Question

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.

Short answer

With the given equilibrium constant and the provided volumes of solutions, the fraction of iodine left in the aqueous phase after each extraction can be calculated. The comparison shows that multiple extractions with smaller volumes are more effective than a single extraction with a larger volume.

Step-by-step solution

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.

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.

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.

Recalculate for the second extraction

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

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.

Key concepts

Equilibrium Constant

The equilibrium constant (K) is crucial in understanding reactions that reach dynamic balance. It is a value that expresses the ratio of concentrations of products and reactants at equilibrium. In the context of iodine partitioning between water and carbon tetrachloride, the equilibrium constant is referred to as the partition coefficient. This coefficient helps determine how iodine distributes itself between the two phases.
For our iodine partitioning problem, the equilibrium constant is given as 83. This means that for every unit of iodine in the aqueous phase, 83 units will be present in the CCl₄ phase at equilibrium. The formula is:
\[ K = \frac{[I_2(CCl_4)]}{[I_2(aq)]} \]
where \[ [I_2(CCl_4)] \] represents the concentration of iodine in carbon tetrachloride, and \[ [I_2(aq)] \] represents the concentration of iodine in the aqueous phase. A high equilibrium constant value like 83 indicates that iodine prefers being in the CCl₄ phase over the aqueous phase.

Phase Distribution

Phase distribution relates to how a substance like iodine divides itself between two immiscible liquids, such as water and CCl₄. This process is often termed extraction, where a substance is removed from one phase and transferred to another, leveraging differences in solubility.
In our scenario, iodine exhibits a far greater solubility in CCl₄, which implies that iodine would predominantly move from the aqueous phase into the CCl₄ phase upon contact. The partition coefficient of 83 is a measure of this tendency. To distribute iodine between phases, we mix the phases and allow them to settle.
After equilibrium is reached, the solution separates into two distinct layers: the aqueous phase with less iodine and the CCl₄ phase with more iodine. The objective is usually to maximize the iodine collected in the CCl₄, which means repeating extractions can be more effective to isolate the substance fully.

Molarity Calculation

Molarity is a measure of concentration, defined as moles of solute per liter of solution. Calculating molarity is essential for determining the amounts of substances in different phases, especially after extraction processes.
To find the initial iodine molarity in our exercise, we would calculate as follows:

• First, convert the mass of iodine (0.032 g) into moles using its molar mass (253.8089 g/mol).
• Calculate the number of moles by dividing the mass of iodine by its molar mass: \[ \text{moles of } I_2 = \frac{0.032}{253.8089} \]
• Next, divide the moles of iodine by the volume of the aqueous solution (0.200 L) to establish molarity: \[ \text{Molarity of } I_2 = \frac{\text{moles of } I_2}{0.200} \]

This initial molarity helps us ascertain how much iodine remains in each phase after equilibrium is established. By recalculating this after each extraction, you can track how effective the extraction is, with results showing the percentage of iodine still left in the aqueous phase.