The decomposition of SO2 Cl2 in the gas phase, SO2 Cl2 ⟶SO2+Cl2 can be studied by measuring the

step 1 Using the data provided for A, let's plot the concentration of chlorine versus time. So a plot o

The decomposition of SO2 Cl2 in the gas phase, SO2 Cl2...

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ in the gas phase, $$\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2}$$ can be studied by measuring the concentration of $\mathrm{Cl}_{2}$ as the reaction proceeds. We begin with $\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]_{0}=0.250 \mathrm{M}$. Holding the temperature constant at $320 .{ }^{\circ} \mathrm{C}$, we monitor the $\mathrm{Cl}_{2}$ concentration, with the following results. $$\begin{array}{cc}t \text { (hours) } & {\left[\mathrm{Cl}_{2}\right](\mathrm{mol} / \mathrm{L})} \\\hline 0.00 & 0.000 \\2.00 & 0.037 \\4.00 & 0.068 \\ 6.00 & 0.095 \\8.00 & 0.117 \\10.00 & 0.137 \\12.00 & 0.153 \\14.00 & 0.168 \\16.00 & 0.180 \\ 18.00 & 0.190 \\20.00 & 0.199\end{array}$$ (a) Plot $\left[\mathrm{Cl}_{2}\right]$ versus $t .$ (b) Plot $\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$ versus $t .$ (c) Determine the rate law for this reaction. (d) What is the value, with units, for the specific rate constant at $320 .{ }^{\circ} \mathrm{C}$ ? (e) How long would it take for $95 \%$ of the original $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to react?

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ in the gas phase,
$$\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2}$$
can be studied by measuring the concentration of $\mathrm{Cl}_{2}$ as the reaction proceeds. We begin with $\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]_{0}=0.250 \mathrm{M}$. Holding the temperature constant at $320 .{ }^{\circ} \mathrm{C}$, we monitor the $\mathrm{Cl}_{2}$ concentration, with the following results.
$$\begin{array}{cc}t \text { (hours) } & {\left[\mathrm{Cl}_{2}\right](\mathrm{mol} / \mathrm{L})} \\\hline 0.00 & 0.000 \\2.00 & 0.037 \\4.00 & 0.068 \\
6.00 & 0.095 \\8.00 & 0.117 \\10.00 & 0.137 \\12.00 & 0.153 \\14.00 & 0.168 \\16.00 & 0.180 \\
18.00 & 0.190 \\20.00 & 0.199\end{array}$$
(a) Plot $\left[\mathrm{Cl}_{2}\right]$ versus $t .$ (b) Plot $\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$ versus $t .$
(c) Determine the rate law for this reaction. (d) What is the value, with units, for the specific rate constant at $320 .{ }^{\circ} \mathrm{C}$ ?
(e) How long would it take for $95 \%$ of the original $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to react?

Key Concepts

Graphical Analysis in Kinetics

Graphical analysis involves plotting concentration data (or its transformations) versus time to obtain a straight line when the correct integrated rate law has been applied. This method helps in identifying the reaction order and determining the rate constant from the slope of the linear plot.

Specific Rate Constant

The specific rate constant, often denoted by k, is a numerical value that quantifies the speed of a reaction under given conditions. Finding k often requires experimental data and is critical for predicting reaction progress and for scaling reactions in practical applications.

Integrated Rate Laws

Integrated rate laws relate the concentrations of reactants to time for reactions of a specific order. These equations are essential for analyzing experimental data in order to determine the reaction order and the corresponding rate constant by fitting concentration versus time data.

Percent Completion and Reaction Time Prediction

Calculating the time required for a certain percentage of reactant conversion (such as 95% completion) involves using the integrated rate law alongside the determined rate constant. This concept is important for understanding and predicting how long a reaction will take to reach a desired level of progress.

Rate Laws

A rate law expresses the relationship between the reaction rate and the concentrations of the reactants, usually in the form rate = k[A]^m[B]^n. Determining the rate law reveals the order of the reaction with respect to each reactant and allows for quantitative predictions of reaction behavior.

Reaction Order

The reaction order, indicated by the exponents in the rate law, specifies how the rate is affected by the concentration of each reactant. This concept is crucial in kinetic studies because it informs how changes in concentration will impact the reaction rate.

Chemical Kinetics

Chemical kinetics is the study of the rates of chemical reactions and the factors that affect these rates. It involves measuring how concentrations of reactants and products change over time in order to understand the mechanism and dynamics of the reaction.

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