows an exponential pattern over time.

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