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Ch.17 - Aqueous Ionic Equilibrium
All textbooksTro 4th EditionCh.17 - Aqueous Ionic EquilibriumProblem 47
Chapter 17, Problem 47

A 250.0-mL buffer solution is 0.250 M in acetic acid and 0.250 M in sodium acetate. a. What is the initial pH of this solution? b. What is the pH after the addition of 0.0050 mol of HCl? c. What is the pH after the addition of 0.0050 mol of NaOH?

Verified step by step guidance
1
Identify the components of the buffer solution: acetic acid (CH₃COOH) and sodium acetate (CH₃COONa). Note that acetic acid is a weak acid and sodium acetate is its conjugate base.
Use the Henderson-Hasselbalch equation to find the initial pH of the buffer solution: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \( \text{pK}_a \) is the negative logarithm of the acid dissociation constant of acetic acid, \( [\text{A}^-] \) is the concentration of acetate ion, and \( [\text{HA}] \) is the concentration of acetic acid.
For part b, calculate the change in moles of acetic acid and acetate ion after adding 0.0050 mol of HCl. HCl will react with the acetate ion to form more acetic acid: \( \text{CH}_3\text{COO}^- + \text{HCl} \rightarrow \text{CH}_3\text{COOH} + \text{Cl}^- \).
Use the Henderson-Hasselbalch equation again to find the new pH after the addition of HCl, using the updated concentrations of acetic acid and acetate ion.
For part c, calculate the change in moles of acetic acid and acetate ion after adding 0.0050 mol of NaOH. NaOH will react with acetic acid to form more acetate ion: \( \text{CH}_3\text{COOH} + \text{NaOH} \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O} + \text{Na}^+ \). Use the Henderson-Hasselbalch equation to find the new pH after the addition of NaOH.

Key Concepts

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

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, the acetic acid and sodium acetate form a buffer that helps maintain a stable pH when HCl or NaOH is added.
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Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. This equation is essential for determining the initial pH of the buffer solution.
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Acid-Base Neutralization

Acid-base neutralization is a chemical reaction where an acid reacts with a base to produce water and a salt, often resulting in a change in pH. In the context of the question, adding HCl (an acid) and NaOH (a base) to the buffer will affect the concentrations of acetic acid and sodium acetate, thus altering the pH. Understanding this concept is crucial for predicting the pH changes after the addition of these substances.
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Related Practice
Textbook Question

What mass of sodium benzoate should you add to 150.0 mL of a 0.15 M benzoic acid solution to obtain a buffer with a pH of 4.25? (Assume no volume change.)

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Textbook Question

A 100.0-mL buffer solution is 0.175 M in HClO and 0.150 M in NaClO. a. What is the initial pH of this solution?

Textbook Question

A 100.0-mL buffer solution is 0.175 M in HClO and 0.150 M in NaClO. b. What is the pH after addition of 150.0 mg of HBr?

Textbook Question

A 100.0-mL buffer solution is 0.175 M in HClO and 0.150 M in NaClO. c. What is the pH after addition of 85.0 mg of NaOH?