17. The decomposition of \( \mathrm{SO}_{2} \mathrm{Cl}_{2} \) is a first-order reaction:
\[
\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})
\]
The rate-constant for the reaction is, \( 2.8 \times 10^{-3} \mathrm{~min}^{-1} \) at 800 K . If the initial concentration of \( \mathrm{SO}_{2} \mathrm{Cl}_{2} \) is \( 1.24 \times 10^{-3} \mathrm{~mol} / \mathrm{L} \), how long will it take for the conce tration to drop to \( 0.31 \times 10^{-3} \mathrm{~mol} / \mathrm{L} \) ? \( 5.0 \times 10^{2} \mathrm{mir} \)
