Ch.17 - Additional Aspects of Aqueous Equilibria

Problem 118

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Chapter 17, Problem 118

Fluoridation of drinking water is employed in many places to aid in the prevention of tooth decay. Typically. the Fion concentration is adjusted to about 1 ppm. Some water supplies are also 'hard'; that is, they contain certain cations such as Ca2 + that interfere with the action of soap. Consider a case where the concentration of Ca2 + is 8 ppm. Could a precipitate of CaF2 form under these conditions? (Make any necessary approximations.)

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Convert the concentration of fluoride ions (F^-) from ppm to molarity. Assume the density of water is approximately 1 g/mL, so 1 ppm is equivalent to 1 mg/L.

Convert the concentration of calcium ions (Ca^{2+}) from ppm to molarity using the same assumption about water density.

Write the solubility product expression for calcium fluoride (CaF_2), which is K_{sp} = [Ca^{2+}][F^-]^2.

Use the molarity values obtained for [Ca^{2+}] and [F^-] to calculate the ion product, Q = [Ca^{2+}][F^-]^2.

Compare the ion product, Q, to the known solubility product constant, K_{sp}, for CaF_2. If Q > K_{sp}, a precipitate will form; if Q < K_{sp}, no precipitate will form.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is a numerical value that represents the equilibrium between a solid and its ions in a saturated solution. For calcium fluoride (CaF2), Ksp can be used to determine whether a precipitate will form when the concentrations of its constituent ions exceed the Ksp value. Understanding Ksp is crucial for predicting precipitation reactions in solutions.

Ion Concentration and Precipitation

The concentration of ions in a solution directly influences the likelihood of precipitation. When the product of the concentrations of the ions in solution exceeds the Ksp, a precipitate will form. In this case, the concentrations of Ca2+ and F- ions must be calculated to assess whether CaF2 will precipitate when Ca2+ is present at 8 ppm and F- at 1 ppm.

Hard Water and Its Effects

Hard water contains high concentrations of cations such as Ca2+ and Mg2+, which can interfere with various chemical processes, including soap effectiveness and precipitation reactions. The presence of Ca2+ in the water can affect the solubility of compounds like CaF2, making it essential to consider the hardness of the water when evaluating potential precipitate formation.

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Related Practice

Excess Ca(OH)₂ is shaken with water to produce a saturated solution. The solution is filtered, and a 50.00-mL sample is titrated with HCl, requiring 11.23 mL of 0.0983 M HCl to reach the endpoint. Calculate Ksp for Ca(OH)₂. Compare your result with that in Appendix D. Suggest a reason for any differences you find between your value and the one in Appendix D.

Textbook Question

The osmotic pressure of a saturated solution of strontium sulfate at 25 C is 21 torr. What is the solubility product of this salt at 25 C?

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Textbook Question

A concentration of 10–100 parts per billion (by mass) of Ag+ is an effective disinfectant in swimming pools. However, if the concentration exceeds this range, the Ag+ can cause adverse health effects. One way to maintain an appropriate concentration of Ag+ is to add a slightly soluble salt to the pool. Using Ksp values from Appendix D, calculate the equilibrium concentration of Ag+ in parts per billion that would exist in equilibrium with (c) AgI.

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Textbook Question

Baking soda (sodium bicarbonate, NaHCO3) reacts with acids in foods to form carbonic acid 1H2CO32, which in turn decomposes to water and carbon dioxide gas. In a cake batter, the CO21g2 forms bubbles and causes the cake to rise. (a) A rule of thumb in baking is that 1/2 teaspoon of baking soda is neutralized by one cup of sour milk. The acid component in sour milk is lactic acid, CH3CH1OH2COOH. Write the chemical equation for this neutralization reaction.

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Textbook Question

Baking soda (sodium bicarbonate, NaHCO3) reacts with acids in foods to form carbonic acid 1H2CO32, which in turn decomposes to water and carbon dioxide gas. In a cake batter, the CO21g2 forms bubbles and causes the cake to rise. (c) If 1/2 teaspoon of baking soda is indeed completely neutralized by the lactic acid in sour milk, calculate the volume of carbon dioxide gas that would be produced at 1 atm pressure, in an oven set to 350 F.

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Textbook Question

In nonaqueous solvents, it is possible to react HF to create H2F+. Which of these statements follows from this observation? (a) HF can act like a strong acid in nonaqueous solvents, (b) HF can act like a base in nonaqueous solvents, (c) HF is thermodynamically unstable, (d) There is an acid in the nonaqueous medium that is a stronger acid than HF.

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