Book cover for Chemistry: The Molecular Nature of Matter

Chemistry: The Molecular Nature of Matter

Neil D. Jespersen, James E. Brady, Alison Hyslop

ISBN #9781118413920

7th Edition

3,064 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter provides a comprehensive examination of acidā€“base equilibria in aqueous solutions. Key topics include the definition and measurement of pH, the use of pā€“notation to express acid and base strengths, and the utilization of equilibrium constants (Ka and Kb) in defining acid-base behavior. Techniques such as ICE tables are introduced to effectively approach equilibrium problems, while the Hendersonā€“Hasselbalch equation offers insight into buffer systems. Special cases such as polyprotic acids and titration curves further enhance the analytical tools available. Overall, the chapter equips learners with the quantitative methods essential for applications in laboratory research, pharmaceuticals, and environmental analysis.

Learning Objectives

1

Understand the fundamental principles of acidā€“base equilibria in aqueous solutions including pH, pā€“notation, and equilibrium constants (Ka and Kb).

2

Develop the skills to set up and solve equilibrium problems using ICE tables and appropriate simplifying assumptions.

3

Analyze and interpret the behavior of buffer solutions using the Hendersonā€“Hasselbalch equation and titration curves.

4

Evaluate the unique challenges presented by polyprotic acids and salt solutions in acidā€“base chemistry.

5

Apply quantitative concepts from acidā€“base equilibria to real-world scenarios in laboratory research, pharmaceuticals, and environmental chemistry.

Key Concepts

CONCEPT

DEFINITION

pH

A measure of the hydrogen ion concentration in a solution, defined as pH = -log[Hāŗ].

pā€“notation

A logarithmic way to express concentrations or equilibrium constants, such as pKa and pKb, making them easier to compare and interpret.

Ka (Acid Ionization Constant)

A quantitative measure of the strength of an acid in solution, indicating its tendency to donate protons (Hāŗ).

Kb (Base Ionization Constant)

A quantitative measure of the strength of a base in solution, indicating its tendency to accept protons.

ICE Table

A systematic method (Initial, Change, Equilibrium) used to set up and solve equilibrium problems in acid-base reactions.

Buffer Solution

A solution that resists changes in pH when small amounts of acid or base are added, typically consisting of a weak acid and its conjugate base or a weak base and its conjugate acid.

Hendersonā€“Hasselbalch Equation

An equation that relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of the conjugate base and the acid.

Polyprotic Acids

Acids capable of donating more than one proton (Hāŗ), with successive ionizations occurring at different equilibrium constants.

Example Problems

Example 1

Write the chemical equation for (a) the autoionization of water and (b) the equilibrium law for $K_{\mathrm{w}}$.

Example 2

How are acidic, basic, and neutral solutions in water defined (a) in terms of $\left[\mathrm{H}^{+}\right]$ and $\left[\mathrm{OH}^{-}\right]$ and $(\mathbf{b})$ in terms of $\mathrm{pH}$ and $\mathrm{pOH}$ ?

Example 3

At $25^{\circ} \mathrm{C}$, how are the $\mathrm{pH}$ and $\mathrm{pOH}$ of a solution related to each other?

Example 4

Why do chemists use $\mathrm{pH}$ notation instead of the concentration of $\mathrm{H}^{+}$ ions?

Example 5

Explain how acids and bases suppress the ionization of water, often called the common ion effect.
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Step-by-Step Explanations

QUESTION

Calculate the pH of a 0.01 M HCl solution.

STEP-BY-STEP ANSWER:

Step 1: Recognize HCl is a strong acid and completely dissociates, so [Hāŗ] is 0.01 M.
Step 2: Apply the definition of pH: pH = -log[Hāŗ].
Step 3: Calculate pH = -log(0.01) = 2.
Final Answer: pH = 2.

pH Calculation for a Strong Acid

QUESTION

For a weak acid HA (with Ka = 1Ɨ10ā»āµ) and an initial concentration of 0.10 M, set up an ICE table and determine the equilibrium concentration of HA.

STEP-BY-STEP ANSWER:

Step 1: Write the equilibrium reaction: HA ā‡Œ Hāŗ + Aā».
Step 2: Set up the ICE table:
Step 3: Write the expression for Ka: Ka = (x * x)/(0.10 - x) = xĀ²/(0.10 - x).
Step 4: Substitute Ka = 1Ɨ10ā»āµ and solve (often assuming x <<< 0.10 to simplify to xĀ²/0.10).
Step 5: Solve for x: xĀ² = (1Ɨ10ā»āµ)*(0.10), thus xĀ² = 1Ɨ10ā»ā¶, and so x ā‰ˆ 1Ɨ10ā»Ā³ M.
Final Answer: The equilibrium concentration of HA is approximately 0.10 - 1Ɨ10ā»Ā³ M.

Setting Up an ICE Table for a Weak Acid

QUESTION

Determine the pH of a buffer solution containing 0.2 M acetic acid and 0.1 M sodium acetate, given that the pKa of acetic acid is 4.76.

STEP-BY-STEP ANSWER:

Step 1: Write the Hendersonā€“Hasselbalch equation: pH = pKa + log([Aā»]/[HA]).
Step 2: Substitute the given concentrations into the equation: pH = 4.76 + log(0.1/0.2).
Step 3: Calculate the ratio: 0.1/0.2 = 0.5, then log(0.5) ā‰ˆ -0.301.
Step 4: Compute the pH: pH = 4.76 - 0.301 ā‰ˆ 4.46.
Final Answer: The pH of the buffer solution is approximately 4.46.

Using the Hendersonā€“Hasselbalch Equation

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Common Mistakes

  • Assuming that the simplifying assumptions in ICE tables are valid in every scenario, leading to significant calculation errors.
  • Confusing the complete ionization of a strong acid with the partial ionization of a weak acid, which may result in inaccurately calculated pH values.
  • Misapplying the Hendersonā€“Hasselbalch equation by using incorrect concentration ratios or pKa values.
  • Overlooking the sequential nature of ionizations in polyprotic acids, thereby neglecting the complexity of subsequent ionization steps.
  • Neglecting the influence of salt solutions on the overall pH of the solution due to hydrolysis reactions.