Chapter 12, Problem 80QAP

Hydrogen iodide gas decomposes to hydrogen gas and iodine gas:

$2\text{HI}\left(g\right)\rightleftharpoons {\text{H}}_2\left(g\right)+{\text{I}}_2\left(g\right)$To determine the equilibrium constant of the system, identical one-liter glass bulbs are filled with 3.20 g of HI and maintained at a certain temperature. Each bulb is periodically opened and analyzed for iodine formation by titration with sodium thiosulfate, Na₂S₂O₃.

${\text{I}}_2\left(aq\right)+2{\text{S}}_2{\text{O}}_3{}^{2-}\left(aq\right)\to {\text{S}}_4{\text{O}}_6{}^{2-}\left(aq\right)+2{\text{I}}^{-}\left(aq\right)$It is determined that when equilibrium is reached, 37.0 mL of 0.200 M Na₂S₂O₃ is required to titrate the iodine. What is K at the temperature of the experiment?