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. $$ \begin{array}{cc} t \text { (hours) } & {\left[\mathrm{Cl}_{2}\right](\mathrm{mol} / \mathrm{L})} \\ \hline 0.00 & 0.000 \\ 2.00 & 0.037 \\ 4.00 & 0.068 \\ 6.00 & 0.095 \\ 8.00 & 0.117 \\ 10.00 & 0.137 \\ 12.00 & 0.153 \\ 14.00 & 0.168 \\ 16.00 & 0.180 \\ 18.00 & 0.190 \\ 20.00 & 0.199 \\ \hline \end{array} $$
(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 $\mathrm{SO}, \mathrm{Cl}$, to react?