Explan why one never obtains a hundred percent recovery from an extraction?

Extractions aren't perfect.

Let's say that we're going to recover a chemical using a process that recovers 90.0% of the product per extraction.

• If we're trying to extract 10.0 grams of compound, the first extraction step will recover 9.00 grams of it.
• If we do the extraction twice, we'll recover 9.90 grams of the compound.
• If we do it three times, we'll recover 9.99 grams of the compound.

And so forth. No matter how many times you actually try to extract the product, you'll always leave 10% of the product behind.

The math above, however, explains why it's pretty common to do an extraction three times. Even though you won't get everything, you get enough of it that the rest doesn't really matter. After all, a chemical would have to be pretty expensive for 0.01 grams to matter!

OK.