Question

We have a 1 liter sample of water containing 1.4 mg lead per mL. Lead levels in water above 0.25 ug/mL are unsafe to drink. We can use a chemical to complex the aqueous Pb2 and that complex will partition selectively into isooctane. The isooctane/water partitioning constant for the Pb2 complex is 12/1. How many extractions using 1 liter of isooctane are necessary to reach the safe drinking level

Answer 1

79 extractions

Step-by-step explanation:

An isooctane/water partinioning constant of 12/1 means that 12 out of 13 parts of the Pb²⁺ complex will be found in isooctane, while the remaining 1 out of 13 part will remain in water.

• 12/13 * 100 = 92.3% of the Pb²⁺ will be removed with each extraction.

Now we convert 1.4 mg/mL to ug/mL:

• 1.4
  `(mg)/(mL) * (100ug)/(1mg)` = 140 ug/mL

We're looking to have a final concentration of 0.25 ug/mL, so we can write:

• 140 mg/mL * (0.923)ⁿ = 0.25 ug/mL

Where n is the number of extractions.

We solve for n:

• (0.923)ⁿ = 1.786x10⁻³

• n = ln (1.786x10⁻³) / ln (0.923)

• n = 79