Table of contents

1. Matter and Measurements4h 31m
2. Atoms and the Periodic Table5h 23m
3. Ionic Compounds2h 18m
4. Molecular Compounds2h 18m
5. Classification & Balancing of Chemical Reactions3h 17m
6. Chemical Reactions & Quantities2h 27m
7. Energy, Rate and Equilibrium3h 46m
8. Gases, Liquids and Solids3h 25m
9. Solutions4h 10m
10. Acids and Bases3h 29m
11. Nuclear Chemistry56m
BONUS: Lab Techniques and Procedures1h 38m
BONUS: Mathematical Operations and Functions47m
12. Introduction to Organic Chemistry1h 34m
13. Alkenes, Alkynes, and Aromatic Compounds2h 12m
14. Compounds with Oxygen or Sulfur1h 6m
15. Aldehydes and Ketones1h 1m
16. Carboxylic Acids and Their Derivatives1h 11m
17. Amines39m
18. Amino Acids and Proteins1h 51m
19. Enzymes1h 37m
20. Carbohydrates1h 41m
21. The Generation of Biochemical Energy2h 8m
22. Carbohydrate Metabolism2h 22m
23. Lipids2h 26m
24. Lipid Metabolism1h 45m
25. Protein and Amino Acid Metabolism1h 37m
26. Nucleic Acids and Protein Synthesis2h 54m

10. Acids and Bases

Ka and Kb

GOB Chemistry

10. Acids and Bases

Ka and Kb

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2:13 minutes

Problem 71

Textbook Question

Rearrange the equation you wrote in Problem 10.50 to solve for [H₃O⁺] in terms of K_a.

Verified step by step guidance

Start with the general expression for the acid dissociation constant (Kₐ), which is defined as:

K

_a=[H3O][A⁻][HA], where [H₃O⁺] is the hydronium ion concentration, [A⁻] is the conjugate base concentration, and [HA] is the concentration of the weak acid.

Rearrange the equation to isolate [H₃O⁺] on one side. Multiply both sides of the equation by [HA] to eliminate the denominator:

K

_a⋅[HA]=[H3O][A⁻].

Next, divide both sides of the equation by [A⁻] to solve for [H₃O⁺]:

[H_{3 O] = K}

_a⋅[HA][A⁻].

Interpret the result: The equation now expresses [H₃O⁺] in terms of the acid dissociation constant (Kₐ), the concentration of the weak acid ([HA]), and the concentration of the conjugate base ([A⁻]).

To apply this equation, substitute the known values for Kₐ, [HA], and [A⁻] into the formula and calculate [H₃O⁺]. Ensure that the units are consistent throughout the calculation.

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Key Concepts

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

Equilibrium Constant (Kₐ)

The acid dissociation constant (Kₐ) quantifies the strength of an acid in solution. It is defined as the ratio of the concentration of the products to the concentration of the reactants at equilibrium, specifically for the dissociation of an acid into its ions. A higher Kₐ value indicates a stronger acid that dissociates more completely in solution.

Hydronium Ion Concentration ([H₃O⁺])

The concentration of hydronium ions ([H₃O⁺]) in a solution is a measure of its acidity. It is derived from the dissociation of acids in water, where an acid donates a proton (H⁺) to water, forming H₃O⁺. Understanding how to express [H₃O⁺] in terms of Kₐ is crucial for calculating pH and assessing the strength of acids.

Rearranging Equations

Rearranging equations involves manipulating algebraic expressions to isolate a specific variable. In this context, solving for [H₃O⁺] in terms of Kₐ requires applying algebraic techniques such as addition, subtraction, multiplication, and division to express the desired variable clearly. Mastery of this skill is essential for solving chemical equilibrium problems.

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