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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

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Answer:

79 extractions

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 [tex]\frac{mg}{mL} * \frac{100ug}{1mg}[/tex] = 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

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