Table of contents

1. A Review of General Chemistry5h 5m
2. Molecular Representations1h 14m
3. Acids and Bases2h 46m
4. Alkanes and Cycloalkanes4h 17m
5. Chirality3h 39m
6. Thermodynamics and Kinetics1h 22m
7. Substitution Reactions1h 48m
8. Elimination Reactions2h 30m
9. Alkenes and Alkynes2h 9m
10. Addition Reactions3h 19m
11. Radical Reactions1h 58m
12. Alcohols, Ethers, Epoxides and Thiols2h 42m
13. Alcohols and Carbonyl Compounds2h 17m
14. Synthetic Techniques1h 26m
15. Analytical Techniques:IR, NMR, Mass Spect7h 3m
16. Conjugated Systems6h 13m
17. Ultraviolet Spectroscopy51m
18. Aromaticity2h 34m
19. Reactions of Aromatics: EAS and Beyond5h 1m
20. Phenols55m
21. Aldehydes and Ketones: Nucleophilic Addition4h 56m
22. Carboxylic Acid Derivatives: NAS2h 51m
23. The Chemistry of Thioesters, Phophate Ester and Phosphate Anhydrides1h 10m
24. Enolate Chemistry: Reactions at the Alpha-Carbon1h 53m
25. Condensation Chemistry2h 9m
26. Amines1h 43m
27. Heterocycles2h 0m
28. Carbohydrates5h 53m
29. Amino Acids4h 20m
30. Peptides and Proteins2h 42m
31. Catalysis in Organic Reactions1h 30m
32. Lipids 2h 50m
33. The Organic Chemistry of Metabolic Pathways2h 52m
34. Nucleic Acids1h 32m
35. Transition Metals6h 14m
36. Synthetic Polymers1h 49m

3. Acids and Bases

Equilibrium Constant

Organic Chemistry

3. Acids and Bases

Equilibrium Constant

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5:33 minutes

Problem 15

Textbook Question

We usually calculate K_eq for acid–base reactions using pK_a values.
(a) Derive an equation to calculate K_eq using pK_b values, then
(b) use it to calculate the equilibrium constant for the following reaction.

Verified step by step guidance

Step 1: Recall the relationship between pKa and pKb. The relationship is given by the equation:

p K a + p K b = 14

(at 25°C). This equation connects the acid dissociation constant (Ka) and the base dissociation constant (Kb).

Step 2: Express the equilibrium constant (Keq) for an acid-base reaction in terms of Ka and Kb. For an acid-base reaction,

K e q = \frac{K}{a}

. This equation shows that Keq is the ratio of the acid's Ka to the base's Kb.

Step 3: Convert the Ka and Kb values into their logarithmic forms using the pKa and pKb values. Recall that

K a = 10

^-pKa and

K b = 10

^-pKb. Substitute these into the Keq equation.

Step 4: Simplify the equation for Keq in terms of pKa and pKb. Using the properties of exponents, the equation becomes:

K e q = 10

^{(pKbbase - pKaacid)}. This is the derived equation to calculate Keq using pKb values.

Step 5: Apply the derived equation to the given reaction. Identify the pKa of the acid and the pKb of the base involved in the reaction. Substitute these values into the equation

K e q = 10

^{(pKbbase - pKaacid)} to calculate the equilibrium constant.

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Key Concepts

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

pKₐ and pKₑq Relationship

The pKₐ value is a measure of the strength of an acid in solution, defined as the negative logarithm of the acid dissociation constant (Kₐ). Similarly, pKₑq is the negative logarithm of the equilibrium constant (Kₑq) for a reaction. The relationship between pKₐ and pKₑq allows us to derive equations that connect these values, facilitating the calculation of equilibrium constants for acid-base reactions.

pKₑq Calculation from pKₐ and pKₑb

For acid-base reactions, the equilibrium constant can be calculated using the pKₐ of the acid and the pKₑb of the base involved. The equation Kₑq = 10^(pKₐ + pKₑb) allows us to derive Kₑq from the respective pK values. This relationship is crucial for understanding how the strengths of acids and bases influence the position of equilibrium in a reaction.

Equilibrium Constant (Kₑq)

The equilibrium constant (Kₑq) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It provides insight into the extent to which a reaction proceeds and is influenced by temperature and the nature of the reactants and products. Understanding Kₑq is essential for predicting the behavior of acid-base reactions and their equilibria.

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