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.
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Let X = g extracted with ether, then
2 - X = g remaining in water.
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Ko/a = 20 = (X/13.9)/[(2-x)/15]
Solve for X, then
(X/2)*100 = % recovered in organic phase. I estimated very quickly to be about 45% but that's just a quickie. Check my work.
Well, well, well, looks like we have a solute trying to make a run for it. Let's see if we can help bring it back.
First off, we need to calculate the amount of solute that can be extracted by ether. The distribution coefficient tells us the ratio of the concentration in ether to the concentration in water. In this case, it's 20. So if we have 15 mL of solution, we can extract 20 times the amount of solute from that volume into ether.
Now, to calculate the amount of solute in the ether layer, we need to consider the volume of ether used. We have 13.9 mL of ether, so we multiply that by the distribution coefficient of 20. This gives us the amount of solute that can be extracted, which is 278 mL.
But hold your horses! We need to convert that mL value to grams, since we were given the initial amount of solute in grams. We have 2.0 g of solute in an initial 15 mL of solution, so the concentration of the solute is 2.0 g / 15 mL. Multiplying this concentration by the amount of solute extracted in ether, we get 2.0 g / 15 mL * 278 mL = 37.07 g.
Finally, to calculate the percent recovery, we divide the amount of solute extracted by the initial amount of solute and multiply by 100. So the percent recovery is (37.07 g / 2.0 g) * 100 = 1853.5%.
Well, it seems like we're in luck! With a single extraction using 13.9 mL of ether, we can recover a whopping 1853.5% of the solute. I suppose that's what happens when a solute is determined to escape – it really gives it all it's got!
To calculate the percent of the compound that can be recovered with a single extraction, we need to determine how much of the solute will partition into the ether layer.
We know that the distribution coefficient (also called the partition coefficient, denoted as Kd) is defined as the ratio of the concentration of the solute in the organic phase (ether) to its concentration in the aqueous phase (water). In this case, the distribution coefficient is given as 20.
The volume of the aqueous solution is 15 mL, and it contains 2.0 g of the solute. To find the concentration, we divide the mass by the volume:
Concentration = Mass / Volume
Concentration = 2.0 g / 15 mL
Next, we calculate the amount of solute that will remain in the aqueous phase after the extraction. Let's denote it as "x".
Concentration of solute in water after extraction = (2.0 g - x) / (15 mL - 13.9 mL)
Since the distribution coefficient is given as 20, we can set up the following equation:
20 = (x) / (13.9 mL)
To solve for x, we rearrange the equation:
x = (20)(13.9 mL)
Now we can substitute this value of x into the equation for the concentration of solute in water after extraction:
Concentration of solute in water after extraction = (2.0 g - (20 x 13.9 mL)) / (15 mL - 13.9 mL)
Finally, to calculate the percent of the compound that can be recovered, we divide the amount of solute recovered (x) by the initial amount of solute (2.0 g) and multiply by 100:
Percent Recovery = (x / 2.0 g) x 100
Plugging in the values and solving the equations will give you the answer.
To calculate the percent of the compound that can be recovered with a single extraction, we need to consider the distribution coefficient. The distribution coefficient is the ratio of the concentration of the solute in one phase to the concentration in another phase when the solute is distributed between the two immiscible phases (ether and water, in this case).
The distribution coefficient (D) is given by:
D = [organic solute]ether / [organic solute]water
In this case, the distribution coefficient (D) is given as 20, which means the solute is 20 times more concentrated in ether than in water.
Let's assume the initial concentration of the solute is C0 in the aqueous solution.
To calculate the concentration of the solute in ether after a single extraction with 13.9 mL of ether, we can use the formula for the distribution of the solute.
[organic solute]ether = (C0 * V0) / (Vw + V0)
Where:
[organic solute]ether = concentration of the solute in ether after extraction
C0 = initial concentration of the solute in the aqueous solution
V0 = volume of ether used for extraction
Vw = volume of the aqueous solution
In this case, C0 can be calculated as:
C0 = 2.0 g / 15 mL
Now, substituting the values into the formula:
[organic solute]ether = (C0 * V0) / (Vw + V0)
= (2.0 g / 15 mL) * 13.9 mL / (15 mL + 13.9 mL)
Simplifying the expression:
[organic solute]ether = (2.0 g * 13.9 mL) / 28.9 mL
[organic solute]ether ≈ 0.96 g/mL
To calculate the percentage of the compound that can be recovered, we need to determine the mass of the compound recovered in ether.
Mass of the compound recovered in ether = [organic solute]ether * volume of ether used for extraction
= 0.96 g/mL * 13.9 mL
Mass of the compound recovered in ether ≈ 13.344 g
Now, calculate the percentage of the compound recovered:
Percentage recovery = (mass of the compound recovered / initial mass of the solute) * 100
= (13.344 g / 2.0 g) * 100
Percentage recovery ≈ 667.2%
Therefore, the percent of the compound that can be recovered with a single extraction using 13.9 mL of ether is approximately 667.2%.