Ch.16 - Aqueous Equilibria: Acids & Bases

Problem 154

Chapter 16, Problem 154

In aqueous solution, sodium acetate behaves as a strong electrolyte, yielding Na+ cations and CH3CO2 - anions. A particular solution of sodium acetate has a pH of 9.07 and a density of 1.0085 g/mL. What is the molality of this solution, and what is its freezing point?

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Identify the dissociation of sodium acetate in water: \( \text{CH}_3\text{COONa} \rightarrow \text{Na}^+ + \text{CH}_3\text{COO}^- \).

Use the given pH to find the concentration of \( \text{OH}^- \) ions, since the solution is basic: \( \text{pH} + \text{pOH} = 14 \).

Calculate the concentration of \( \text{CH}_3\text{COO}^- \) using the equilibrium expression for the hydrolysis of acetate ions: \( \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^- \).

Determine the molality of the solution using the concentration of \( \text{CH}_3\text{COO}^- \) and the density of the solution to find the mass of the solvent.

Calculate the freezing point depression using the formula \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor, \( K_f \) is the cryoscopic constant, and \( m \) is the molality.

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Key Concepts

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

Electrolytes

Electrolytes are substances that dissociate into ions when dissolved in water, allowing the solution to conduct electricity. Sodium acetate, a strong electrolyte, completely dissociates into sodium (Na+) and acetate (CH3CO2-) ions in solution. Understanding the behavior of electrolytes is crucial for calculating properties like pH and colligative effects, which are relevant to the freezing point of the solution.

pH and Acid-Base Chemistry

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. A pH of 9.07 indicates a basic solution, which can affect the dissociation of weak acids and bases. In the case of sodium acetate, the acetate ion can act as a weak base, influencing the overall pH and the calculations related to the solution's properties.

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation and freezing point depression. To determine the freezing point of the sodium acetate solution, one must calculate its molality, which is essential for applying the freezing point depression formula.

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Colligative Properties

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Textbook Question

Acid and base behavior can be observed in solvents other than water. One commonly used solvent is dimethyl sulfoxide (DMSO), which can be treated as a monoprotic acid 'HSol.' Just as water can behave either as an acid or a base, so HSol can behave either as a Brønsted–Lowry acid or base. (b) The weak acid HCN has an acid dissociation constant Ka = 1.3 * 10-13 in the solvent HSol. If 0.010 mol of NaCN is dissolved in 1.00 L of HSol, what is the equilibrium concentration of H2Sol + ?

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Textbook Question

A 7.0 mass % solution of H3PO4 in water has a density of 1.0353 g/mL. Calculate the pH and the molar concentrations of all species present (H3PO4, H2PO4-, PO43-, H3O+ , and OH-) in the solution. Values of equilibrium constants are listed in Appendix C.

In the case of very weak acids, 3H3O+ 4 from the dissociation of water is significant compared with 3H3O+ 4 from the dissociation of the weak acid. The sugar substitute saccharin 1C7H5NO3S2, for example, is a very weak acid having Ka = 2.1 * 10-12 and a solubility in water of 348 mg/100 mL. Calculate 3H3O+ 4 in a saturated solution of saccharin. (Hint: Equilibrium equations for the dissociation of saccharin and water must be solved simultaneously.)

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Textbook Question

During a certain time period, 4.0 million tons of SO₂ were released into the atmosphere and subsequently oxidized to SO₃. As explained in the Inquiry, the acid rain produced when the SO₃ dissolves in water can damage marble statues: CaCO₃(s) + H₂SO₄(aq) → CaSO₄(aq) + CO₂(g) + H₂O(l) (a) How many 500 pound marble statues could be damaged by the acid rain? (Assume that the statues are pure CaCO₃ and that a statue is damaged when 3.0% of its mass is dissolved.)

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Open Question

We’ve said that alkali metal cations do not react appreciably with water to produce H3O+ ions, but in fact, all cations are acidic to some extent. The most acidic alkali metal cation is the smallest one, Li+, which has Ka = 2.5 * 10^-14 for the reaction: Li(H2O)4+ (aq) + H2O (l) ⇌ H3O+ (aq) + Li(H2O)3(OH) (aq). This reaction and the dissociation of water must be considered simultaneously in calculating the pH of Li+ solutions, which nevertheless have pH ≈ 7. Check this by calculating the pH of a 0.10 M LiCl solution.

Textbook Question

A 1.000 L sample of HF gas at 20.0 °C and 0.601 atm pressure was dissolved in enough water to make 50.0 mL of hydrofluoric acid. (a) What is the pH of the solution?

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