Consider 15 mL of an aqueous solution containing 2.0 g of an organic solute. If the distribution coefficient for the solute between ether and water is 20, calculate the percent of the compound that can be recovered with a single extraction with 13.9 mL of ether
To calculate the percent of the compound that can be recovered with a single extraction, we need to consider the distribution of the solute between the two immiscible solvents, water and ether.
First, let's calculate the amount of solute that will distribute into the ether phase. We can use the formula:
Amount of solute in ether (in grams) = (Amount of solute in aqueous solution / Total volume of aqueous solution) * Volume of ether
Amount of solute in ether = (2.0 g / 15 mL) * 13.9 mL
Amount of solute in ether = 1.8533 g
Next, we need to calculate the amount of solute left in the aqueous phase after extraction. This can be determined by subtracting the amount of solute extracted into the ether phase from the initial amount of solute:
Amount of solute in aqueous phase after extraction = Initial amount of solute - Amount of solute in ether
Amount of solute in aqueous phase after extraction = 2.0 g - 1.8533 g
Amount of solute in aqueous phase after extraction = 0.1467 g
Finally, we can calculate the percent of the compound that can be recovered after a single extraction by dividing the amount of solute in the aqueous phase after extraction by the initial amount of solute, and then multiplying by 100:
Percent recovery = (Amount of solute in aqueous phase after extraction / Initial amount of solute) * 100
Percent recovery = (0.1467 g / 2.0 g) * 100
Percent recovery = 7.335%
Therefore, the percent of the compound that can be recovered with a single extraction using 13.9 mL of ether is approximately 7.335%.
Let x = grams in organic layer,
then 2-x = grams in water layer.
Kd = 20
Kd = g/mL in organic layer/g/mL in aq layer.
Then organic layer = xgrams/13.9 mL
aq layer = (2-x)grams/15 mL.