The decomposition of \(\mathrm{HI}(\mathrm{g})\) is represented by the equation
$$2 \mathrm{HI}(\mathrm{g}) \rightleftharpoons
\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g})$$
\(\mathrm{HI}(\mathrm{g})\) is introduced into five identical \(400
\mathrm{cm}^{3}\) glass bulbs, and the five bulbs are maintained at \(623
\mathrm{K}\) Each bulb is opened after a period of time and analyzed for
\(I_{2}\) by titration with \(0.0150 \mathrm{M} \mathrm{Na}_{2} \mathrm{S}_{2}
\mathrm{O}_{3}(\mathrm{aq})\)
$$\begin{array}{l}
\mathrm{I}_{2}(\mathrm{aq})+2 \mathrm{Na}_{2} \mathrm{S}_{2}
\mathrm{O}_{3}(\mathrm{aq}) \longrightarrow \\
\quad \mathrm{Na}_{2} \mathrm{S}_{4} \mathrm{O}_{6}(\mathrm{aq})+2
\mathrm{NaI}(\mathrm{aq})
\end{array}$$
Data for this experiment are provided in the table below. What is the value of
\(K_{\mathrm{c}}\) at \(623 \mathrm{K} ?\)
$$\begin{array}{llll}
\hline & & & \text { Volume } \\
& \text { Initial } & \text { Time } & 0.0150 \mathrm{M} \mathrm{Na}_{2}
\mathrm{S}_{2} \mathrm{O}_{3} \\
\text { Bulb } & \text { Mass of } & \text { Bulb } & \text { Required for }
\\\
\text { Number } & \mathrm{Hl}(\mathrm{g}), \mathrm{g} & \text { Opened, }
\mathrm{h} & \text { Titration, in } \mathrm{mL} \\
\hline 1 & 0.300 & 2 & 20.96 \\
2 & 0.320 & 4 & 27.90 \\
3 & 0.315 & 12 & 32.31 \\
4 & 0.406 & 20 & 41.50 \\
5 & 0.280 & 40 & 28.68 \\
\hline
\end{array}$$