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.

Respuesta :

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 = [tex]\frac{\frac{40 - x_{1}}{2}}{\frac{x_{1}}{2}}[/tex]

                [tex]x_{1}[/tex] = 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 = [tex]\frac{\frac{7.2 - x}{2}}{\frac{x_{2}}{2}}[/tex]

                  [tex]x_{2}[/tex] = 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 = [tex]\frac{\frac{1.29 - x_{3}}{2}}{\frac{x_{3}}{2}}[/tex]

                      [tex]x_{3}[/tex] = 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.