7. One gram of aspirin dissolves in 300 mL of water and in 17 mL of chloroform at room temperature. An aqueous solution of 0.25g aspirin (100 mL water) was extracted with 100 mL of chloroform. How much aspirin was recovered from the chloroform layer? What if instead, the aqueous solution was extracted twice, each time with 50 mL of chloroform, keeping the water amount at 100mL. How much total aspirin would be recovered from the two extractions?

Partition coefficient is the ratio of concentrations of a chemical substance in two inmiscible solvents. The partition coefficient of aspirin in chloroform-water is:

[tex]\frac{\frac{1gAspirin}{17mLChloroform} }{\frac{1gAspirin}{300mLWater} }[/tex] = 17,6

According this theory, if you want to extract 0,25 g of aspirin in water with chlorofotm you will recover from chloroform layer:

17,6 = [tex]\frac{\frac{XgAspirin}{100mLChloroform} }{\frac{(0,25g-X)gAspirin}{100mLWater} }[/tex]

Where x are the grams of aspirin recovered from chloroform layer

17,6 = [tex]\frac{X}{0,25-X}[/tex]

4,4 - 17,6X = X

4,4 = 18,6X

X = 0,237 g of chloroform you will recover

Now, if you extract twice, in the first extraction you will recover:

17,6 = [tex]\frac{\frac{XgAspirin}{50mLChloroform} }{\frac{(0,25g-X)gAspirin}{100mLWater} }[/tex]

17,6 = [tex]\frac{2X}{0,25-X}[/tex]

4,4 - 17,6X = 2X

4,4 = 19,6X

X = 0,224 g of chloroform you will recover in the first extraction.

In aqueous layer you will have 0,25g-0,224g = 0,026 g

In the second extraction you will recover:

17,6 = [tex]\frac{\frac{XgAspirin}{50mLChloroform} }{\frac{(0,026g-X)gAspirin}{100mLWater} }[/tex]

17,6 = [tex]\frac{2X}{0,026-X}[/tex]

0,4576 - 17,6X = 2X

0,4576 = 19,6X

X = 0,023g of aspirin you will recover in the second extraction

The total chloroform you recover extracting twice is 0,224g + 0,023g = 0,247g

I hope it helps!