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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Baking soda (sodium bicarbonate, NaHCO₃) reacts with acids in foods to form carbonic acid (H₂CO₃), which in turn decomposes to water and carbon dioxide gas. In a cake batter, the CO₂(g) 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, CH₃CH(OH)COOH. 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 (H₂CO₃), which in turn decomposes to water and carbon dioxide gas. In a cake batter, the CO₂(g) forms bubbles and causes the cake to rise. (b) The density of baking soda is 2.16 g/cm³. Calculate the concentration of lactic acid in one cup of sour milk (assuming the rule of thumb applies), in units of mol/L. (One cup = 236.6 mL = 48 teaspoons).

Textbook Question

Baking soda (sodium bicarbonate, NaHCO₃) reacts with acids in foods to form carbonic acid (H₂CO₃), which in turn decomposes to water and carbon dioxide gas. In a cake batter, the CO₂(g) 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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