CAIE A-Level Chemistry 25.2.2 Partition Coefficient Calculations

Iodine is found naturally in compounds in many different oxidation states.

Iodide ions, $\mathrm{I}^{-}$, react with acidified $\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq})$ to form iodine, $\mathrm{I}_{2}$, and water. This reaction mixture is shaken with cyclohexane, $\mathrm{C}_{6} \mathrm{H}_{12}$, to extract the $\mathrm{I}_{2}$. Cyclohexane is immiscible with water.

$15.0 \mathrm{~cm}^{3}$ of $\mathrm{C}_{6} \mathrm{H}_{12}$ is shaken with $20.0 \mathrm{~cm}^{3}$ of an aqueous solution containing $\mathrm{I}_{2}$ until no further change is seen.
It is found that 0.390 g of $\mathrm{I}_{2}$ is extracted into the $\mathrm{C}_{6} \mathrm{H}_{12}$.
The partition coefficient of $\mathrm{I}_{2}$ between $\mathrm{C}_{6} \mathrm{H}_{12}$ and water, $K_{\mathrm{pc}}$, is 93.8.
Calculate the mass of $\mathrm{I}_{2}$ that remains in the aqueous layer.
Show your working.
mass of $I_{2}$ in aqueous layer =