Answer:
There are needed 3 extractions to extract at least 95%
Explanation:
The distribution coefficient of a compound is defined as the ratio in concentration of the compound in the organic solvent and the concentration in the aqueous solution:
K = Concentration organic solvent / Concentration in water
Assuming as initial amount of the organic solvent: 100% and X as the amount of Y that is extracted
<em>First extraction:</em>
4 = X / 10mL / (100-X) / 50mL
4 = 50X / 1000-X
4000 - 4X = 50X
4000 = 54X
X = 74.1%
In the first extraction, 74.1% of Y is extracted
And will remain: 100 - 74.1 = 25.9%
<em>Second extraction:</em>
4 = X / 10mL / (25.9-X) / 50mL
4 = 50X / 259-X
1036 - 4X = 50X
1036 = 54X
X = 19.2%
In the second extraction, 19.2% of Y is extracted
And will remain: 25.9 - 19.2 = 6.7%
<em>Third extraction</em>
4 = X / 10mL / (6.7-X) / 50mL
4 = 50X / 67-X
268 - 4X = 50X
268 = 54X
X = 5.0%
In the first extraction, 5.0% of Y is extracted
And are extracted:
74.1% + 19.2% + 5.0% = 98.3%
That means there are needed 3 extractions to extract at least 95%
