Assume an organic compound has a partition coefficient between water and diethyl ether equal to 7.33. If there are initially 9.81 grams of the compound dissolved in 100.0 mL of water, how many grams will remain in the aqueous layer after extraction with one 30.0 mL portion of ether?
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The usual way of expressing this is as organic/aqueous layer. I will assume that is the 7.33 value. Ko/a = 7.33.
7.33 = (concn organic layer)/(concn aq layer)
Let x = grams in organic layer, then 9.81-x = grams in aq layer.
7.33 = (x/30)/(9.81-x)/100
Solve for x and 9.81-x
To answer this question, we need to understand the concept of partition coefficient and how it relates to the extraction process.
The partition coefficient, represented as K, is the ratio of the concentrations of a solute in two immiscible solvents at equilibrium. It helps determine how a solute distributes between these two solvents during an extraction process.
Here, the partition coefficient between water and diethyl ether is given as 7.33. This means that the compound is more soluble in diethyl ether than in water, as a higher partition coefficient indicates a greater affinity for the solvent.
Now, let's calculate the quantity of the compound that will remain in the aqueous layer after extraction with diethyl ether.
Step 1: Calculate the quantity of the compound in the water phase before extraction.
Given: Initial quantity of the compound in water = 9.81 grams
Since the compound is dissolved in 100.0 mL of water, we can determine its concentration (Cw) in the water phase:
Cw = Mass of solute / Volume of solvent
Cw = 9.81 grams / 100.0 mL
Cw = 0.0981 grams/mL
Step 2: Apply the partition coefficient to calculate the quantity of the compound in the ethereal phase after extraction.
Given: Volume of diethyl ether used = 30.0 mL
The compound's concentration (Ce) in the ethereal phase can be calculated using the partition coefficient:
Ce = Cw * K
Ce = 0.0981 grams/mL * 7.33
Ce ≈ 0.7180 grams/mL
Step 3: Calculate the quantity of the compound in the ethereal phase after extraction.
Cethereal = Ce * Volume of diethyl ether used
Cethereal = 0.7180 grams/mL * 30.0 mL
Cethereal = 21.54 grams
Step 4: Calculate the quantity of the compound remaining in the aqueous phase after extraction.
Given: Initial quantity of the compound in water = 9.81 grams
Since a portion of 21.54 grams has been transferred to the ethereal phase, the remaining quantity (R) in the aqueous phase can be calculated:
R = Initial quantity - Transferred quantity
R = 9.81 grams - 21.54 grams
R ≈ -11.73 grams
Since we cannot have negative quantities of the compound remaining in the aqueous phase, the calculated value is not feasible. It is likely that an error occurred in the calculations or the given data. Please double-check the provided values and try again.