If $1.0 \mathrm{~g}$ of hyoscyamine was dissolved in $200 \mathrm{~mL}$ of water, how much hyoscyamine would be left remaining in the aqueous solution after extracting once with $100 \mathrm{~mL}$ of diethyl ether? How much hyoscyamine would be left remaining in the aqueous solution if two extractions with $50 \mathrm{~mL}$ of diethyl ether were performed instead? Which extraction method would be more efficient at removing hyoscyamine from the aqueous solution? The partition coefficient, $\mathrm{K}$, of hyoscyamine in this system is 4.07 .

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∻Solution∻ ‖ 1 ⋮ **Calculate the amount of hyoscyamine in diethyl ether after the first extraction**: Use the partition coefficient $K$ to determine the ratio of concentrations between diethyl ether and water. The partition coefficient $K$ is defined as $K = \frac{[hyoscyamine]_{ether}}{[hyoscyamine]_{water}}$. ‖ ‖ 2 ⋮ **Determine the initial concentration of hyoscyamine in water**: The initial concentration $C_{water}$ is calculated by dividing the mass of hyoscyamine by the volume of water, $C_{water} = \frac{1.0 ext{ g}}{200 ext{ mL}}$. ‖ ‖ 3 ⋮ **Apply the partition coefficient to find the final concentrations**: After the first extraction, the concentration in diethyl ether $C_{ether}$ can be found using $C_{ether} = K \cdot C_{water}$. The amount of hyoscyamine in 100 mL of diethyl ether is then $C_{ether} imes 100 ext{ mL}$. ‖ ‖ 4 ⋮ **Calculate the remaining amount of hyoscyamine in water after the first extraction**: Subtract the amount extracted by diethyl ether from the initial amount to find the remaining amount in water. ‖ ‖ 5 ⋮ **Repeat the calculation for two extractions with 50 mL of diethyl ether**: For each extraction, recalculate the concentration in water and use the partition coefficient to find the new concentration in diethyl ether. Then, calculate the remaining amount in water after each extraction. ‖ ‖ 6 ⋮ **Compare the efficiency of the two extraction methods**: The method that results in the least amount of hyoscyamine remaining in the aqueous solution is more efficient. ‖ ∻1 Answer∻ ⚹ [Insert final answer for the first extraction here] ⚹ ∻2 Answer∻ ⚹ [Insert final answer for the two extractions here] ⚹ ∻3 Answer∻ ⚹ [Insert which method is more efficient here] ⚹ ∻Key Concept∻ ⚹ The partition coefficient is a measure of a compound's distribution between two immiscible solvents and is key to solving extraction problems. ⚹ ∻Explanation∻ ⚹ The partition coefficient allows us to calculate the concentration of a solute in two phases at equilibrium, which is essential for determining the amount of solute remaining after extraction. ⚹◊What is the formula for calculating the distribution coefficient (D)?⍭ Generate me a similar question◊

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