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?

Name: Chemistry
Author: McMurry
ISBN: 9781292336145

Verified step by step guidance

Convert the initial conditions of HF gas to moles using the ideal gas law: \( PV = nRT \).

Calculate the concentration of HF in the solution by dividing the moles of HF by the volume of the solution in liters.

Use the expression for the ionization of HF in water: \( HF \rightleftharpoons H^+ + F^- \) and set up an ICE table to find the equilibrium concentrations.

Apply the expression for the acid dissociation constant \( K_a \) of HF to solve for \([H^+]\) at equilibrium.

Calculate the pH of the solution using the formula \( \text{pH} = -\log[H^+] \).

Key Concepts

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

Acid-Base Chemistry

Acid-base chemistry involves the study of acids, bases, and their reactions. Acids are substances that donate protons (H+) in solution, while bases accept protons. The strength of an acid is often measured by its dissociation constant (Ka), which indicates how completely it ionizes in water. Understanding these principles is essential for calculating pH and determining the behavior of hydrofluoric acid (HF) in solution.

pH Scale

The pH scale quantifies the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is neutral, while values below 7 indicate acidic solutions and values above 7 indicate basic solutions. The pH is calculated using the formula pH = -log[H+], where [H+] is the concentration of hydrogen ions in the solution. This concept is crucial for determining the pH of the hydrofluoric acid solution formed from the HF gas.

Dilution and Concentration

Dilution refers to the process of reducing the concentration of a solute in a solution, typically by adding more solvent. The relationship between the initial and final concentrations and volumes can be described by the equation C1V1 = C2V2, where C is concentration and V is volume. In this question, understanding how the concentration of HF changes when it is dissolved in water is vital for calculating the resulting pH of the solution.

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Related Practice

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. (b) To what volume must you dilute the solution to triple the percent dissociation?

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Textbook Question

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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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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