Question

You want to decaffeinate your coffee by extracting the caffeine outwith dichloromethane. It's too late to extract the caffeinefrom the coffee beans because you've already brewed yourself a 200mL cup of coffee. Your particular brand of coffee contains100 mg of caffeine in that 200mL cup. The partitioncoefficient of caffeine in dichloromethane/water is 9.0. How much caffeine would still be in your 200 mL if you did: A. One extraction using 200 mL ofdichloromethane B. Two extractions using 100 mL ofdichloromethan each.

Answer 1

partition coefficient of caffeine in dichloromethane/water is 9.0.

Which means that everytime you do the partitioning 9 parts go to dichloromethane and 1 part stays in water when extracting with same volume of solvent.

A. One extraction using 200 mL ofdichloromethane

Let the concentration of the concentration of caffeine in water at equilibrium = c, then is the concentration of caffeine in DCM = 9c.

c x 200 + 9 c x 200 = 100 mg

200c + 1800c = 100 mg

2000c = 100 mg

c= 0.05 mg/mL

In water 200 mL x 0.05 mg/mL = 10 mg

out of the 100 mg 90 mg will be in dichloromethane and 10 mg will be left in the coffee cup

B)Two extractions using 100 mL ofdichloromethan each.

In the first extraction a 9:1 partitioning

Let the concentration of the concentration of caffeine in water at equilibrium = c, then is the concentration of caffeine in DCM = 9c.

c x 200 + 9 c x 100 = 100 mg

200c + 900c = 100 mg

1100c = 100 mg

c= 0.0909 mg/mL

In water 200 mL x 0.0909 mg/mL = 18.18 mg

Second extraction

c x 200 + 9 c x 100 = 18.18 mg

200c + 900c = 18.18 mg

1100c = 18.18 mg

c= 0.0165 mg/mL

In water 200 mL x 0.0165 mg/mL = 3.307 mg

So the coffee cup will have 3.307 mg of caffeine