Final answer:
To calculate the recovery percent of solute with a single ether extraction, utilize the distribution coefficient and the known volumes and masses to find the concentrations in each layer. Then, calculate the amount extracted and express it as a percentage of the initial amount.
Step-by-step explanation:
To calculate the percent of the organic solute that can be recovered with a single extraction with ether, given a distribution coefficient of 20, we can use the following approach:
Given the distribution coefficient (Kd) is 20, it means that at equilibrium, the concentration of solute in ether is 20 times greater than in water. Thus, we can use the equation C1V1 = C2V2, where C1 and V1 are the concentration and volume of solute in water, respectively, and C2 and V2 are the concentration and volume of solute in ether, respectively. The initial amounts of solute and volumes are known (Cinitial = mass of solute / volume of water = 2.0 g / 15 mL and Vether = 5.9 mL), so we can solve for C2 (concentration in ether) and then for the new concentration in water (C1' = C1 - C2 x V2 / V1). The amount of solute in ether can then be found, and the recovery percent can be calculated.
Using this method:
- Cinitial = 2.0 g / 15 mL
- C1' = unknown
- V1 = 15 mL
- C2 = Kd x C1'
- V2 = 5.9 mL
After the calculations:
- Recovery % = (amount of solute in ether / initial amount of solute) x 100%