5. The partition coefficient of Compound A is 7.5 in dichloromethane (a. k.a. methylene chloride) with respect to water. a. If 5 grams of Compound A were dissolved in 100 mL of water, how much of Compound A would be extracted with four 25-mL portions of dichloromethane

4.93g are extracted

Explanation:

Partition coefficient (P) is defined as the ratio of solute dissolved in the organic solvent and the solute dissolved in the aqueous phase.

That is:

P = 7.5 = Concentration in dichloromethane / Concentration in water.

Knowing this, in the first extraction with 25mL of dichloromethane you will extract:

7.5 = (X/25mL) / (5g - X) / 100mL

Where X is the amount of compound A that is extracted.

7.5 = 100X / (125 - 25X)

937.5 - 187.5X = 100X

937.5 = 287.5X

3.26g of A are extracted in the first extraction.

In water will remain 5g - 3.26g = 1.74g

In the second extraction you will extract:

7.5 = (X/25mL) / (1.74g - X) / 100mL

7.5 = 100X / (43.5 - 25X)

326.25 - 187.5X = 100X

326.25 = 287.5X

1.13g are extracted in the second extraction.

And remain: 1.74g - 1.13g = 0.61g

In the third extraction you will extract:

7.5 = (X/25mL) / (0.61g - X) / 100mL

7.5 = 100X / (15.25 - 25X)

114.375 - 187.5X = 100X

114.375 = 287.5X

0.40g are extracted in the third extraction.

And remain: 0.61g - 0.40g = 0.21g

In the second extraction you will extract:

7.5 = (X/25mL) / (0.21g - X) / 100mL

7.5 = 100X / (5.25 - 25X)

39.375 - 187.5X = 100X

39.375 = 287.5X

0.14g are extracted in the fourth extraction.

Thus, after the three extractions you will extract: 0.14g + 0.40g + 1.13g + 3.26g = 4.93g are extracted