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Chapter 20: Problem 21

The U.S. Public Health Service recommends the fluoridation of water as a means for preventing tooth decay. The recommended concentration is \(1 \mathrm{mg} \mathrm{F}^{-}\) per liter. The presence of calcium ions in hard water can precipitate the added fluoride. What is the maximum molarity of calcium ions in hard water if the fluoride concentration is at the USPHS recommended level? ( \(K_{\text {sp }}\) for \(\left.\mathrm{CaF}_{2}=4.0 \times 10^{-11} .\right)\)

Short Answer

Expert verified
The maximum molarity of calcium ions in hard water with the USPHS recommended fluoride concentration is 2.87 x 10⁻⁵ mol/L.

Step by step solution

01

Convert the concentration of fluoride ions from mg/L to mol/L.

First, we need to convert the given concentration of fluoride ions from mg per liter to mol per liter to work with molarity. The molar mass of F- is 19 g/mol. Given Concentration of F- = 1 mg/L Since 1 g = 1000 mg, we have 1 mg = 0.001 g Molarity of F- = (mass of F-) / (molar mass of F- * volume of solution) = (0.001 g) / (19 g/mol * 1L) So, the molarity of F- = \( \frac{0.001}{19} \) mol/L.
02

Write the balanced equation and Ksp expression for CaF2.

The balanced equation for the dissolution of CaF2 in water is: CaF2 (s) ↔ Ca²⁺ (aq) + 2 F⁻ (aq) The Ksp expression is given by: Ksp = [Ca²⁺] x [F⁻]² Using the given value of Ksp: 4.0 x 10⁻¹¹
03

Find the maximum molarity of calcium ions with the given fluoride concentration.

Let [Ca²⁺] be the maximum molarity of Ca²⁺ in the water and [F⁻] = \( \frac{0.001}{19} \) mol/L. Then from the balanced equation, we have the concentration of F- ions as twice the concentration of Ca²⁺ ions. Using the Ksp expression: Ksp = [Ca²⁺] x [F⁻]² 4.0 x 10⁻¹¹ = [Ca²⁺] x \( (\frac{0.001}{19}) \)² Now, solve for [Ca²⁺]: [Ca²⁺] = \(\frac{4.0 \times 10^{-11}}{(\frac{0.001}{19})^2}\)
04

Calculate the maximum molarity of calcium ions.

By evaluating the previous expression: [Ca²⁺] = 2.87 x 10⁻⁵ mol/L Therefore, the maximum molarity of calcium ions in hard water with the USPHS recommended fluoride concentration is 2.87 x 10⁻⁵ mol/L.

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