Question

A student is extracting caffeine from water with dichloromethane. The K value is 4.6. If the student starts with a total of 40 mg of caffeine in 2 mL of water and extracts once with 6 mL of nioromethane, how much caffeine will be in the dichloromethane extract? Show all work.

Answer 1

Step-by-step explanation:

The given value of K = 4.6

As before extraction, 40 mg of caffeine in 2 ml of water.

Hence, after the first extraction,

4.6 =
`((40 - x_(1))/(2))/((x_(1))/(2))`

`x_(1)` = 7.2 mg

Therefore, caffeine extracted from dichloromethane is as follows.

40 mg - 7.2 mg = 32.8 mg

Now, after the second extraction

4.6 =
`((7.2 - x)/(2))/((x_(2))/(2))`

`x_(2)` = 1.29 mg

So, (7.2 - 1.29) mg = 5.91 mg

This means that 5.91 mg of caffeine is extracted from dichloromethane.

After the third extraction,

4.6 =
`((1.29 - x_(3))/(2))/((x_(3))/(2))`

`x_(3)` = 0.229 mg

Hence, caffeine extracted from dichloromethane is as follows.

(1.29 - 0.229) mg

= 1.061 mg

Therefore, we can calculate the total amount of caffeine extracted as follows.

Total caffeine extracted = 40 - caffeine remains in dichloromethane after three extraction

= 40 - 0.229

= 39.771 mg

Thus, we can conclude that the total extracted caffeine is 39.771 mg.