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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2:04 minutes

Problem 46b

Textbook Question

Given the pK_b, calculate the pK_a of the conjugate acid.
(b)

Verified step by step guidance

Understand the relationship between pKa and pKb. The pKa of a conjugate acid and the pKb of its conjugate base are related by the equation:

p K a + p K b = 14

(at 25°C). This is derived from the ionization constant of water, Kw, where

K w = 10

^-14.

Rearrange the equation to solve for pKa:

p K a = 14 - p K b

Substitute the given value of pKb into the equation. For example, if pKb = 4.75, substitute it into the equation:

p K a = 14 - 4.75

Perform the subtraction to determine the pKa value. This step involves simple arithmetic, but ensure you understand the concept of how pKa and pKb are inversely related.

Interpret the result. A lower pKa value indicates a stronger conjugate acid, while a higher pKa value indicates a weaker conjugate acid. This relationship is important in understanding acid-base chemistry.

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Key Concepts

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

pKb and pKa Definitions

pKb is the negative logarithm of the base dissociation constant (Kb) of a weak base, indicating its strength. Conversely, pKa is the negative logarithm of the acid dissociation constant (Ka) of a weak acid. The relationship between pKa and pKb is crucial for understanding acid-base equilibria, as they are related through the equation: pKa + pKb = 14 at 25°C.

Conjugate Acid-Base Pairs

In acid-base chemistry, a conjugate acid is formed when a base accepts a proton (H+). Each acid has a corresponding conjugate base, which is what remains after the acid donates a proton. Understanding these pairs is essential for calculating pKa from pKb, as it allows for the identification of the acid's strength based on its conjugate base's properties.

Calculating pKa from pKb

To calculate the pKa of a conjugate acid from its pKb, one can use the formula: pKa = 14 - pKb. This equation reflects the inverse relationship between the strength of a base and its conjugate acid. By knowing the pKb value, one can easily determine the pKa, which is vital for predicting the behavior of acids and bases in various chemical reactions.

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Related Practice

Textbook Question

Given the pK_b, calculate the pK_a of the conjugate acid.

(c)

Textbook Question

Calculate the equilibrium constant for each of the acid–base reactions shown.

Textbook Question

Predict the K_eq for the following acid–base reaction.

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.

Textbook Question

Calculate K_eq for these acid–base reactions.

(d)

Textbook Question

Using pK_a values for the conjugate acids of the bases on each side of the reaction arrow, identify which side of the equilibrium would be favored in the following hypothetical reactions.

(c)

Textbook Question

Calculate K_eq for the acid–base reaction shown. Which side is favored and why?

Textbook Question

Write the K_eq expression for the following acid–base reactions. [You don't need to calculate K_eq here.]

(c)

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