You want to decaffeinate your coffee by extracting the caffeine outwith dichloro

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.

Please explain. Thanks

Explanation / Answer

Ai/Ao = [ Vaq / ( Vorg*K + Vaq ) ]^i

so, caffene left will be 100mg*(Ai/Ao)

1. caffene left = 100*( 200 / (200*9 + 200) mg = 100/10 mg = 10 mg

2. caffene left = 100*( 200 / 100*9 + 200 )^2 = 3.305 mg

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