Iodine is sparingly soluble in water but much more so in carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\). The equilibrium constant, also called the partition coefficient, for the distribution of \(\mathrm{I}_{2}\) between these two phases $$ \mathrm{I}_{2}(a q) \rightleftharpoons \mathrm{I}_{2}\left(\mathrm{CCl}_{4}\right) $$ is 83 at \(20^{\circ} \mathrm{C}\). (a) A student adds \(0.030 \mathrm{~L}\) of \(\mathrm{CCl}_{4}\) to \(0.200 \mathrm{~L}\) of an aqueous solution containing \(0.032 \mathrm{~g}\) \(\mathrm{I}_{2} .\) The mixture is shaken and the two phases are then allowed to separate. Calculate the fraction of \(\mathrm{I}_{2}\) remaining in the aqueous phase. (b) The student now repeats the extraction of \(I_{2}\) with another 0.030 \(\mathrm{L}\) of \(\mathrm{CCl}_{4}\). Calculate the fraction of the \(\mathrm{I}_{2}\) from the original solution that remains in the aqueous phase. (c) Compare the result in (b) with a single extraction using \(0.060 \mathrm{~L}\) of \(\mathrm{CCl}_{4}\). Comment on the difference.

Step by step solution

01

Determine the initial amount of iodine

First, determine the initial amount of iodine by dividing the mass of iodine (\(0.032 \, g\)) by its molar mass (\(253.8089 \, g/mol\)), then multiply by the volume of the solution \(0.200 \, L\). This will give the molarity of iodine in the solution. Let's denote this value as x.

02

Apply the partition coefficient

In equilibrium, the iodine in \(CCl_{4}\) is in ratio to the iodine in water given by partition coefficient. Therefore, we can write: \(83 = [I_{2}(CCl_{4})] / [I_{2}(aq)]\), where \( [I_{2}(CCl_{4})]\) and \([I_{2}(aq)]\) are the molarities of iodine in carbon tetrachloride and in water, respectively. From this, we can calculate the new concentration of iodine in the aqueous solution after extraction.

03

Calculate the fraction of iodine in aqueous phase after the first extraction

The fraction of iodine remaining in the aqueous phase after extraction can be found by dividing the new molarity of iodine in the aqueous phase by the initial molarity.

04

Recalculate for the second extraction

The same procedure will be repeated for the second extraction with the new values.

05

Comparison with single extraction using double volume

Finally, for part (c), repeat step 2 and step 3 with a doubled volume of carbon tetrachloride and compare these two methods.

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