A 0.0100 mol sample of solid Cd(OH)2 (Ksp = 5.3 x 10^-15) in 100.0 mL of water is titrated with 0.100 M HNO3. (c) How many milliliters of 0.100 M HNO3 must be added to completely neutralize the Cd(OH)2?

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Identify the balanced chemical equation for the reaction: \[ \text{Cd(OH)}_2 (s) + 2\text{HNO}_3 (aq) \rightarrow \text{Cd}^{2+} (aq) + 2\text{NO}_3^- (aq) + 2\text{H}_2\text{O} (l) \]

Determine the moles of \( \text{Cd(OH)}_2 \) present: Given as 0.0100 mol.

Use the stoichiometry of the balanced equation to find the moles of \( \text{HNO}_3 \) required: According to the equation, 2 moles of \( \text{HNO}_3 \) are needed for every mole of \( \text{Cd(OH)}_2 \).

Calculate the moles of \( \text{HNO}_3 \) needed: \( 0.0100 \text{ mol Cd(OH)}_2 \times \frac{2 \text{ mol HNO}_3}{1 \text{ mol Cd(OH)}_2} = 0.0200 \text{ mol HNO}_3 \).

Convert moles of \( \text{HNO}_3 \) to volume using its concentration: \( \text{Volume} = \frac{0.0200 \text{ mol}}{0.100 \text{ M}} \).

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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 an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It represents the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For Cd(OH)2, Ksp indicates how much of the compound can dissolve in water before reaching saturation, which is crucial for determining the amount of reactants needed in a titration.

Neutralization Reaction

A neutralization reaction occurs when an acid reacts with a base to produce water and a salt. In this case, HNO3, a strong acid, reacts with Cd(OH)2, a base, to form water and cadmium nitrate. Understanding the stoichiometry of this reaction is essential for calculating the volume of HNO3 required to completely neutralize the base, as it involves a 1:2 molar ratio between HNO3 and Cd(OH)2.

Molarity and Volume Calculations

Molarity (M) is a measure of concentration defined as moles of solute per liter of solution. To find the volume of HNO3 needed for neutralization, one must use the molarity of the acid and the moles of Cd(OH)2 present. The relationship between moles, molarity, and volume is given by the equation M1V1 = M2V2, which allows for the calculation of the required volume of HNO3 to achieve complete neutralization.

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