Book cover for General Chemistry: Principles and Modern Applications

General Chemistry: Principles and Modern Applications

Ralph H. Petrucci, F. Geoffrey Herring, Jeffry D. Madura, Carey Bissonnette

ISBN #9780132931281

11th Edition

3,230 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter explores additional aspects of acid–base equilibria with a special focus on the interplay between acid–base reactions and solubility. Key topics include the design and function of buffer solutions, application of the Henderson–Hasselbalch equation, detailed analysis of titration curves to determine equivalence and half-neutralization points, and the influence of the common-ion effect in controlling ionization. Mastery of these concepts is fundamental for achieving accurate pH control in biological, environmental, and industrial processes.

Learning Objectives

1

Explain the interplay between acid–base equilibria and solubility in chemical systems.

2

Describe the formation and function of buffer solutions and their importance in pH control.

3

Apply the Henderson–Hasselbalch equation to calculate the pH of buffer systems.

4

Analyze titration curves to identify equivalence and half-neutralization points.

5

Understand the common-ion effect and its impact on ionization and solubility in various contexts.

Key Concepts

CONCEPT

DEFINITION

Buffer Solution

A solution containing a weak acid and its conjugate base (or a weak base and its conjugate acid) that resists significant pH changes upon the addition of small amounts of acid or base.

Henderson–Hasselbalch Equation

A simplified equation used to estimate the pH of a buffer solution by relating the acid dissociation constant (pKa) to the ratio of the concentrations of the conjugate base and acid.

Titration Curve

A graph that plots pH as a function of the volume of titrant added, used to identify key points such as the equivalence point and the half-neutralization (midpoint) of the titration.

Equivalence Point

The point in a titration at which the amount of titrant added exactly neutralizes the analyte in the solution.

Half-neutralization Point

The point in the titration of a weak acid or base at which half of the analyte has been neutralized; at this point, the pH equals the pKa of the weak acid (or pKb for a weak base).

Common-Ion Effect

The phenomenon where the addition of an ion that is a part of an equilibrium system shifts the equilibrium position, usually reducing the ionization of a weak acid or base and potentially its solubility.

Example Problems

Example 1

For a solution that is $0.275 \mathrm{M} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}$ (propionic acid, $\left.K_{\mathrm{a}}=1.3 \times 10^{-5}\right)$ and $0.0892 \mathrm{M} \mathrm{HI},$ calculate (a) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] ;$ (b) $\left[\mathrm{OH}^{-}\right] ;$ (c) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO} ;$ (d) $\left[\mathrm{I}^{-}\right]$.

Example 2

For a solution that is $0.164 \mathrm{M} \mathrm{NH}_{3}$ and $0.102 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}$ calculate (a) $\left[\mathrm{OH}^{-}\right] ;$ (b) $\left[\mathrm{NH}_{4}^{+}\right] ;$ (c) $\left[\mathrm{Cl}^{-}\right] ;$ (d) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$.

Example 3

Calculate the change in pH that results from adding (a) $0.100 \mathrm{mol} \mathrm{NaNO}_{2}$ to $1.00 \mathrm{L}$ of $0.100 \mathrm{M} \mathrm{HNO}_{2}(\mathrm{aq})$ (b) $0.100 \mathrm{mol} \mathrm{NaNO}_{3}$ to $1.00 \mathrm{L}$ of $0.100 \mathrm{M} \mathrm{HNO}_{3}(\mathrm{aq})$ Why are the changes not the same?

Example 4

In Example $16-4,$ we calculated the percent ionization of $\mathrm{CH}_{3} \mathrm{COOH}$ in (a) $1.0 \mathrm{M} ;$ (b) $0.10 \mathrm{M} ;$ and $(\mathrm{c}) 0.010 \mathrm{M}$ $\mathrm{CH}_{3} \mathrm{COOH}$ solutions. Recalculate those percent ionizations if each solution also contains $0.10 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{COO}$ Explain why the results are different from those of Example $16-4$.

Example 5

Calculate $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ in a solution that is $(\mathrm{a}) 0.035 \mathrm{M}$ HCl and 0.075 M HOCl; (b) 0.100 M NaNO $_{2}$ and $0.0550 \mathrm{M} \mathrm{HNO}_{2} ;$ (c) $0.0525 \mathrm{M} \mathrm{HCl}$ and $0.0768 \mathrm{M}$ $\mathrm{NaCH}_{3} \mathrm{COO}$.
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Step-by-Step Explanations

QUESTION

Calculate the pH of a buffer solution containing 0.1 M acetic acid (CH3COOH) and 0.1 M sodium acetate (CH3COONa) given that the pKa of acetic acid is 4.76.

STEP-BY-STEP ANSWER:

Step 1: Recall the Henderson–Hasselbalch equation: pH = pKa + log([A-]/[HA]).
Step 2: Identify [HA] as 0.1 M (acetic acid) and [A-] as 0.1 M (acetate from sodium acetate).
Step 3: Substitute values into the equation: pH = 4.76 + log(0.1/0.1).
Step 4: Calculate log(1) which equals 0.
Step 5: Therefore, pH = 4.76 + 0 = 4.76.
Final Answer: The pH of the buffer solution is 4.76.

Buffer pH Calculation using the Henderson–Hasselbalch Equation

QUESTION

How can you identify the half-neutralization (midpoint) on a titration curve of a weak acid titrated with a strong base?

STEP-BY-STEP ANSWER:

Step 1: Understand that at the half-neutralization point, exactly half of the weak acid has been neutralized.
Step 2: Recognize that at this point, the concentrations of the weak acid and its conjugate base are equal.
Step 3: Use the Henderson–Hasselbalch equation, where pH equals pKa when [A-] = [HA].
Step 4: Locate the point on the titration curve where the measured pH matches the known pKa value.
Final Answer: The half-neutralization point is identified at the pH equal to the pKa of the weak acid.

Identifying the Half-Neutralization Point in a Titration Curve

QUESTION

Explain how the addition of a common ion affects the ionization of a weak acid in solution.

STEP-BY-STEP ANSWER:

Step 1: Write the ionization equilibrium for a weak acid (HA): HA ⇌ H+ + A-.
Step 2: Recognize that adding a salt containing the common ion (A-) increases the concentration of A- in the solution.
Step 3: According to Le Chatelier’s principle, an increase in the concentration of a product (A-) shifts the equilibrium to the left, reducing the ionization of HA.
Step 4: This reduction in ionization leads to a decrease in [H+], which affects the pH of the solution.
Final Answer: The addition of a common ion suppresses the ionization of the weak acid, thereby shifting the equilibrium to favor the undissociated form of the acid.

Effect of the Common-Ion on Weak Acid Ionization

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Common Mistakes

  • Assuming the Henderson–Hasselbalch equation is applicable beyond its valid pH range or buffer conditions.
  • Misidentifying the half-neutralization point on a titration curve due to overlooking the equality of acid and conjugate base concentrations.
  • Confusing the common-ion effect with dilution effects or not recognizing its impact on both ionization and solubility.
  • Overlooking the role of weak acid and conjugate base pairs in buffer solutions, leading to miscalculations in pH determination.