Answer:
159 mg caffeine is being extracted in 60 mL dichloromethane
Explanation:
Given that:
mass of caffeine in 100 mL of water =  600 mg 
Volume of the water = 100 mL
Partition co-efficient (K) = 4.6
mass of caffeine extracted = ??? (unknown)
The portion of the DCM = 60 mL
Partial co-efficient (K) = 
where;  solubility of compound in the organic solvent and
 solubility of compound in the organic solvent and  = solubility in aqueous water.
 = solubility in aqueous water.
So; we can represent our data as:
 ÷
 ÷ 
Since one part of the portion is A and the other part is B 
A+B = 60 mL
A+B = 0.60
A= 0.60 - B
4.6= ÷
 ÷ 
4.6 = 
4.6 ×  =
 =  
 
4.6 B  = 0.6 - B
 = 0.6 - B
2.76 B = 0.6 - B
2.76 + B = 0.6
3.76 B = 0.6
B = 
B = 0.159 g
B = 159 mg 
∴ 159 mg caffeine is being extracted from the 100 mL of water containing 600 mg of caffeine with one portion of in 60 mL dichloromethane.